Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2201.04143 · International Journal of Quantum Information

All quantum mixtures are proper

Leonardo Castellani

Published Mar 10, 2023• 2 citations
arXivHTMLPDF

Abstract

It is argued that proper and improper quantum mixed states have no observable differences, and hence should not be distinguished. This has implications for subjective approaches to quantum mechanics, and invalidates one of the main motivations for relational interpretations.
DOI
10.1142/s0219749923500193

Related papers

Proper and Improper Mixtures

Bernard d’Espagnat

Observable dynamical quantities are described by Hermitean operators, and in the early days of quantum mechanics the correspondence was believed to be one-to-one. It was assumed that (i) every observable can be related to some Hermitean operator and (ii) every Hermitean operator corresponds to one observable. The arguments concerning the difference between proper and improper mixtures are conceived of for the benefit of the physicists with a "realist" turn of mind who, prima facie, would tend to consider that, quite on the contrary, the statement in question is meaningful and true. Two ensembles are said to be different with respect to some observable A if the statistical frequencies of the prospective measurement outcomes on observable A are different on the two ensembles. Also, two ensembles are said to be different if there exists at least one observable A with respect to which they are different.

CRC Press eBooks•May 4, 2018•0 citations

The modal interpretation of quantum mechanics and the distinction between proper and improper mixtures

Chunghyoung Lee

•Jun 1, 2011•1 citation

Statistics of observations for «Proper» and « Improper » mixtures in quantum mechanics

Angelo Baracca, Silvio Bergia, R. Bigoni +1 more

Rivista Del Nuovo Cimento•Apr 1, 1974•10 citations

The Logical Difference in Quantum Mathematics Separating Pure States from Mixed States

Steve Faulkner

Abstract I give a short explanation of how mathematics representing pure states is logically distinct from mixed states. This is intended as understandable to the undergraduate.

•Mar 1, 2015•0 citations

Mixture equivalence principles and postquantum theories of gravity

Samuel Fedida, Adrian Kent

We examine the mixture equivalence principle (MEP), which states that proper and improper mixed states with the same density matrix are always experimentally indistinguishable, and a weaker version, which states that this is sometimes true in gravity theories. We point out that Møller-Rosenfeld semiclassical gravity violates the weak MEP and that nonlinear extensions of quantum mechanics violate the MEP. We further demonstrate that modifications of the Born rule in quantum theory also typically violate the MEP. We analyze such violations in the context of thermal baths, where proper and improper thermal states induce different physical situations. This has significant implications in the context of black hole physics. We argue that Møller-Rosenfeld semiclassical gravity is not the semiclassical limit of quantum gravity in the context of black hole spacetimes, even in the presence of N ≫ 1 matter fields.

arXiv:2412.12288•Physical review. D/Physical review. D.•Jun 3, 2025•4 citations

On Relationalist Reconstructions of Quantum Theory

Blake C. Stacey

Why I'm not happy with how Relational Quantum Mechanics has addressed the reconstruction of quantum theory, and why you shouldn't be either.

arXiv:2109.03186•Sep 7, 2021•1 citation
Observable dynamical quantities are described by Hermitean operators, and in the early days of quantum mechanics the correspondence was believed to be one-to-one. It was assumed that (i) every observable can be related to some Hermitean operator and (ii) every Hermitean operator corresponds to one observable. The arguments concerning the difference between proper and improper mixtures are conceived of for the benefit of the physicists with a "realist" turn of mind who, prima facie, would tend to consider that, quite on the contrary, the statement in question is meaningful and true. Two ensembles are said to be different with respect to some observable A if the statistical frequencies of the prospective measurement outcomes on observable A are different on the two ensembles. Also, two ensembles are said to be different if there exists at least one observable A with respect to which they are different.
We examine the mixture equivalence principle (MEP), which states that proper and improper mixed states with the same density matrix are always experimentally indistinguishable, and a weaker version, which states that this is sometimes true in gravity theories. We point out that Møller-Rosenfeld semiclassical gravity violates the weak MEP and that nonlinear extensions of quantum mechanics violate the MEP. We further demonstrate that modifications of the Born rule in quantum theory also typically violate the MEP. We analyze such violations in the context of thermal baths, where proper and improper thermal states induce different physical situations. This has significant implications in the context of black hole physics. We argue that Møller-Rosenfeld semiclassical gravity is not the semiclassical limit of quantum gravity in the context of black hole spacetimes, even in the presence of N ≫ 1 matter fields.