Continuous Measurements in Probability    Representation of Quantum Mechanics

Przhiyalkovskiy, Yan

doi:10.1134/s0081543821020188

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…The latter composes a rapidly developing area of quantum research, aimed not only at measuring purposes [29] but also at controlling quantum systems [30]. The continuous measurement formalism within the tomographic representation is investigated in detail in reference [21] and uses the restricted path integral approach, being especially intuitive and promising to study continuous decoherence processes [31,32]. Moreover, it is favourably distinguished by its suitability to study spectral measurements when one is interested in particular spectral components of the observable.…”

Section: Continuous Measurementmentioning

confidence: 99%

“…For a non-unitary quantum process, this kernel is broken into several partial kernels in the same fashion as it occurs in the conventional operatorsum representation. Note, that this is the process decomposition that was encountered in [21] for a system undergone a non-selective continuous measurement. The constraints imposed to operator symbols and partial operation kernels to be appropriate for describing a general quantum process are derived.…”

Section: Introductionmentioning

confidence: 99%

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Quantum process in probability representation of quantum mechanics

Przhiyalkovskiy¹

2022

J. Phys. A: Math. Theor.

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In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposition for the projection to a certain basis state and a Gaussian-type projection is demonstrated as well as qubit ﬂipping and amplitude damping processes.

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Section: Continuous Measurementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum process in probability representation of quantum mechanics

Przhiyalkovskiy¹

2022

J. Phys. A: Math. Theor.

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Probability Representation of Quantum States

Манько

Man’ko

2021

Entropy

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The review of new formulation of conventional quantum mechanics where the quantum states are identified with probability distributions is presented. The invertible map of density operators and wave functions onto the probability distributions describing the quantum states in quantum mechanics is constructed both for systems with continuous variables and systems with discrete variables by using the Born’s rule and recently suggested method of dequantizer–quantizer operators. Examples of discussed probability representations of qubits (spin-1/2, two-level atoms), harmonic oscillator and free particle are studied in detail. Schrödinger and von Neumann equations, as well as equations for the evolution of open systems, are written in the form of linear classical–like equations for the probability distributions determining the quantum system states. Relations to phase–space representation of quantum states (Wigner functions) with quantum tomography and classical mechanics are elucidated.

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Continuous Measurements in Probability Representation of Quantum Mechanics

Cited by 2 publications

References 31 publications

Quantum process in probability representation of quantum mechanics

Quantum process in probability representation of quantum mechanics

Probability Representation of Quantum States

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