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Physical Review Letters, Vol. 95, No. 20. (2005)
Abstract
We define the algorithmic complexity of a quantum state relative to a given precision parameter, and give upper bounds for various examples of states. We also establish a connection between the entanglement of a quantum state and its algorithmic complexity. ...
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Physical Review Letters, Vol. 98, No. 26. (2007)
Abstract
It is shown that the ensemble P(),||*, where P() is a Gaussian distribution of finite variance and | is a coherent state, can be better discriminated with an entangled measurement than with any local strategy supplemented by classical communication. Although this ensemble consists of products of quasiclassical states without any squeezing, it thus exhibits a purely quantum feature. This remarkable effect is demonstrated experimentally by implementing the optimal local strategy on coherent states of light together with a global strategy that ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 6. (2007)
Abstract
The evolution of the lower bound of entanglement proposed by Chen et al. [Phys. Rev. Lett. 95, 210501 (2005)] in high-dimensional bipartite systems under dissipation is studied. Discontinuities for the time derivative of this bound are found depending on the initial conditions for entangled states. These abrupt changes along the evolution of the entanglement bound appear as precursors of sudden death. ...
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(13 Jun 2007)
Abstract
It is shown that, if the loss of entanglement is small, then approximate quantum error correction is possible, thereby generalizing what happens for coherent information. The result is obtained for the entanglement of formation, and naturally extends to all entanglement measures upper bounded by that. ...
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(29 May 2007)
Abstract
Quantum mechanics imposes 'monogamy' constraints on the sharing of entanglement. We show that, despite these limitations, entanglement can be fully 'promiscuous', i.e. simultaneously present in unlimited two-body and many-body forms in states living in an infinite-dimensional Hilbert space. Monogamy just bounds the divergence rate of the various entanglement contributions. This is demonstrated in simple families of N-mode (N >= 4) Gaussian states of light fields or atomic ensembles, which therefore enable infinitely more freedom in the distribution of information, as opposed to systems of individual qubits. Such a finding ...
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Journal of Optics B: Quantum and Semiclassical Optics, Vol. 6, No. 9. (2004), pp. 373-377.
Abstract
We study the quantum entanglement between two coupled cavities, in which one is initially prepared in a mesoscopic superposition state and the other is in the vacuum in dissipative environment, and show how the entanglement between two cavities can arise in the dissipative environment. The dynamic behaviour of the nonlocality for the system is also investigated. ...
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New J. Phys., Vol. 8, No. 11. (November 2006), 266.
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(16 May 2006)
Abstract
Coupling a set of initially uncorrelated subsystems leads to the generation of correlations. If in addition these subsystems interact with a dissipative local environments the generation of correlation can be restricted. It is found that the generation of quantum and classical correlations between the subsystems is qualitatively different in this respect. Quantum correlations (entanglement) display $k$-independent asymptotic behavior at large effective Hilbert space dimension $k$ of the composite system. As a consequence, the quantum correlations are bounded. Classical correlations are found numerically to develop on a scale growing with ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 5. (2007)
Abstract
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 ...
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Physical Review Letters, Vol. 92, No. 21. (2004)
Abstract
We demonstrate that a necessary precondition for an unconditionally secure quantum key distribution is that both sender and receiver can use the available measurement results to prove the presence of entanglement in a quantum state that is effectively distributed between them. One can thus systematically search for entanglement using the class of entanglement witness operators that can be constructed from the observed data. We apply such analysis to two well-known quantum key distribution protocols, namely, the 4-state protocol and the 6-state ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 5. (2007)
Abstract
We give an overview of different types of entanglement that can be generated in experiments, as well as of various protocols that can be used to verify or quantify entanglement. We propose several criteria that, we argue, should be applied to experimental entanglement verification procedures. Explicit examples demonstrate that not following these criteria will tend to result in overestimating the amount of entanglement generated in an experiment or in inferring entanglement when there is none. We distinguish protocols meant to refute ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 71, No. 6. (2005)
Abstract
Recently, Markham and Vedral [Phys. Rev. A 67, 042113 (2003)] investigated the effect of beam splitting on the spin, or SU(2), coherent states for a single mode field. The spin coherent state is a binomial coherent state related to the Holstein-Primakoff realization of the su(2) Lie algebra given in terms of a set of single mode bose annihilation and creation operators. Upon beam splitting, the ordinary (or Glauber) coherent states merely split into products of ordinary coherent states with reduced amplitudes ...
