General probabilistic theories: An introduction

Plávala, Martin

doi:10.1016/j.physrep.2023.09.001

Cited by 18 publications

(2 citation statements)

References 138 publications

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“…Let us now comment on possible future developments of our results. In the current manuscript we have provided only a quantum-mechanical analysis of our task; however, we believe that the latter, as presented abstractly at the beginning of section 3, can be transposed into the framework of generalized probabilistic theories [45,46], which would enable the assessment of how much of our results hinge on the specificities of quantum theory. We may thereby gain a better understanding of the general relationship between indistinguishability and entanglement, by analyzing questions such as the following.…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, if the initial state of D is not equal to any (M) D (but is e.g. a probabilistic mixture, a quantum superposition state or some generalized probabilistic state [45,46]), we assume that it is still the case that, were one to find the final state of D to be (M) D , one would find the final state of T and A to be (α(M, α)) A (M⃗ x, k) T . Stated more precisely, for any initial state of D, post-selecting the final state on a definite state (M) D of D results in the postselected joint state being equal to the RHS of equation ( 2).…”

Section: Formalization Of the Taskmentioning

confidence: 99%

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Accessing inaccessible information via quantum indistinguishability

Horvat,

Dakić

2023

New J. Phys.

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In this paper we present and analyze an information-theoretic task that consists in learning a bit of information by spatially moving the ``target'' particle that encodes it. We show that, on one hand, the task can be solved with the use of additional independently prepared quantum particles, only if these are indistinguishable from the target particle. On the other hand, the task can be solved with the use of distinguishable quantum particles, only if they are entangled with the target particle. Our task thus provides a new example in which the entanglement apparently inherent to independently prepared indistinguishable quantum particles is put into use for information processing. Importantly, a novelty of our protocol lies in that it does not require any spatial overlap between the involved particles. Besides analyzing the class of quantum-mechanical protocols that solve our task, we gesture towards possible ways of generalizing our results and of applying them in cryptography.

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Section: Discussionmentioning

confidence: 99%

Section: Formalization Of the Taskmentioning

confidence: 99%

Accessing inaccessible information via quantum indistinguishability

Horvat,

Dakić

2023

New J. Phys.

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Constraints on a generalization of geometric quantum mechanics from neutrino and B0-$$ \overline{B^0} $$ oscillations

Bhatta,

Minic,

Takeuchi

2024

J. High Energ. Phys.

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Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which the manifold over which the “phase” of an energy eigenstate time evolves is modified. This generalization affects oscillation and interference phenomena through the introduction of two deformation parameters that quantify the extent of deviation from canonical Quantum Mechanics. In this paper, we constrain these parameters utilizing atmospheric neutrino oscillation data, and B0-$$ \overline{B^0} $$ B 0 ¯ oscillation data from Belle. Surprisingly, the bound from atmospheric neutrinos is stronger than the bound from Belle. Various features of Nambu Quantum Mechanics are also discussed.

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Quantum Theory in Finite Dimension Cannot Explain Every General Process with Finite Memory

Fanizza,

Lumbreras,

Winter

2024

Commun. Math. Phys.

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Arguably, the largest class of stochastic processes generated by means of a finite memory consists of those that are sequences of observations produced by sequential measurements in a suitable generalized probabilistic theory (GPT). These are constructed from a finite-dimensional memory evolving under a set of possible linear maps, and with probabilities of outcomes determined by linear functions of the memory state. Examples of such models are given by classical hidden Markov processes, where the memory state is a probability distribution, and at each step it evolves according to a non-negative matrix, and hidden quantum Markov processes, where the memory is a finite-dimensional quantum system, and at each step it evolves according to a completely positive map. Here we show that the set of processes admitting a finite-dimensional explanation do not need to be explainable in terms of either classical probability or quantum mechanics. To wit, we exhibit families of processes that have a finite-dimensional explanation, defined manifestly by the dynamics of an explicitly given GPT, but that do not admit a quantum, and therefore not even classical, explanation in finite dimension. Furthermore, we present a family of quantum processes on qubits and qutrits that do not admit a classical finite-dimensional realization, which includes examples introduced earlier by Fox, Rubin, Dharmadikari and Nadkarni as functions of infinite-dimensional Markov chains, and lower bound the size of the memory of a classical model realizing a noisy version of the qubit processes.

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General probabilistic theories: An introduction

Cited by 18 publications

References 138 publications

Accessing inaccessible information via quantum indistinguishability

Accessing inaccessible information via quantum indistinguishability

Constraints on a generalization of geometric quantum mechanics from neutrino and B0-$$ \overline{B^0} $$ oscillations

Quantum Theory in Finite Dimension Cannot Explain Every General Process with Finite Memory

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