CiteULike: kevina's library [749 articles]

Adiabatic Theorem without a Gap Condition

JE Avron — 2007-03-29T20:35:42-00:00

(19 Apr 1999)

We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the adiabatic theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adiabatic limit is approached. With additional spectral information one can also estimate this rate.

Can the Universe Create Itself?

Richard Gott — 2007-05-27T07:14:55-00:00

(30 Dec 1997)

The question of first-cause has troubled philosophers and cosmologists alike. Now that it is apparent that our universe began in a Big Bang explosion, the question of what happened before the Big Bang arises. Inflation seems like a very promising answer, but as Borde and Vilenkin have shown, the inflationary state preceding the Big Bang must have had a beginning also. Ultimately, the difficult question seems to be how to make something out of nothing. This paper explores the idea that this is the wrong question --- that that is not how the Universe got here. Instead, we explore the idea of whether there is anything in the laws of physics that would prevent the Universe from creating itself. Because spacetimes can be curved and multiply connected, general relativity allows for the possibility of closed timelike curves (CTCs). Thus, tracing backwards in time through the original inflationary state we may eventually encounter a region of CTCs giving no first-cause. This region of CTCs, may well be over by now (being bounded toward the future by a Cauchy horizon). We illustrate that such models --- with CTCs --- are not necessarily inconsistent by demonstrating self-consistent vacuums for Misner space and a multiply connected de Sitter space in which the renormalized energy-momentum tensor does not diverge as one approaches the Cauchy horizon and solves Einstein's equations. We show such a Universe can be classically stable and self-consistent if and only if the potentials are retarded, giving a natural explanation of the arrow of time. Some specific scenarios (out of many possible ones) for this type of model are described. For example: an inflationary universe gives rise to baby universes, one of which turns out to be itself. Interestingly, the laws of physics may allow the Universe to be its own mother.

Noisy quantum computation

D Aharonov — 2007-05-26T09:10:54-00:00

Localising Relational Degrees of Freedom in Quantum Mechanics

HV Cable — 2007-05-26T07:17:01-00:00

Quantum information theory and the foundations of quantum mechanics

CG Timpson — 2007-05-26T07:15:08-00:00

Maximally entangled mixed states under nonlocal unitary operations in two qubits

Satoshi Ishizaka — 2007-05-24T19:58:04-00:00

Physical Review A, Vol. 62, No. 2. (18 July 2000), 022310.

We propose mixed states in two qubits that have a property that the amount of entanglement of these states cannot be increased by any unitary transformation. The property is proven when the rank of the states is less than 4; and confirmed numerically in the other general cases. The corresponding entanglement of formation specified by its eigenvalues gives an upper bound of that for density matrices with the same eigenvalues. Further; as a simple application of the upper bound of the entanglement of formation; we analyze the entanglement of formation of the state generated by a decohered controlled- not gate in the spin-boson model.

Partial transposition in quantum information theory

MM Wolf — 2007-05-24T08:27:41-00:00

Universal noiseless quantum computation - Mathematical theory and applications

J Kempe — 2007-05-24T08:15:38-00:00

Quantum walks and entanglement

J Kempe — 2007-05-24T08:13:46-00:00

Frames, designs, and spherical quantum codes in quantum information theory

JM Renes — 2007-05-24T07:55:05-00:00

Theoretical investigations of separability and entanglement of bipartite quantum systems

P Rungta — 2007-05-24T07:52:26-00:00

Quantum information theory

HN Barnum — 2007-05-24T07:49:29-00:00

(1999)

An introduction to entanglement measures

Martin Plenio — 2006-07-19T13:26:56-00:00

(10 Jun 2006)

We review the theory of entanglement measures, concentrating mostly on the finite dimensional two-party case. Topics covered include: single-copy and asymptotic entanglement manipulation; the entanglement of formation; the entanglement cost; the distillable entanglement; the relative entropic measures; the squashed entanglement; log-negativity; the robustness monotones; the greatest cross-norm; uniqueness and extremality theorems. Infinite dimensional systems and multi-party settings will be discussed briefly.

