Statistical distance and Hilbert space Export

@article{citeulike:4232977, abstract = {A concept of "statistical distance" is defined between different preparations of the same quantum system; or in other words; between different rays in the same Hilbert space. Statistical distance is determined entirely by the size of statistical fluctuations occurring in measurements designed to distinguish one state from another. It is not related; a priori ; to the usual distance (or angle) between rays. One finds; however; that these two kinds of distance are in fact the same; a result which depends on certain peculiarities of quantum mechanics.}, author = {Wootters, W. K.}, citeulike-article-id = {4232977}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevD.23.357}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRD/v23/i2/p357_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PRD/v23/i2/p357_1}, comment = {Contains key argument showing how the concept of the statistical distance in quantum mechanics is actually a very general idea that first arose in the study of genetic variation by Fisher. Thus the Hilbert space structure is not as arbitrary as thought. The question as to how the complex structure of H arises remains - this is likely due to geometrical considerations}, doi = {10.1103/PhysRevD.23.357}, journal = {Physical Review D}, keywords = {foundations, geometrical-quantum-mechanics, quantum-mechanics}, month = {Jan}, number = {2}, pages = {357--362}, posted-at = {2009-03-27 17:01:05}, priority = {5}, publisher = {American Physical Society}, title = {Statistical distance and Hilbert space}, url = {http://dx.doi.org/10.1103/PhysRevD.23.357}, volume = {23}, year = {1981} }

TY - JOUR ID - citeulike:4232977 L3 - citeulike-article-id:4232977 N2 - A concept of "statistical distance" is defined between different preparations of the same quantum system; or in other words; between different rays in the same Hilbert space. Statistical distance is determined entirely by the size of statistical fluctuations occurring in measurements designed to distinguish one state from another. It is not related; a priori ; to the usual distance (or angle) between rays. One finds; however; that these two kinds of distance are in fact the same; a result which depends on certain peculiarities of quantum mechanics. IS - 2 JF - Physical Review D EP - 362 TI - Statistical distance and Hilbert space PB - American Physical Society VL - 23 SP - 357 KW - foundations KW - geometrical-quantum-mechanics KW - quantum-mechanics N1 - Contains key argument showing how the concept of the statistical distance in quantum mechanics is actually a very general idea that first arose in the study of genetic variation by Fisher. Thus the Hilbert space structure is not as arbitrary as thought. The question as to how the complex structure of H arises remains - this is likely due to geometrical considerations AU - Wootters, WK PY - 1981/Jan// UR - http://dx.doi.org/10.1103/PhysRevD.23.357 ER -