Asymptotic properties for Markovian dynamics in quantum theory and general probabilistic theories

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories which also admit Gleason-type theorems. It contains theories satisfying the no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.

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A formalism-local framework for general probabilistic theories, including quantum theory

Mathematical Structures in Computer Science ◽

10.1017/s0960129512000163 ◽

2013 ◽

Vol 23 (02) ◽

pp. 399-440 ◽

Cited By ~ 7

Author(s):

LUCIEN HARDY

Keyword(s):

Quantum Theory ◽

General Probabilistic Theories ◽

Probabilistic Theories

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No-free-information principle in general probabilistic theories

Quantum ◽

10.22331/q-2019-07-08-157 ◽

2019 ◽

Vol 3 ◽

pp. 157 ◽

Cited By ~ 2

Author(s):

Teiko Heinosaari ◽

Leevi Leppäjärvi ◽

Martin Plávala

Keyword(s):

Quantum Theory ◽

State Spaces ◽

Coin Tossing ◽

Free Information ◽

General Probabilistic Theories ◽

Probabilistic Theories

In quantum theory, the no-information-without-disturbance and no-free-information theorems express that those observables that do not disturb the measurement of another observable and those that can be measured jointly with any other observable must be trivial, i.e., coin tossing observables. We show that in the framework of general probabilistic theories these statements do not hold in general and continue to completely specify these two classes of observables. In this way, we obtain characterizations of the probabilistic theories where these statements hold. As a particular class of state spaces we consider the polygon state spaces, in which we demonstrate our results and show that while the no-information-without-disturbance principle always holds, the validity of the no-free-information principle depends on the parity of the number of vertices of the polygons.

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Perfect Discrimination in Approximate Quantum Theory of General Probabilistic Theories

Physical Review Letters ◽

10.1103/physrevlett.125.150402 ◽

2020 ◽

Vol 125 (15) ◽

Author(s):

Yuuya Yoshida ◽

Hayato Arai ◽

Masahito Hayashi

Keyword(s):

Quantum Theory ◽

Perfect Discrimination ◽

General Probabilistic Theories ◽

Probabilistic Theories

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Almost Quantum Correlations are Inconsistent with Specker's Principle

Quantum ◽

10.22331/q-2018-08-27-87 ◽

2018 ◽

Vol 2 ◽

pp. 87 ◽

Cited By ~ 2

Author(s):

Tomáš Gonda ◽

Ravi Kunjwal ◽

David Schmid ◽

Elie Wolfe ◽

Ana Belén Sainz

Keyword(s):

Quantum Theory ◽

Quantum Correlations ◽

Popular Belief ◽

Joint Measurability ◽

Rule Out ◽

General Probabilistic Theories ◽

Probabilistic Theories

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic theories. In particular, its well-known consequence for experimental statistics, the principle of consistent exclusivity, does not rule out the set of correlations known as almost quantum, which is strictly larger than the set of quantum correlations. Here we show that, contrary to the popular belief, Specker's principle cannot be satisfied in any theory that yields almost quantum correlations.

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