Information, Relative Entropy of Entanglement, and Irreversibility

L Henderson — 2007-05-24T06:34:07-00:00

Physical Review Letters, Vol. 84, No. 10. (6 March 2000), 2263.

Previously proposed measures of entanglement; such as entanglement of formation and assistance; are shown to be special cases of the relative entropy of entanglement. The difference between these measures for an ensemble of mixed states is shown to depend on the availability of classical information about particular members of the ensemble. Based on this; relations between relative entropy of entanglement and mutual information are derived.

Finding a maximally correlated state: Simultaneous Schmidt decomposition of bipartite pure states

Tohya Hiroshima — 2007-05-24T06:30:34-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 70, No. 3. (2004)

We consider a bipartite mixed state of the form = alpha,beta = 1l" align="middle">a|, where | are normalized bipartite state vectors, and matrix (a) is positive semidefinite. We provide a necessary and sufficient condition for the state taking the form of maximally correlated states by a local unitary transformation. More precisely, we give a criterion for simultaneous Schmidt decomposability of | for = 1,2,,l. Using this criterion, we can judge completely whether or not the state is equivalent to the maximally correlated state, in which the distillable entanglement is given by a simple formula. For generalized Bell states, this criterion is written as a simple algebraic relation between indices of the states. We also discuss the local distinguishability of the generalized Bell states that are simultaneously Schmidt decomposable.

Optimal local discrimination of two multipartite pure states

S Virmani — 2007-05-24T06:25:00-00:00

Physics Letters A, Vol. 288, No. 2. (17 September 2001), pp. 62-68.

In a recent paper, Walgate et al. (Phys. Rev. Lett. 85 (2000) 4972) demonstrated that any two orthogonal multipartite pure states can be optimally distinguished using only local operations. We utilise their result to show that this is true for any two multipartite pure states, in the sense of inconclusive discrimination. There are also certain regimes of conclusive discrimination for which the same also applies, although we can only conjecture that the result is true for all conclusive regimes. We also discuss a class of states that can be distinguished locally according to any discrimination measure, as they can be locally recreated in the possession of one party. A consequence of this is that any two maximally entangled states can always be optimally discriminated locally, according to any figure of merit.

Bound on distillable entanglement

EM Rains — 2007-05-24T06:16:37-00:00

Physical Review A, Vol. 60, No. 1. (July 1999), 179.

The best bound known on 2-locally distillable entanglement is that of Vedral and Plenio; involving a certain measure of entanglement based on relative entropy. It turns out that a related argument can be used to give an even stronger bound; we give this bound; and examine some of its properties. In particular; and in contrast to the earlier bounds; the new bound is not additive in general. We give an example of a state for which the bound fails to be additive; as well as a number of states for which the bound is additive.

When are correlations quantum?—verification and quantification of entanglement by simple measurements

KMR Audenaert — 2006-11-08T18:47:31-00:00

New J. Phys., Vol. 8, No. 11. (November 2006), 266.

Sensitivity of Hilbert and Bures distances to qubit perturbation

S Salvini — 2007-05-22T17:35:34-00:00

International Journal of Quantum Information, Vol. 5, No. 1-2. (2007), pp. 119-124.

We compare the sensitivity of Hilbert and Bures distances between two qubits in revealing small perturbations occurring to one of the qubits. We also analyze sensitivity in revealing perturbations to noise parameter of a depolarizing channel.

Negativity as a distance from a separable state

M Khasin — 2007-05-22T16:17:51-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 5. (2007)

The computable measure of the mixed-state entanglement, the negativity, is shown to admit a clear geometrical interpretation, when applied to Schmidt-correlated (SC) states: the negativity of a SC state equals a distance of the state from a pertinent separable state. As a consequence, the Peres-Horodecki criterion of separability is both necessary and sufficient for SC states. Another remarkable consequence is that the negativity of a SC can be estimated “at a glance” on the density matrix. These results are generalized to mixtures of SC states, which emerge in bipartite evolutions with additive integrals of motion.

