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

Physica A Statistical Mechanics and its Applications

Robertson's formalism with explicitly time-dependent observables

David Holzer, Eugen Fick

Published Oct 1, 1990• 2 citations
Publisher
DOI
10.1016/0378-4371(90)90035-q

Related papers

Time-Dependent Formalism

Ingvar Lindgren

Springer series on atomic, optical, and plasma physics•Jan 1, 2016•0 citations

Robertson intelligent states

D. A. Trifonov

The diagonalization of the uncertainty matrix and the minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In the case of canonical observables, this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group-related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are a particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1,1), su(2), and sp(N,R) algebras. Unlike the group-related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators (q>0) and of any k power of are positive definite and can be diagonalized by symplectic linear transformations.

arXiv:quant-ph/9701018•Journal of Physics A Mathematical and General•Sep 7, 1997•56 citations

Photon and photon-added intelligent states of coupled parametric oscillators

Angel E Neira, Roberto Mulet

We study a quantum system of coupled oscillators subject to a periodic time dependence of its parameters. Using the Floquet-Lyapunov theory we derive linear non-Hermitian integrals of motion of the system and relate their covariance matrix to that of the canonical observables. The operator integrals allow us to construct states that saturate the Robertson uncertainty relation (intelligent states) for canonical operators and the corresponding photon-added states. We found explicit expressions for the wave function, Wigner function and covariance matrices of the latter.

Europhysics Letters (EPL)•Aug 20, 2021•0 citations

Time-Dependent Formalism

Ingvar Lindgren

Springer series on atomic, optical, and plasma physics•Jan 1, 2011•0 citations

The Maccone-Pati uncertainty relation

Jonas Maziero

The existence of incompatible observables constitutes one of the most prominent characteristics of quantum mechanics (QM) and can be revealed and formalized through uncertainty relations. The Heisenberg-Robertson-Schrödinger uncertainty relation (HRSUR) was proved at the dawn of quantum formalism and is ever-present in the teaching and research on QM. Notwithstanding, the HRSUR possess the so called triviality problem. That is to say, the HRSUR yields no information about the possible incompatibility between two observables if the system was prepared in a state which is an eigenvector of one of them. After about 85 years of existence of the HRSUR, this problem was solved recently by Lorenzo Maccone and Arun K. Pati. In this article, we start doing a brief discussion of general aspects of the uncertainty principle in QM and recapitulating the proof of HRSUR. Afterwards we present in simple terms the proof of the Maccone-Pati uncertainty relation, which can be obtained basically via the application of the parallelogram law and Cauchy-Schwarz inequality.

arXiv:1705.09139•May 25, 2017•1 citation

Time-Dependent Hamiltonians

Ladislav Šamaj

Springer eBooks•Mar 31, 2006•1 citation
The diagonalization of the uncertainty matrix and the minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In the case of canonical observables, this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group-related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are a particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1,1), su(2), and sp(N,R) algebras. Unlike the group-related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators (q>0) and of any k power of are positive definite and can be diagonalized by symplectic linear transformations.
We study a quantum system of coupled oscillators subject to a periodic time dependence of its parameters. Using the Floquet-Lyapunov theory we derive linear non-Hermitian integrals of motion of the system and relate their covariance matrix to that of the canonical observables. The operator integrals allow us to construct states that saturate the Robertson uncertainty relation (intelligent states) for canonical operators and the corresponding photon-added states. We found explicit expressions for the wave function, Wigner function and covariance matrices of the latter.
The existence of incompatible observables constitutes one of the most prominent characteristics of quantum mechanics (QM) and can be revealed and formalized through uncertainty relations. The Heisenberg-Robertson-Schrödinger uncertainty relation (HRSUR) was proved at the dawn of quantum formalism and is ever-present in the teaching and research on QM. Notwithstanding, the HRSUR possess the so called triviality problem. That is to say, the HRSUR yields no information about the possible incompatibility between two observables if the system was prepared in a state which is an eigenvector of one of them. After about 85 years of existence of the HRSUR, this problem was solved recently by Lorenzo Maccone and Arun K. Pati. In this article, we start doing a brief discussion of general aspects of the uncertainty principle in QM and recapitulating the proof of HRSUR. Afterwards we present in simple terms the proof of the Maccone-Pati uncertainty relation, which can be obtained basically via the application of the parallelogram law and Cauchy-Schwarz inequality.