Probability representation of quantum dynamics using pseudostochastic maps

Kiktenko, Evgeniy O.; Malyshev, Aleksei; Mastiukova, Alena S.; Man’ko, Vladimir I.; Fedorov, Aleksey K.; Chruściński, Dariusz

doi:10.1103/physreva.101.052320

Cited by 25 publications

(23 citation statements)

References 61 publications

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“…In line with Ref. [28,33,34] in our work we prefer to use a term pseudostochastic to emphasize that we deal with classical probability distributions rather than quasiprobabilities.…”

Section: A Definitions and Notationsmentioning

confidence: 94%

“…The use of MIC-POVM probability vectors allows one to employ a simpler description of tensor products. This is an important advantage in comparison to the SIC-POVM case [28]. Let H A and H B be Hilbert spaces with MIC-POVMs…”

Section: Representation Of Tensor Productsmentioning

confidence: 99%

“…Here we construct pseudostochastic maps that act on probability distributions, which are obtained by MIC-POVM measurements. We demonstrate that this approach is a generalization of the SIC-POVMbased representation [28], and it has a number of important features. First, such an approach allows for preserving the tensor product structure, which is important for the description of multi-qubit systems.…”

Section: Introductionmentioning

confidence: 96%

“…The SIC-POVM description of quantum systems can be used for the representation of dynamics of finitedimensional quantum systems. The difference with the quasiprobability representation is that quantum systems are described via true probability distributions, which are obtained by SIC-POVMs [28]. These probability distributions evolve under the action of pseudostochastic maps -stochastic maps, which are described by matrices that may have negative elements.…”

Section: Introductionmentioning

confidence: 99%

“…ator, can be derived [28]. Moreover, practical measures of non-Markovianity of quantum processes can be obtained and applied for studying existing quantum computing devices.…”

Section: Introductionmentioning

confidence: 99%

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Minimal informationally complete measurements for probability representation of quantum dynamics

Yashin,

Kiktenko,

Mastiukova

et al. 2020

Preprint

Self Cite

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“…In line with Ref. [28,33,34] in our work we prefer to use a term pseudostochastic to emphasize that we deal with classical probability distributions rather than quasiprobabilities.…”

Section: A Definitions and Notationsmentioning

confidence: 94%

Section: Representation Of Tensor Productsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

“…ator, can be derived [28]. Moreover, practical measures of non-Markovianity of quantum processes can be obtained and applied for studying existing quantum computing devices.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Minimal informationally complete measurements for probability representation of quantum dynamics

Yashin,

Kiktenko,

Mastiukova

et al. 2020

Preprint

Self Cite

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Classical Invasive Description of Informationally‐Complete Quantum Processes

Richter,

Smirne,

Strunz

et al. 2023

Annalen der Physik

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In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic outcomes, these conditions reflect that the measurements do not alter the state of the underlying physical system. Prominently, this assumption has to be abandoned in the context of quantum mechanics, yet there are also classical processes in which measurements influence the measured system. Here, conditions that characterize uniquely classical processes that are probed by a reasonable class of such invasive measurements are derived. We then analyze under what circumstances such classical processes can simulate the statistics arising from quantum processes associated with informationally‐complete measurements. It is expected that this investigation will help build a bridge between two fundamental traits of non‐classicality, namely, coherence and contextuality.

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Probability Representation of Photon States and Tomography†

2019

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We give a review of the tomographic probability representation of quantum mechanics.We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random variables. We study the coherent and number states of photons in the probability representation and obtain the evolution equation and energy spectra in the form of equations for probability distributions.

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Probability representation of quantum dynamics using pseudostochastic maps

Cited by 25 publications

References 61 publications

Minimal informationally complete measurements for probability representation of quantum dynamics

Minimal informationally complete measurements for probability representation of quantum dynamics

Classical Invasive Description of Informationally‐Complete Quantum Processes

Probability Representation of Photon States and Tomography†

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