Decoherence, Control, and Symmetry in Quantum Computers

D Bacon — 2006-07-18T03:23:29-00:00

(5 May 2003)

In this thesis we describe methods for avoiding the detrimental effects of decoherence while at the same time still allowing for computation of the quantum information. The philosophy of the method discussed in the first part of this thesis is to use a symmetry of the decoherence mechanism to find robust encodings of the quantum information. Stability, control, and methods for using decoherence-free information in a quantum computer are presented with a specific emphasis on decoherence due to a collective coupling between the system and its environment. Universal quantum computation on such collective decoherence decoherence-free encodings is demonstrated. Rigorous definitions of control and the use of encoded universality in quantum computers are addressed. Explicit gate constructions for encoded universality on ion trap and exchange based quantum computers are given. In the second part of the thesis we examine physical systems with error correcting properties. We examine systems that can store quantum information in their ground state such that decoherence processes are prohibited via energetics. We present the theory of supercoherent systems whose ground states are quantum error detecting codes and describe a spin ladder whose ground state has both the error detecting and correcting properties. We conclude by discussing naturally fault-tolerant quantum computation.

Statistical mechanics of complex networks

Reka Albert — 2006-03-18T18:52:14-00:00

Reviews of Modern Physics, Vol. 74, No. 1. (2002)

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include the cell, a network of chemicals linked by chemical reactions, and the Internet, a network of routers and computers connected by physical links. While traditionally these systems have been modeled as random graphs, it is increasingly recognized that the topology and evolution of real networks are governed by robust organizing principles. This article reviews the recent advances in the field of complex networks, focusing on the statistical mechanics of network topology and dynamics. After reviewing the empirical data that motivated the recent interest in networks, the authors discuss the main models and analytical tools, covering random graphs, small-world and scale-free networks, the emerging theory of evolving networks, and the interplay between topology and the network's robustness against failures and attacks.

How generic scale invariance influences quantum and classical phase transitions

D Belitz — 2007-05-18T08:38:32-00:00

Reviews of Modern Physics, Vol. 77, No. 2. (2005)

This review discusses a paradigm that has become of increasing importance in the theory of quantum phase transitions, namely, the coupling of the order-parameter fluctuations to other soft modes and the resulting impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms of the order parameter only. The soft modes in question are manifestations of generic scale invariance, i.e., the appearance of long-range order in whole regions in the phase diagram. The concept of generic scale invariance and its influence on critical behavior is explained using various examples, both classical and quantum mechanical. The peculiarities of quantum phase transitions are discussed, with emphasis on the fact that they are more susceptible to the effects of generic scale invariance than their classical counterparts. Explicit examples include the quantum ferromagnetic transition in metals, with or without quenched disorder; the metal-superconductor transition at zero temperature; and the quantum antiferromagnetic transition. Analogies with classical phase transitions in liquid crystals and classical fluids are pointed out, and a unifying conceptual framework is developed for all transitions that are influenced by generic scale invariance.

Optics in the relativistic regime

Gerard Mourou — 2007-05-18T08:34:44-00:00

Reviews of Modern Physics, Vol. 78, No. 2. (2006)

The advent of ultraintense laser pulses generated by the technique of chirped pulse amplification (CPA) along with the development of high-fluence laser materials has opened up an entirely new field of optics. The electromagnetic field intensities produced by these techniques, in excess of 1018 W/cm2, lead to relativistic electron motion in the laser field. The CPA method is reviewed and the future growth of laser technique is discussed, including the prospect of generating the ultimate power of a zettawatt. A number of consequences of relativistic-strength optical fields are surveyed. In contrast to the nonrelativistic regime, these laser fields are capable of moving matter more effectively, including motion in the direction of laser propagation. One of the consequences of this is wakefield generation, a relativistic version of optical rectification, in which longitudinal field effects could be as large as the transverse ones. In addition to this, other effects may occur, including relativistic focusing, relativistic transparency, nonlinear modulation and multiple harmonic generation, and strong coupling to matter and other fields (such as high-frequency radiation). A proper utilization of these phenomena and effects leads to the new technology of relativistic engineering, in which light-matter interactions in the relativistic regime drives the development of laser-driven accelerator science. A number of significant applications are reviewed, including the fast ignition of an inertially confined fusion target by short-pulsed laser energy and potential sources of energetic particles (electrons, protons, other ions, positrons, pions, etc.). The coupling of an intense laser field to matter also has implications for the study of the highest energies in astrophysics, such as ultrahigh-energy cosmic rays, with energies in excess of 1020 eV. The laser fields can be so intense as to make the accelerating field large enough for general relativistic effects (via the equivalence principle) to be examined in the laboratory. It will also enable one to access the nonlinear regime of quantum electrodynamics, where the effects of radiative damping are no longer negligible. Furthermore, when the fields are close to the Schwinger value, the vacuum can behave like a nonlinear medium in much the same way as ordinary dielectric matter expanded to laser radiation in the early days of laser research.

