Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics A Mathematical and General

On classical properties of thermal squeezed states

A. Mann, M. Revzen, Hiroomi Umezawa, Y. Yamanaka

Published Oct 7, 1991• 3 citations
Publisher

Abstract

The authors use the formalism of thermo field dynamics and the classical Cramer's theorem to show that if two quantum systems are prepared independently and their centre of mass is found to be a thermal squeezed state, then both systems were prepared in thermal squeezed states. This constitutes an alternative derivation of the quantum version of Cramer's theorem. Further, they consider the case of two systems that are prepared independently and their centre of mass is in a pure state in the expanded space of thermo field dynamics. In this case it is shown that the system is also separable in the centre of mass and relative coordinates, and again all the states involved are thermal squeezed states.

DOI
10.1088/0305-4470/24/19/016

Related papers

New classical properties of quantum coherent states

Gérard G. Emch, Gerhard C. Hegerfeldt

A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones.

Journal of Mathematical Physics•Nov 1, 1986•20 citations

Gaussian Density Matrices: Quantum Analogs of Classical States

A. Mann, M. Revzen

We study quantum analogs of classical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space.

Fortschritte der Physik/Progress of Physics•Jan 1, 1993•10 citations

Phase Transitions of Thermal Squeezed states

Jianbin Wu, Wen-Zhou Li, Hiroomi Umezawa

By using thermo field dynamics, we studied the phase transitions of thermal squeezed states. Two critical points are obtained in certain cases. They correspond to the transitions from thermal squeezed state to pure squeezed state and to thermal state respectively.

Communications in Theoretical Physics•Jan 1, 1992•0 citations

Thermalized displaced squeezed thermal states

Wen-Fa Lu

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeezing and coherence components. Moreover, different from the properties of the position, the average value and variance of the particle number operator as well as the second-order correlation function are time independent.

arXiv:quant-ph/9905073•Journal of Physics A Mathematical and General•Jan 7, 2000•2 citations

Thermalized Displaced Squeezed Thermal States

Lu, W F

In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have diffenent correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.

•Jan 1, 2000•1 citation

QUANTUM FLUCTUATION OF TWO-MODE SQUEEZED THERMAL VACUUM STATES AND THE THERMAL WIGNER OPERATOR STUDIED BY VIRTUE OF <η| REPRESENTATION

Hong-Yi Fan, Hui Wang

Based on the <η| representation in Thermo Field Dynamics3 we introduce the thermal Wigner operator, with which we reach the conclusion that due to the thermal effect the quantum fluctuation of two-mode squeezed vacuum state increases by a factor cosh 2θ, where tanh θ = exp (-ℏω/2kT). We also mathematically analyse the formalism of Thermo Field Dynamics in the context of entanglement theory.

Modern Physics Letters B•Jun 10, 2001•3 citations
The authors use the formalism of thermo field dynamics and the classical Cramer's theorem to show that if two quantum systems are prepared independently and their centre of mass is found to be a thermal squeezed state, then both systems were prepared in thermal squeezed states. This constitutes an alternative derivation of the quantum version of Cramer's theorem. Further, they consider the case of two systems that are prepared independently and their centre of mass is in a pure state in the expanded space of thermo field dynamics. In this case it is shown that the system is also separable in the centre of mass and relative coordinates, and again all the states involved are thermal squeezed states.
We study quantum analogs of classical situations, i.e. quantum states possessing some specific classical attribute(s). These states seem quite generally, to have the form of gaussian density matrices. Such states can always be parametrized as thermal squeezed states (TSS). We consider the following specific cases: (a) Two beams that are built from initial beams which passed through a beam splitter cannot, classically, be distinguished from (appropriately prepared) two independent beams that did not go through a splitter. The only quantum states possessing this classical attribute are TSS. (b) The classical Cramer's theorem was shown to have a quantum version (Hegerfeldt). Again, the states here are Gaussian density matrices. (c) The special case in the study of the quantum version of Cramer's theorem, viz. when the state obtained after partial tracing is a pure state, leads to the conclusion that all states involved are zero temperature limit TSS. The classical analog here are gaussians of zero width, i.e. all distributions are δ functions in phase space.
In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have different correlations with the squeezing and coherence components. Moreover, different from the properties of the position, the average value and variance of the particle number operator as well as the second-order correlation function are time independent.
In the coordinate representation of thermofield dynamics, we investigate the thermalized displaced squeezed thermal state which involves two temperatures successively. We give the wavefunction and the matrix element of the density operator at any time, and accordingly calculate some quantities related to the position, momentum and particle number operator, special cases of which are consistent with the results in the literature. The two temperatures have diffenent correlations with the squeeze and coherence components. Moreover, different from the properties of the position and momentum, the average value and variance of the particle number operator as well as the second-order correlation function are time-independent.