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Physical Review Letters, Vol. 98, No. 19. (2007)
Abstract
We show how to detect and quantify entanglement of atoms in optical lattices in terms of correlation functions of the momentum distribution. These distributions can be measured directly in the experiments. We introduce two kinds of entanglement measures related to the position and the spin of the atoms. ...
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Physical Review Letters, Vol. 98, No. 19. (2007)
Abstract
We show that, for experimentally relevant systems, there is an optimal measurement strategy to monitor the time evolution of entanglement under open system dynamics. This suggests an efficient, dynamical characterization of the entanglement of composite, open quantum systems. ...
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Physical Review Letters, Vol. 86, No. 5. (29 January 2001), 910.
Abstract
We study the entanglement properties of a class of N -qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They also have a high persistency of entanglement which means that â¼ N / 2 qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of ...
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(4 May 2007)
Abstract
We investigate the conditions for entanglement in a system of two atoms and two photon modes in a vacuum, using the Jaynes-Cummings model in the rotating-wave approximation. It is found that the strength of atom entanglement is a periodic function of time, generalizing the results of other workers. We explicitly show that our results are in agreement with existing results and reproduce existing entanglement conditions under appropriate limits. Results for the two-atoms two-photons system are generailzed to the case of arbitrary values for the atomic energies, relative to ...
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Physical Review Letters, Vol. 92, No. 10. (2004)
Abstract
We present a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to this observable-based setting, suggesting new ways of measuring and classifying multipartite entanglement. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel ...
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Physical Review Letters, Vol. 92, No. 10. (12 March 2004)
Abstract
We present a generalization of entanglement based on the idea that entanglement is relative to a distinguished subspace of observables rather than a distinguished subsystem decomposition. A pure quantum state is entangled relative to such a subspace if its expectations are a proper mixture of those of other states. Many information-theoretic aspects of entanglement can be extended to this observablebased setting, suggesting new ways of measuring and classifying multipartite entanglement. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in ...
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(1 May 2007)
Abstract
We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled N-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the 2-photon coherence of down-converted light into an almost optimal N-photon coherence. ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 75, No. 5. (2007)
Abstract
We derive an experimentally observable lower bound on concurrence of mixed quantum states in terms of an entanglement witness, relating measurements on single states with those on two copies. ...
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Journal of Physics A: Mathematical and General, Vol. 35, No. 17. (2002), pp. 3911-3923.
Abstract
We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite dimensional, most notably the fact that the set of states with infinite entropy of entanglement is trace-norm dense in state space, implying that in any neighbourhood of every product state lies an arbitrarily strongly entangled state. The starting point for a clarification of this counterintuitive property is the observation that if one imposes the natural ...
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Physical Review Letters, Vol. 87, No. 16. (1 October 2001), 167904.
Abstract
We provide a necessary and sufficient condition for separability of Gaussian states of bipartite systems of arbitrarily many modes. The condition provides an operational criterion since it can be checked by simple computation. Moreover; it allows us to find a pure product-state decomposition of any given separable Gaussian state. We also show that all bipartite Gaussian states with nonpositive partial transpose are distillable. ...
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Physical Review A, Vol. 64, No. 6. (16 November 2001), 063811.
Abstract
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied; with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices; the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure; the bounds can substantially overestimate the entanglement. In particular; they do not show the ...
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(31 Jul 2002)
Abstract
We discuss properties of entanglement measures called I-concurrence and tangle. For a bipartite pure state, I-concurrence and tangle are simply related to the purity of the marginal density operators. The I-concurrence (tangle) of a bipartite mixed state is the minimum average I-concurrence (tangle) of ensemble decompositions of pure states of the joint density operator. Terhal and Vollbrecht [Phys. Rev. Lett. 85, 2625 (2000)] have given an explicit formula for the entanglement of formation of isotropic states in arbitrary dimensions. We use their formalism to derive comparable expressions for ...
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(16 Apr 2007)
Abstract
We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence in a vacuum environment. The sufficient conditions enable to clarify a class of bipartite entangled states which preserve their entanglement or, in other words, are tolerant against decoherence in a vacuum. We also discuss such a class for entangled qubits. ...
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Physical Review A, Vol. 59, No. 2. (February 1999), 1615.
Abstract
We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are functions of the internal phase shift of the interferometer; with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing function of the input squeezing parameter. A couple of squeezed vacuums at the input lead to maximum entangled state at the output. ...
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Physical Review A, Vol. 62, No. 4. (2000), 043803.
Abstract
Dielectric four-port devices play an important role in optical quantum information processing. Since for causality reasons the permittivity is a complex function of frequency; dielectrics are typical examples of noisy quantum channels; which cannot preserve quantum coherence. To study the effects of quantum decoherence; we start from the quantized electromagnetic field in an arbitrary Kramers-Kronig dielectric of given complex permittivity and construct the transformation relating the output quantum state to the input quantum state; without placing restrictions on the frequency. We ...