The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography

Matthias Christandl — 2007-05-17T20:17:34-00:00

(25 Apr 2006)

This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to derive a one-to-one relation between the spectra of a bipartite quantum state and its reduced states, and the Kronecker coefficients of the symmetric group. In the second part, the focus lies on the entanglement of bipartite quantum states. Drawing on an analogy between entanglement distillation and secret-key agreement in classical cryptography, a new entanglement measure, `squashed entanglement', is introduced.

The Interpretation of Quantum Mechanics: Many Worlds or Many Words?

Max Tegmark — 2007-05-16T04:00:23-00:00

(15 Sep 1997)

As cutting-edge experiments display ever more extreme forms of non-classical behavior, the prevailing view on the interpretation of quantum mechanics appears to be gradually changing. A (highly unscientific) poll taken at the 1997 UMBC quantum mechanics workshop gave the once all-dominant Copenhagen interpretation less than half of the votes. The Many Worlds interpretation (MWI) scored second, comfortably ahead of the Consistent Histories and Bohm interpretations. It is argued that since all the above-mentioned approaches to nonrelativistic quantum mechanics give identical cookbook prescriptions for how to calculate things in practice, practical-minded experimentalists, who have traditionally adopted the “shut-up-and-calculate interpretation”, typically show little interest in whether cozy classical concepts are in fact real in some untestable metaphysical sense or merely the way we subjectively perceive a mathematically simpler world where the Schrodinger equation describes everything - and that they are therefore becoming less bothered by a profusion of worlds than by a profusion of words. Common objections to the MWI are discussed. It is argued that when environment-induced decoherence is taken into account, the experimental predictions of the MWI are identical to those of the Copenhagen interpretation except for an experiment involving a Byzantine form of “quantum suicide”. This makes the choice between them purely a matter of taste, roughly equivalent to whether one believes mathematical language or human language to be more fundamental.

On Math, Matter and Mind

Piet Hut — 2007-05-16T03:56:34-00:00

(15 Jan 2006)

We discuss the nature of reality in the ontological context of Penrose's math-matter-mind triangle. The triangle suggests the circularity of the widespread view that math arises from the mind, the mind arises out of matter, and that matter can be explained in terms of math. Non-physicists should be wary of any claim that modern physics leads us to any particular resolution of this circularity, since even the sample of three theoretical physicists writing this paper hold three divergent views. Some physicists believe that current physics has already found the basic framework for a complete description of reality, and only has to fill in the details. Others suspect that no single framework, from physics or other sources, will ever capture reality. Yet others guess that reality might be approached arbitrarily closely by some form of future physics, but probably based on completely different frameworks. We will designate these three approaches as the fundamentalist, secular and mystic views of the world, as seen by practicing physicists. We present and contrast each of these views, which arguably form broad categories capturing most if not all interpretations of physics. We argue that this diversity in the physics community is more useful than an ontological monoculture, since it motivates physicists to tackle unsolved problems with a wide variety of approaches.

Intelligent Life in Cosmology

Frank Tipler — 2007-05-16T03:13:49-00:00

(31 Mar 2007)

I shall present three arguments for the proposition that intelligent life is very rare in the universe. First, I shall summarize the consensus opinion of the founders of the Modern Synthesis (Simpson, Dobzhanski, and Mayr) that the evolution of intelligent life is exceedingly improbable. Second, I shall develop the Fermi Paradox: if they existed they'd be here. Third, I shall show that if intelligent life were too common, it would use up all available resources and die out. But I shall show that the quantum mechanical principle of unitarity (actually a form of teleology!) requires intelligent life to survive to the end of time. Finally, I shall argue that, if the universe is indeed accelerating, then survival to the end of time requires that intelligent life, though rare, to have evolved several times in the visible universe. I shall argue that the acceleration is a consequence of the excess of matter over antimatter in the universe. I shall suggest experiments to test these claims.

