Attempt of an axiomatic foundation of quantum mechanics and more general theories. III

Ludwig, Günther

doi:10.1007/bf01654027

Cited by 76 publications

(104 citation statements)

References 5 publications

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“…This leads to the notions of states and effects (see [15,26] From now on we will identify preparation-events with states and observation-events with effects, without keeping the distinction between an event ρ i (a j ) and the corresponding functionρ i (â j ). Accordingly, a preparation(observation)-test will be a collection of states (effects), and the sets S(A), E(A) will be the set of states and and the set of effects of system A, respectively.…”

Section: E Relation With Category Theorymentioning

confidence: 99%

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Probabilistic theories with purification

2010

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We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamio lkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

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Section: E Relation With Category Theorymentioning

confidence: 99%

“…In the past there have been many attempts to find a more basic description of quantum theory, in particular by discussing it from the point of view of logic [12][13][14][15] (see also Ref. [16] and references therein).…”

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confidence: 99%

Probabilistic theories with purification

2010

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“…The framework was initially introduced in the 1960s by researchers in quantum foundations who used it to investigate axiomatic derivations of the Hilbert space formalism of quantum mechanics from operational postulates [14][15][16][17]. Due to the emphasis on the convex structure of the set of states and the use of operations to model state transformations, the approach is called the convex state approach.…”

Section: Convex Operational Theoriesmentioning

confidence: 99%

“…At this point it should be noted that the degree of incompatibility of a theory puts a limit on the maximum strength of CHSH inequality violations of the theory via the relation expressed in Equation (16). However, this result does not tell whether a theory saturates this bound or not.…”

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Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

et al. 2016

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Abstract:It has been recently shown that measurement incompatibility and fine grained uncertainty-a particular form of preparation uncertainty relation-are deeply related to the nonlocal feature of quantum mechanics. In particular, the degree of measurement incompatibility in a no-signaling theory determines the bound on the violation of Bell-CHSH inequality, and a similar role is also played by (fine-grained) uncertainty along with steering, a subtle non-local phenomenon. We review these connections, along with comments on the difference in the roles played by measurement incompatibility and uncertainty. We also discuss why the toy model of Spekkens (Phys. Rev. A 75, 032110 (2007)) shows no nonlocal feature even though steering is present in this theory.

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Advantage of Quantum Theory over Nonclassical Models of Communication

et al. 2020

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Quantum correlations provide dramatic advantage over the corresponding classical resources in several communication tasks. However, a broad class of probabilistic theories exists that attributes greater success than quantum theory in many of these tasks by allowing supra-quantum correlations in "space-like" and/or "time-like" paradigms. In this letter, a communication task involving three spatially separated parties is proposed where one party (verifier) aims to verify whether the bit strings possessed by the other two parties (terminals) are equal or not. This task is called authentication with limited communication, the restrictions on communication being: i) the terminals cannot communicate with each other, but (ii) each of them can communicate with the verifier through single use of channels with limited capacity. Manifestly, classical resources are not sufficient for perfect success of this task. Moreover, it is also not possible to perform this task with certainty in several nonclassical theories although they might possess stronger "space-like" and/or "time-like" correlations. Surprisingly, quantum resources can achieve the perfect winning strategy. The proposed task thus stands apart from all previously known communication tasks as it exhibits quantum advantage over other nonclassical strategies.

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Attempt of an axiomatic foundation of quantum mechanics and more general theories. III

Cited by 76 publications

References 5 publications

Probabilistic theories with purification

Probabilistic theories with purification

Role of Measurement Incompatibility and Uncertainty in Determining Nonlocality

Advantage of Quantum Theory over Nonclassical Models of Communication

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