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Physical Review Letters, Vol. 80, No. 18. (4 May 1998), 3891.
Abstract
We experimentally entangle freely propagating particles that never physically interacted with one another or which have never been dynamically coupled by any other means. This demonstrates that quantum entanglement requires the entangled particles neither to come from a common source nor to have interacted in the past. In our experiment we take two pairs of polarization entangled photons and subject one photon from each pair to a Bell-state measurement. This results in projecting the other two outgoing photons into an entangled ...
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Physical Review A, Vol. 65, No. 3. (27 February 2002), 032323.
Abstract
A beam splitter is a simple; readily available device which can act to entangle output optical fields. We show that a necessary condition for the fields at the output of the beam splitter to be entangled is that the pure input states exhibit nonclassical behavior. We generalize this proof for arbitrary (pure or impure) Gaussian input states. Specifically; nonclassicality of the input Gaussian fields is a necessary condition for entanglement of the field modes with the help of a beam splitter. ...
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Reviews of Modern Physics, Vol. 73, No. 3. (28 Aug 2001), pp. 565-582.
Abstract
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles ...
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Journal of Modern Optics, Vol. 50 (December 2003), pp. 1809-1815.
Abstract
Some non-classical properties such as squeezing, sub-Poissonian photon statistics or oscillations in photon-number distributions may survive longer in a phase-sensitive environment than in a phase-insensitive environment. We examine if entanglement, which is an inter-mode non-classical feature, can also survive longer in a phase-sensitive environment. Differently from the single-mode case, we find that making the environment phase-sensitive does not aid in prolonging entanglement. ...
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Physical Review Letters, Vol. 71, No. 9. (1993), 1291.
Abstract
If a quantum system of Hilbert space dimension mn is in a random pure state; the average entropy of a subsystem of dimension m ≤ n is conjectured to be S m ; n = S k = n +1 mn 1/ k - m -1/2 n and is shown to be ≃ln m - m /2 n for 1≪ m ≤ n . Thus there is less than one-half unit of ...
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Physical Review Letters, Vol. 92, No. 6. (2004)
Abstract
It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept. ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 73, No. 6. (2006)
Abstract
We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of "singly branching" states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 70, No. 5. (2004)
Abstract
We investigate an imbalance between the sensitivity of the common state measures—fidelity, trace distance, concurrence, tangle, von Neumann entropy, and linear entropy—when acted on by a depolarizing channel. Further, in this context we explore two classes of two-qubit entangled mixed states. Specifically, we illustrate a sensitivity imbalance between three of these measures for depolarized (i.e., Werner-state-like) nonmaximally entangled and maximally entangled mixed states, noting that the size of the imbalance depends on the state's tangle and linear entropy. ...
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Physical Review B (Condensed Matter and Materials Physics), Vol. 75, No. 11. (2007)
Abstract
We compare disentanglement and decoherence rates within two-spin and three-spin entangled systems subjected to all possible combinations of local and collective pure dephasing noise combinations. In all cases, the bipartite entanglement decay rate is found to be greater than or equal to the dephasing-decoherence rates and often significantly greater. This sharpens previous results for two-spin systems [T. Yu and J. H. Ebenly Phys. Rev. B 68, 165322 (2003)] and extends them to the three-spin context. ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 71, No. 3. (2005)
Abstract
We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for Greenberger-Horne-Zeilinger (GHZ) -type superposition states decreases with the size of the system, while for a class of other states—namely, all graph states with constant degree—the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with individual couplings of particles ...
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arXiv: quant-ph/0403044(v1)
Abstract
We present a notion of generalized entanglement which goes beyond the conventional definition based on quantum subsystems. This is accomplished by directly defining entanglement as a property of quantum states relative to a distinguished set of observables singled out by Physics. While recovering standard entanglement as a special case, our notion allows for substantially broader generality and flexibility, being applicable, in particular, to situations where existing tools are not directly useful. ...
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Europhysics Letters, Vol. 76 (15 November 2006), pp. 547-553.
Abstract
We consider spatially separated qubits coupled to a thermal bosonic field that causes pure dephasing. Our focus is on the entanglement of two Bell states which for vanishing separation are known as robust and fragile entangled states. The reduced two-qubit dynamics is solved exactly and explicitly. Our results allow us to gain information about the robustness of two-qubit decoherence-free subspaces with respect to physical parameters such as temperature, qubit-bath coupling strength and spatial separation of the qubits. Moreover, we clarify the relation between single-qubit coherence and two-qubit ...