Extracting the hierarchical organization of complex systems

M Sales-Pardo — 2007-05-16T03:11:47-00:00

(11 May 2007)

Extracting understanding from the growing “sea” of biological and socio-economic data is one of the most pressing scientific challenges facing us. Here, we introduce and validate an unsupervised method that is able to accurately extract the hierarchical organization of complex biological, social, and technological networks. We define an ensemble of hierarchically nested random graphs, which we use to validate the method. We then apply our method to real-world networks, including the air-transportation network, an electronic circuit, an email exchange network, and metabolic networks. We find that our method enables us to obtain an accurate multi-scale descriptions of a complex system.

Why only few are so successful ?

PK Mohanty — 2007-05-16T03:07:12-00:00

(17 Apr 2007)

In many professons employees are rewarded according to their relative performance. Corresponding economy can be modeled by taking $N$ independent agents who gain from the market with a rate which depends on their current gain. We argue that this simple realistic rate generates a scale free distribution even though intrinsic ability of agents are marginally different from each other. As an evidence we provide distribution of scores for two different systems (a) the global stock game where players invest in real stock market and (b) the international cricket.

Monotones and invariants for multi-particle quantum states

H Barnum — 2007-05-15T21:51:35-00:00

(28 Mar 2001)

We introduce new entanglement monotones which generalize, to the case of many parties, those which give rise to the majorization-based partial ordering of bipartite states' entanglement. We give some examples of restrictions they impose on deterministic and probabilistic conversion between multipartite states via local actions and classical communication. These include restrictions which do not follow from any bipartite considerations. We derive supermultiplicativity relations between each state's monotones and the monotones for collective processing when the parties share several states. We also investigate polynomial invariants under local unitary transformations, and show that a large class of these are invariant under collective unitary processing and also multiplicative, putting restrictions, for example, on the exact conversion of multiple copies of one state to multiple copies of another.

Geometry of entangled states

Marek Kuś — 2007-05-15T21:47:05-00:00

Physical Review A, Vol. 63, No. 3. (14 February 2001), 032307.

Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K × M problem and characterize the set of effectively different states (which cannot be related by local transformations). Thus; we generalize earlier results obtained for the simplest 2×2 system; which lead to a stratification of the six-dimensional set of N =4 pure states. We define the concept of absolutely separable states; for which all globally equivalent states are separable.

Majorization and the interconversion of bipartite states

MA Nielsen — 2007-05-15T21:45:08-00:00

Quantum Information and Computation, Vol. 1, No. 1. (28 May 2001), pp. 76-93.

Majorization is a powerful, easy-to-use and exible tool which arises frequently in quan- tum mechanics as a consequence of fundamental connections between unitarity and the majorization relation. Entanglement theory does not escape from its in uence. Thus the interconversion of bipartite pure states by means of local manipulations turns out to be ruled to a great extend by majorization relations. This review both introduces some elements of majorization theory and describes recent results on bipartite entangle- ment transformations, with special emphasis being placed on explaining the connections between these two topics. The latter implies analyzing two other aspects of quantum me- chanics similarly in uenced by majorization, namely the problem of mixing of quantum states and the characterization of quantum measurement.

Relativity of Pure States Entanglement

Karol Zyczkowski — 2007-05-15T21:36:20-00:00

Annals of Physics, Vol. 295, No. 2. (1 February 2002), pp. 115-135.

Entanglement of any pure state of an NxN bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized entropies of the vector of Schmidt coefficients. For N>=3 they generate different ordering in the set of pure states and for some states their ordering depends on the measure of entanglement used. This odd-looking property is acceptable, since these incomparable states cannot be transformed to each other with unit efficiency by any local operation. In analogy to special relativity the set of pure states equivalent under local unitaries has a causal structure so that at each point the set splits into three parts: the "Future," the "Past," and the set of noncomparable states.

