Probabilistic theories with purification

Chiribella, Giulio; D’Ariano, Giacomo Mauro; Perinotti, Paolo

doi:10.1103/physreva.81.062348

Cited by 459 publications

(1,093 citation statements)

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“…We assume that K(N A N B ) = K(N A )K(N B ), which follows from Eqs. (12) and (15), and that K is a monotonically strictly increasing function of N , which follows from Eq. (16).…”

Section: Appendix 2: Functional Formsmentioning

confidence: 94%

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Limited Holism and Real-Vector-Space Quantum Theory

2011

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Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by "bilocal tomography": the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, we derive certain general features of such theories. In particular, we show how the number of state parameters can depend on the number of perfectly distinguishable states. We also show that realvector-space quantum theory, while not locally tomographic, is bilocally tomographic.

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“…We assume that K(N A N B ) = K(N A )K(N B ), which follows from Eqs. (12) and (15), and that K is a monotonically strictly increasing function of N , which follows from Eq. (16).…”

Section: Appendix 2: Functional Formsmentioning

confidence: 94%

“…We employ here some elements of the convex probabilities framework that has been developed by various authors [7,8,9,1,10,11,12,13,14,15,16]. The state of a system A, in general, can be represented by a list of probabilities associated with a fiducial set of measurement outcomes labeled k A ∈ Ω A ,…”

Section: Basic Conceptsmentioning

confidence: 99%

Limited Holism and Real-Vector-Space Quantum Theory

2011

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“…One can build up the network using formal rules as in Ref. [2], making connection in parallel, in sequence, declaring commutativity of parallel composition, etc. This construction is mathematically equivalent to the construction of a symmetric strict monoidal category, and poses a strong bridge with the research line of Coecke and Abramsky [5].…”

Section: ⇐⇒mentioning

confidence: 99%

“…More recently in Ref. [2] a more extensive axiomatic approach has been used, and in addition to NSF and PFAITH, postulate LDISCR (local discriminability) and PURIFY (purifiability of all states, uniquely up to reversible channes on the purifying system) have been considered. These postulates make the probabilistic framework much closer to Quantum Mechanics, with teleportation, error correction, dilation theorems, no cloning, and no bit commitment among its corollaries.…”

Section: Introductionmentioning

confidence: 99%

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Testing axioms for quantum theory on probabilistic toy-theories

D’Ariano

Tosini

2010

Quantum Inf Process

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Abstract. In Ref.[1] one of the authors proposed postulates for axiomatizing Quantum Mechanics as a fair operational framework, namely regarding the theory as a set of rules that allow the experimenter to predict future events on the basis of suitable tests, having local control and low experimental complexity. In addition to causality, the following postulates have been considered: PFAITH (existence of a pure preparationally faithful state), and FAITHE (existence of a faithful effect). These postulates have exhibited an unexpected theoretical power, excluding all known nonquantum probabilistic theories. Later in Ref.[2] in addition to causality and PFAITH, local discriminability and PURIFY (purifiability of all states) have been postulated, narrowing the probabilistic theory to something very close to Quantum Mechanics. In the present paper we test the above postulates on some nonquantum probabilistic models. The first model, the two-box world is an extension of the Popescu-Rohrlich model [3], which achieves the greatest violation of the CHSH inequality compatible with the no-signaling principle. The second model the two-clock world is actually a full class of models, all having a disk as convex set of states for the local system. One of them corresponds to the the two-rebit world, namely qubits with real Hilbert space. The third model-the spin-factor-is a sort of n-dimensional generalization of the clock. Finally the last model is the classical probabilistic theory. We see how each model violates some of the proposed postulates, when and how teleportation can be achieved, and we analyze other interesting connections between these postulate violations, along with deep relations between the local and the non-local structures of the probabilistic theory.

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Information and the Reconstruction of Quantum Physics

Jaeger

2018

Annalen der Physik

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The reconstruction of quantum physics has been connected with the interpretation of the quantum formalism, and has continued to be so with the recent deeper consideration of the relation of information to quantum states and processes. This recent form of reconstruction has mainly involved conceiving quantum theory on the basis of informational principles, providing new perspectives on physical correlations and entanglement that can be used to encode information. By contrast to the traditional, interpretational approach to the foundations of quantum mechanics, which attempts directly to establish the meaning of the elements of the theory and often touches on metaphysical issues, the newer, more purely reconstructive approach sometimes defers this task, focusing instead on the mathematical derivation of the theoretical apparatus from simple principles or axioms. In its most pure form, this sort of theory reconstruction is fundamentally the mathematical derivation of the elements of theory from explicitly presented, often operational principles involving a minimum of extra-mathematical content. Here, a representative series of specifically information-based treatments-from partial reconstructions that make connections with information to rigorous axiomatizations, including those involving the theories of generalized probability and abstract systems-is reviewed.The most basic physical principle of quantum mechanics is that of state superposition: Any sum of physical state vectors is also a physical state, with these states lying in a Hilbert space or related mathematical structure; cf., for example, ref.[1]. The standard view recently has been that superposition lends striking features to quantum informationthat is, information encoded entirely via quantum systems-that are not found in its classical counterpart, that is, information encoded in classical mechanical states. The most striking of the features of the quantum state itself are those associated with entanglement, which arises with the interaction or joint appearance of systems via another basic quantum physical rule, that which assigns the tensor-product space of the linear spaces of the subsystems composing a larger system; as its consequence, quantum signal-state correlations are possible that are stronger than those between classical states-these correlations being often called "nonlocal" because they violate Bell-type inequalities and enable communication and information processing tasks to be accomplished that either cannot be done as efficiently or cannot be done at all using only classical mechanical signals; cf., for example, ref. [2].That nonclassical phenomena involving correlation can arise when quantum systems are entangled was evident early in the history of quantum mechanics to Albert Einstein [3] and to Erwin Schrödinger, [4,5] who named entanglement, even before the explorations of David Bohm, [6] John S. Bell, [7] Abner Shimony, [1] and others, for whom the understanding of nonlocal correlations was a great pursuit and who devised the first ...

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Probabilistic theories with purification

Cited by 459 publications

References 59 publications

Limited Holism and Real-Vector-Space Quantum Theory

Limited Holism and Real-Vector-Space Quantum Theory

Testing axioms for quantum theory on probabilistic toy-theories

Information and the Reconstruction of Quantum Physics

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