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K. A. Kirkpatrick

Publications and source records attributed to K. A. Kirkpatrick.

13 recordsLinked to original sources
arXiv2005

The Schrodinger-HJW Theorem

A concise presentation of Schrodinger's ancilla theorem (1936 Proc. Camb. Phil. Soc. 32, 446) and its several recent rediscoveries.

quant-ph↗
arXiv2005

Classical Three-Box "paradox"

A simple classical probabilistic system (a simple card game) classically exemplifies Aharonov and Vaidman's "Three-Box 'paradox'" [J. Phys. A 24, 2315 (1991)], implying that the Three-Box example is neither quantal nor a paradox and leaving one less difficulty to busy the interpreters of quantum mechanics. An ambiguity in the usual expression of the retrodiction formula is shown to have misled Albert, Aharonov, and D'Amato [Phys. Rev. Lett. 54, 5 (1985)] to a result not, in fact, "curious"; the discussion illustrates how to avoid this ambiguity.

quant-ph↗
arXiv2004

Error in an argument regarding "improper" mixtures

An argument, perhaps originating with Feyerabend a half century ago, and repeated many times since, purporting to establish that an "ignorance interpretation" of a bipartite pure entangled state leads to logical inconsistency, is incorrect: the argument fails to account for the effects of indistinguishability.

quant-ph↗
arXiv2004

Compatibility and probability

A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.

quant-ph↗
arXiv2003

Indistinguishability and the external correlation of mixtures

Experimental evidence, the heuristics of indistinguishability, and its logical inconsistency with quantum formalism all argue against the existence of a quantum mixture uncorrelated with the exterior, that is, argue for the postulate "The state of a system uncorrelated with its exterior is pure." This is shown to be equivalent with "The state of a system describable in terms of indistinguishable pure states is pure," and with "The state of the universe is pure"; further, it yields a quantitative expression of the traditional relation of welcher Weg information to partial coherence. It is concluded that all mixtures are "improper," the trace-reduction of a composite system's pure state.

quant-ph↗
arXiv2003

"Quantal" behavior in classical probability

A number of phenomena generally believed characteristic of quantum mechanics and seen as interpretively problematic--the incompatibility and value-indeterminacy of variables, the non-existence of dispersion-free states, the failure of the standard marginal-probability formula, the failure of the distributive law of disjunction and interference--are exemplified in an emphatically non-quantal system: a deck of playing cards. Thus the appearance, in quantum mechanics, of incompatibility and these associated phenomena requires neither explanation nor interpretation.

quant-ph↗
arXiv2003

Hardy's Second Axiom is insufficiently general

Hardy (quant-ph/0101012) conjectures in his Axiom 2 that K=K(N), and that in classical probability K=N, while in quantum mechanics K=N^2. We offer an example in classical probability for which K=NV, V the number of independent complete variables; with N=V this classical example satisfies the purported quantal relation K=N^2.

quant-ph↗
arXiv2002

Ambiguities in the derivation of retrodictive probability

The derivation of the quantum retrodictive probability formula involves an error, an ambiguity. The end result is correct because this error appears twice, in such a way as to cancel itself. In addition, however, the usual expression for the probability itself contains the same ambiguity; this may lead to errors in its application. A generally applicable method is given to avoid such ambiguities altogether.

quant-ph↗
arXiv2001

Indistinguishability and improper mixtures

All quantum mixtures are what d'Espagnat has termed "improper." His "proper" mixture cannot be created -- if welcher weg, or distinguishing, information exists, an improper mixture results, while in the absence of such information, the resulting "mixture" is a pure state. D'Espagnat has claimed that an interpretation of the improper mixture in terms of subensembles leads to logical inconsistency; this claim is shown to be incorrect, as d'Espagnat's argument fails to account for the indistinguishability of the pure-state subensembles.

quant-ph↗