Quantify entanglement by concurrence hierarchy

Heng Fan — 2007-05-15T17:09:29-00:00

Journal of Physics A: Mathematical and General, Vol. 36, No. 14. (2003), pp. 4151-4158.

We define the concurrence hierarchy as d − 1 independent invariants under local unitary transformations in d -level quantum system. The first one is the original concurrence defined by Wootters (1998 Phys. Rev. Lett. 80 2245) and Hill and Wootters (1997 Phys. Rev. Lett. 78 5022) in a two-level quantum system and generalized to the d -level pure quantum state case. We propose to use this concurrence hierarchy as a measurement of entanglement. This measurement does not increase under local quantum operations and classical communication.

Optimal Entanglement Criterion for Mixed Quantum States

Heinz Breuer — 2007-05-15T01:32:27-00:00

Physical Review Letters, Vol. 97, No. 8. (2006)

We develop a strong and computationally simple entanglement criterion. The criterion is based on an elementary positive map which operates on state spaces with even dimension N4. It is shown that detects many entangled states with a positive partial transposition (PPT) and that it leads to a class of optimal entanglement witnesses. This implies that there are no other witnesses which can detect more entangled PPT states. The map yields a systematic method for the explicit construction of high-dimensional manifolds of bound entangled states.

Concurrence of Arbitrary Dimensional Bipartite Quantum States

Kai Chen — 2007-05-14T02:03:10-00:00

Physical Review Letters, Vol. 95, No. 4. (2005)

We derive an analytical lower bound for the concurrence of a bipartite quantum state in arbitrary dimension. A functional relation is established relating concurrence, the Peres-Horodecki criterion, and the realignment criterion. We demonstrate that our bound is exact for some mixed quantum states. The significance of our method is illustrated by giving a quantitative evaluation of entanglement for many bound entangled states, some of which fail to be identified by the usual concurrence estimation method.

Disentanglement and decoherence by open system dynamics

PJ Dodd — 2007-05-14T00:50:57-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 69, No. 5. (2004)

The destruction of quantum interference, decoherence, and the destruction of entanglement both appear to occur under the same circumstances. To address the connection between these two phenomena, we consider the evolution of arbitrary initial states of a two-particle system under open system dynamics described by a class of master equations which produce decoherence of each particle. We show that all initial states become separable after a finite time, and we produce the explicit form of the separated state. The result extends and amplifies an earlier result of Diósi. We illustrate the general result by considering the case in which the initial state is an Einstein-Podolsky-Rosen state (in which both the positions and momenta of a particle pair are perfectly correlated). This example clearly illustrates how the spreading out in phase space produced by the environment leads to certain disentanglement conditions becoming satisfied.

A semidefinite program for distillable entanglement

Eric Rains — 2007-05-14T00:45:52-00:00

(12 Apr 2001)

We show that the maximum fidelity obtained by a p.p.t. distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and “maximally correlated” states. We conclude with a discussion of possible applications of semidefinite programming to quantum codes and 1-local distillation.

Generalized concurrence and limits of separability for two qutrits

C Herreno-Fierro — 2007-05-12T17:01:34-00:00

(22 Jul 2005)

We present an extension of the Wootters concurrence for the case of two qutrits in mixed states. The reduction of our extension to the case of two levels shows complete agreement with Wootters concurrence for two qubits. As an explicit example, we compute the concurrence for a family of symmetric states and we obtain the bounds on the limit for separability. Our results are compared with those of the negativity.

Quantum Theory From Five Reasonable Axioms

Lucien Hardy — 2005-07-29T04:54:27-00:00

(25 Sep 2001)

The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be derived from five very reasonable axioms. The first four of these are obviously consistent with both quantum theory and classical probability theory. Axiom 5 (which requires that there exists continuous reversible transformations between pure states) rules out classical probability theory. If Axiom 5 (or even just the word "continuous" from Axiom 5) is dropped then we obtain classical probability theory instead. This work provides some insight into the reasons quantum theory is the way it is. For example, it explains the need for complex numbers and where the trace formula comes from. We also gain insight into the relationship between quantum theory and classical probability theory.

