Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

López-Saldívar, Julio A.; Man’ko, Margarita A.; Man’ko, Vladimir I.

doi:10.3390/e23111445

Cited by 8 publications

(4 citation statements)

References 30 publications

(30 reference statements)

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“…Actually, multi-time correlation functions are usually measured by some interference setups, which are indeed not just sequences of separated measurements. Such setups are usual for spectroscopy [44,45] or for measurements based on homodyne detection [46] such as quantum tomography [47,48], which is still actively being developed [49,50].…”

Section: Definitionmentioning

confidence: 99%

Memory Tensor for Non-Markovian Dynamics with Random Hamiltonian

Teretenkov

2023

Mathematics

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In the theory of open quantum systems, the Markovian approximation is very widespread. Usually, it assumes the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation for density matrix dynamics and quantum regression formulae for multi-time correlation functions. Nevertheless, now, quantum non-Markovianity is being actively studied, especially the non-Markovianity of multi-time correlations. In this work, we consider dynamics with a random Hamiltonian, which can lead to GKSL dynamics of the density matrix for some special cases, but correlation functions generally do not satisfy the quantum regression formulae. Despite the fact that random Hamiltonians have been actively studied, dynamics with such Hamiltonians has been little discussed from the viewpoint of multi-time correlations. For specific models with a random Hamiltonian, we provide the formulae for multi-time correlations which occur instead of the usual regression formulae. Moreover, we introduce and calculate the memory tensor, which characterizes multi-time correlations against the Markovian ones. We think that, despite being applied to specific models, the methods developed in this work can be used in a much broader setup.

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Section: Definitionmentioning

confidence: 99%

Memory Tensor for Non-Markovian Dynamics with Random Hamiltonian

Teretenkov

2023

Mathematics

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“…The construction of probability representations was developed using the concept of quantizer and dequantizer [17,18]. Some properties of the probability distributions used in quantum mechanics were discussed in [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Probability Distributions Describing Qubit-State Superpositions

Man’ko,

Man’ko

2023

Entropy

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We discuss qubit-state superpositions in the probability representation of quantum mechanics. We study probability distributions describing separable qubit states. We consider entangled states on the example of a system of two qubits (Bell states) using the corresponding superpositions of the wave functions associated with these states. We establish the connection with the properties and structure of entangled probability distributions.

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“…The probabilistic representation of quantum mechanics has been discussed in different works, namely the symplectic tomographic distribution for cyclic states was obtained in [26], the use of the tomographic representation of states was studied in [27], and some aspects of the time evolution of a quantum system in a parametric amplifier in the tomographic representation was performed in [28]. In [29], the classical Universe emerging from the tomographic representation of quantum systems was presented.…”

Section: Introductionmentioning

confidence: 99%

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States

López-Saldívar,

Man’ko,

Man’ko

et al. 2023

Entropy

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The Jordan–Schwinger map allows us to go from a matrix representation of any arbitrary Lie algebra to an oscillator (bosonic) representation. We show that any Lie algebra can be considered for this map by expressing the algebra generators in terms of the oscillator creation and annihilation operators acting in the Hilbert space of quantum oscillator states. Then, to describe quantum states in the probability representation of quantum oscillator states, we express their density operators in terms of conditional probability distributions (symplectic tomograms) or Husimi-like probability distributions. We illustrate this general scheme by examples of qubit states (spin-1/2 su(2)-group states) and even and odd Schrödinger cat states related to the other representation of su(2)-algebra (spin-j representation). The two-mode coherent-state superpositions associated with cyclic groups are studied, using the Jordan–Schwinger map. This map allows us to visualize and compare different properties of the mentioned states. For this, the su(2) coherent states for different angular momenta j are used to define a Husimi-like Q representation. Some properties of these states are explicitly presented for the cyclic groups C2 and C3. Also, their use in quantum information and computing is mentioned.

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Measurement of the Temperature Using the Tomographic Representation of Thermal States for Quadratic Hamiltonians

Cited by 8 publications

References 30 publications

Memory Tensor for Non-Markovian Dynamics with Random Hamiltonian

Memory Tensor for Non-Markovian Dynamics with Random Hamiltonian

Probability Distributions Describing Qubit-State Superpositions

Bosonic Representation of Matrices and Angular Momentum Probabilistic Representation of Cyclic States

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