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Phys. Rev. A, Vol. 73, No. 1. (January 2006), 012338.
Abstract
We investigate entanglement properties of a recently introduced class of macroscopic quantum superpositions in two-mode mixed states. One of the tools we use in order to infer the entanglement in this non-Gaussian class of states is the power to entangle a qubit system. Our study reveals features which are hidden in a standard approach to entanglement investigation based on the uncertainty principle of the quadrature variables. We briefly describe the experimental setup corresponding to our theoretical scenario and a suitable modification of the protocol which makes our proposal realizable ...
Note (first note only)
1. Entangling power provides a lower bound on entanglement.
2. You can use a Schmidt decomp. to compute a NPT entanglement measure.
3. You don't have to use a Kraus decomp. to get time evolution under noise -- just use the unitary evolution, get ensemble averages _after_ finding the new rho.
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(7 Feb 2007)
Abstract
This Dissertation collects my results on the interpretation, characterization, quantification and application of bipartite and multipartite entanglement in Gaussian states of continuous variable systems. ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 69, No. 2. (2004)
Abstract
It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement." In this paper we present a simple identity which captures the trade off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade offs of a monogamy nature for other entanglement measures and secret and total correlation measures. ...
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Phys. Rev. A, Vol. 65, No. 1. (January 2002), 012303.
Abstract
We propose a scheme for generating multipartite entangled coherent states via entanglement swapping, with an example of a physical realization in ion traps. Bipartite entanglement of these multipartite states is quantified by the concurrence. We also compute multipartite entanglement for certain systems. Finally we establish that these results for entanglement can be applied to more general multipartite entangled nonorthogonal states. ...
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Phys. Rev. A, Vol. 67, No. 2. (February 2003), 024301.
Abstract
We consider entanglement in a system with a fixed number of identical particles. Since any operation should be symmetrized over all the identical particles and there is the precondition that the spatial wave functions overlap, the meaning of identical-particle entanglement is fundamentally different from that of distinguishable particles. The identical-particle counterpart of the Schmidt basis is shown to be the single-particle basis in which the one-particle reduced density matrix is diagonal. But it does not play a special role in the issue of entanglement, which depends on the single-particle ...
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Phys. Rev. A, Vol. 65, No. 4. (April 2002), 042101.
Abstract
The Fock space of a system of indistinguishable particles is isomorphic (in a nonunique way) to the state space of a composite, i.e., many modes, quantum system. One can then discuss quantum entanglement for fermionic as well as bosonic systems. We exemplify the use of this notion-central in quantum information-by studying some, e.g., Hubbard, lattice fermionic models relevant to condensed matter physics. ...
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Phys. Rev. A, Vol. 67, No. 2. (February 2003), 022303.
Abstract
Given a quantum state of the electromagnetic field, one is, in principle, free to redefine the field modes. We show here how the amount of entanglement in a given state depends on redefinitions of the modes, and calculate the minimum and maximum entanglement over all such redefinitions for several examples. Redefinitions can also be interpreted as transformations that one can apply actively, for example, in order to create nonlocal entanglement. ...
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Phys. Rev. A, Vol. 52 (July 1995), pp. 735-741.
Abstract
We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called “Schrödinger cat states”) are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we ...
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Phys. Rev. A, Vol. 51 (February 1995), pp. 989-991.
Abstract
Given an entanglement of two systems involving nonorthogonal states, we find the Schmidt decomposition for the state. The relation between the Schmidt representation and an ideal measurement of the degree of entanglement of the states is discussed, and a Bell inequality is shown to be violated. The maximal violation of the Bell inequality provides a measurement of the degree of entanglement. The entangled coherent states are provided as a concrete example of the Bell inequality for entangled nonorthogonal states. ...
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Journal of the Optical Society of America B Optical Physics, Vol. 4 (October 1987), pp. 1700-1709.
Abstract
Here it is shown that, for a wide class of nonlinear Hamiltonians, an essentially classical initial state will evolve into the coherent superposition of distinguishable quantum states. The detection of the interference fringes can be performed by beating the light leaving the nonlinear optical medium with light from a local oscillator. A model for the loss in the detection apparatus is introduced. The squeezed-vacuum technique is introduced finally as a means of enhancing the interference fringes displaying the distinguishable quantum state. ...
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Physical Review A (Atomic, Molecular, and Optical Physics), Vol. 72, No. 2. (2005)
Abstract
For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multidimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement E provided the number of photons is at least of order 22E. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find ...
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