Degree of entanglement for two qutrits in a pure state

Jose Cereceda — 2007-05-12T02:18:34-00:00

(8 May 2003)

In this paper, a new measure of entanglement for general pure bipartite states of two qutrits is formulated.

Negativity and Concurrence as complete entanglement measures for two arbitrary qudits

Suranjana Rai — 2006-06-18T15:09:27-00:00

(5 Aug 2005)

Two measures of entanglement, negativity and concurrence are studied for two arbitrary qudits. We obtain negativity as an expectation value of an operator. The differences of the squares of negativity and concurrence are invariants of multilevel entanglement. Explicit results for qutrits and quadrits are obtained.

Transition of d-level quantum systems through quantum channels with correlated noise

A Fahmi — 2007-05-11T16:49:17-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 4. (2007)

Entanglement and entanglement assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this paper, we study quantum-communication channels in d-dimensional systems and derive the mutual information of the quantum channels for maximally entangled states and product states coding with correlated noise. Then, we compare fidelity between these states. Our results show that there exists a certain fidelity memory threshold, which depends on the dimension of the Hilbert space (d) and the properties of noisy channels. We calculate the classical capacity of a particular correlated noisy channel and show that in order to achieve Holevo limit, we must use d particles with d degrees of freedom. Our results show that entanglement is a useful means to enhance the mutual information. We choose a special nonmaximally entangled state and show that in the quasiclassical depolarizing and quantum depolarizing channels, maximum classical capacity in the higher memory channels is given by the maximally entangled state. Hence, our results show that for high error channels in every degree of memory, maximally entangled states have better mutual information.

Transition behavior in the channel capacity of two-quibit channels with memory

Chiara Macchiavello — 2007-05-11T16:45:54-00:00

Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 69, No. 1. (2004)

We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold.

Three-qubit quantum error-correction scheme for collective decoherence

Chui-Ping Yang — 2007-05-10T11:16:24-00:00

Physical Review A, Vol. 63, No. 2. (18 January 2001), 022311.

We show a way to correct collective error through a three-qubit quantum code. The encoding and decoding (i.e.; error recovery) operations for such a code; which protects one qubit of quantum information perfectly (with infinite “distance”) against collective decoherence; are presented. The code is actually a manifestation of a noiseless subsystem first reported by Knill; Laflamme; and Viola [Phys. Rev. Lett. 84 ; 2525 (2000)]; and provides a good illustration of the relationship between noiseless subsystems and error-correcting codes already noted by these authors. We also show in detail how this code can be used to preserve an arbitrary joint state (including entangled states) of two qubits; by pairing each of them with two other qubits; even in the case in which the two resulting clusters interact in nonequivalent ways with a common environment.

An index to quantify an individual's scientific output

JE Hirsch — 2005-08-08T10:17:12-00:00

(3 Aug 2005)

I propose the index $h$, defined as the number of papers with citation number higher or equal to $h$, as a useful index to characterize the scientific output of a researcher.

Entanglement of Formation of Bipartite Quantum States

Kai Chen — 2007-05-07T18:34:25-00:00

Physical Review Letters, Vol. 95, No. 21. (2005)

We give an explicit tight lower bound for the entanglement of formation for arbitrary bipartite mixed states by using the convex hull construction of a certain function. This is achieved by revealing a novel connection among the entanglement of formation, the well-known Peres-Horodecki, and realignment criteria. The bound gives a quite simple and efficiently computable way to evaluate quantitatively the degree of entanglement for any bipartite quantum state.

Operator-sum representation of time-dependent density operators and its applications

DM Tong — 2007-05-05T19:01:00-00:00

(15 Jul 2004)

We show that any arbitrary time-dependent density operator of an open system can always be described in terms of an operator-sum representation regardless of its initial condition and the path of its evolution in the state space, and we provide a general expression of Kraus operators for arbitrary time-dependent density operator of an $N$-dimensional system. Moreover, applications of our result are illustrated through several examples.

The Mathematical Universe

Max Tegmark — 2007-05-02T21:10:04-00:00

(5 Apr 2007)

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.