The Schrödinger-HJW Theorem

@article{Kirkpatrick2003TheST,
  title={The Schr{\"o}dinger-HJW Theorem},
  author={K. Kirkpatrick},
  journal={Foundations of Physics Letters},
  year={2003},
  volume={19},
  pages={95-102}
}
A concise presentation of Schrödinger's ancilla theorem (Proc. Camb. Phil. Soc.32, 446 (1936)) and its several recent rediscoveries. 
THE HATSOPOULOS–GYFTOPOULOS RESOLUTION OF THE SCHRÖDINGER–PARK PARADOX ABOUT THE CONCEPT OF "STATE" IN QUANTUM STATISTICAL MECHANICS
A seldom recognized fundamental difficulty undermines the concept of individual "state" in the present formulations of quantum statistical mechanics (and in its quantum information theoryExpand
A statistical-mechanical description of quantum entanglement
We present a description of finite-dimensional quantum entanglement based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of realExpand
Classicality without Decoherence: A Reply to Schlosshauer
Schlosshauer has criticized the conclusion of Wiebe and Ballentine (Phys. Rev. A 72:022109, 2005) that decoherence is not essential for the emergence of classicality from quantum mechanics. I replyExpand
Universality of sudden death of entanglement
We present a constructive argument to demonstrate the universality of the sudden death of entanglement in the case of two non-interacting qubits, each of which generically coupled to independentExpand
Entanglement, einstein-podolsky-rosen correlations, bell nonlocality, and steering
In a recent work [Phys. Rev. Lett. 98, 140402 (2007)] we defined "steering," a type of quantum nonlocality that is logically distinct from both nonseparability and Bell nonlocality. In the bipartiteExpand
Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox.
TLDR
An operational definition is provided, from which it is proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. Expand
Reduced dynamical maps in the presence of initial correlations
TLDR
This approach allows to consider states that can have finite discord, though it does not include entangled states, and it explicitly shows the non-uniqueness of the completely positive extensions of the obtained dynamical map outside the compatibility domain. Expand
On random unitary channels
In this paper, we provide necessary and sufficient conditions for a completely positive trace-preserving (CPT) map to be decomposable into a convex combination of unitary maps. Additionally, we setExpand
Multipartite quantum entanglement evolution in photosynthetic complexes.
TLDR
The hypothesis that entanglement is maximum primary along the two distinct electronic energy transfer pathways is supported and monogamy is used to give a lower bound and an upper bound from the evaluation of the convex roof. Expand
Open quantum systems are harder to track than open classical systems
TLDR
This paper confirms the long-standing conjecture of Karasik and Wiseman that, for generic systems with D>2, Kmin>D, by a computational proof (via Hilbert Nullstellensatz certificates of infeasibility), beyond D=2, D-dimensional open quantum systems are provably harder to track than D- dimensional open classical systems. Expand
...
1
2
3
...

References

SHOWING 1-10 OF 10 REFERENCES
Properties of mixtures on non-orthogonal states
We study the density operators expressed as mixtures of non-orthogonal pure states in quantum mechanics. The general mathematical law of formation of such mixtures is found. Applications are givenExpand
What Do These Correlations Know about Reality? Nonlocality and the Absurd
In honor of Daniel Greenberger's 65th birthday, I record for posterity two superb examples of his wit, offer a proof of an important theorem on quantum correlations that even those of us over 60 canExpand
Philosophy of quantum mechanics
In the recent literature the use of the term “Philosophy of Quantum Mechanics” is very similar to that of the corresponding term “Philosophy of Mathematics”. Its denotation includes a vast class ofExpand
Uniqueness of a convex sum of products of projectors
Relative to a given factoring of the Hilbert space, the decomposition of an operator into a convex sum of correlated products of pairs of distinct 1-projectors, one set of projectors linearlyExpand
A Complete Classification of Quantum Ensembles Having a Given Density Matrix
Abstract A complete constructive classification is given for all discrete ensembles of pure quantum states having a given density matrix. As a special case this provides a classification of positiveExpand
Information Theory and Statistical Mechanics
Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation betweenExpand
Stochastic quantum dynamics and relativity
Probability relations between separated systems
The paper first scrutinizes thoroughly the variety of compositions which lead to the same quantum-mechanical mixture (as opposed to state or pure state ). With respect to a given mixture every stateExpand
A complete classification
  • 1993
Information theory and statistical mechanics. II
  • Phys. Rev
  • 1957