Dynamics of a Set of Quantum States Generated by a Nonlinear Liouville–von Neumann Equation

2020 ◽  
Vol 60 (8) ◽  
pp. 1337-1347
Author(s):  
A. D. Grekhneva ◽  
V. Zh. Sakbaev
Keyword(s):  
Quantum States ◽  
Von Neumann ◽  
Von Neumann Equation

scholarly journals Lagrangian description of Heisenberg and Landau–von Neumann equations of motion

2020 ◽  
Vol 35 (19) ◽  
pp. 2050161
Author(s):  
F. M. Ciaglia ◽  
F. Di Cosmo ◽  
A. Ibort ◽  
G. Marmo ◽  
L. Schiavone ◽  
...  
Keyword(s):  
Quantum System ◽  
Quantum State ◽  
Equations Of Motion ◽  
Quantum States ◽  
Heisenberg Equation ◽  
Lagrangian Description ◽  
Von Neumann ◽  
Fixed Reference ◽  
Von Neumann Equation ◽  
Algebra Of Operators

An explicit Lagrangian description is given for the Heisenberg equation on the algebra of operators of a quantum system, and for the Landau–von Neumann equation on the manifold of quantum states which are isospectral with respect to a fixed reference quantum state.

scholarly journals Zero uncertainty states in the presence of quantum memory

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Huangjun Zhu
Keyword(s):  
Uncertainty Principle ◽  
Quantum States ◽  
Quantum Memory ◽  
System State ◽  
Von Neumann ◽  
Practical Applications ◽  
Classical Information ◽  
Fundamental Limit ◽  
Minimum Uncertainty ◽  
Incompatible Observables

AbstractThe uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The situation is different if one can build a quantum memory entangled with the system. Zero uncertainty states (in contrast with minimum uncertainty states) are peculiar quantum states that can eliminate uncertainties of incompatible von Neumann observables once assisted by suitable measurements on the memory. Here we determine all zero uncertainty states of any given set of nondegenerate observables and determine the minimum entanglement required. It turns out all zero uncertainty states are maximally entangled in a generic case, and vice versa, even if these observables are only weakly incompatible. Our work establishes a simple and precise connection between zero uncertainty and maximum entanglement, which is of interest to foundational studies and practical applications, including quantum certification and verification.

scholarly journals ENTANGLEMENT DYNAMICS IN FINITE QUDIT CHAIN IN CONSISTENT MAGNETIC FIELD

2012 ◽  
Vol 10 (06) ◽  
pp. 1250068 ◽  
Author(s):  
E. A. IVANCHENKO
Keyword(s):  
Magnetic Field ◽  
Entanglement Dynamics ◽  
Von Neumann ◽  
Magnetic Field Modulation ◽  
Entanglement Measures ◽  
Analytical Formulae ◽  
Initial States ◽  
Von Neumann Equation ◽  
Field Modulation ◽  
The Magnetic Field

Based on the Liouville–von Neumann equation, we obtain a closed system of equations for the description of a qutrit or coupled qutrits in an arbitrary, time-dependent, external magnetic field. The dependence of the dynamics on the initial states and the magnetic field modulation is studied analytically and numerically. We compare the relative entanglement measure's dynamics in bi-qudits with permutation particle symmetry. We find the magnetic field modulation which retains the entanglement in the system of two coupled qutrits. Analytical formulae for the entanglement measures in finite chains from two to six qutrits or three quartits are presented.

scholarly journals Concepts of Phenomenological Irreversible Quantum Thermodynamics I: Closed Undecomposed Schottky Systems in Semi-Classical Description

2019 ◽  
Vol 44 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Wolfgang Muschik
Keyword(s):  
Time Dependent ◽  
Quantum Thermodynamics ◽  
Time Rate ◽  
Von Neumann ◽  
Classical Description ◽  
Von Neumann Equation

Abstract If the von Neumann equation is modified by time dependent statistical weights, the time rate of entropy, the entropy exchange and the production of a Schottky system are derived whose Hamiltonian does not contain the interaction with the system’s environment. This interaction is semi-classically described by the quantum theoretical expressions of power and entropy exchange.

scholarly journals PARAMETRIC DOWN CONVERSION OF A BOSONIC THERMOFIELD VACUUM

2012 ◽  
Vol 27 (22) ◽  
pp. 1250124 ◽  
Author(s):  
THIAGO PRUDÊNCIO
Keyword(s):  
Input State ◽  
Von Neumann ◽  
Vacuum States ◽  
Parametric Down Conversion ◽  
Von Neumann Equation ◽  
Down Conversion

We consider a process of parametric down conversion where the input state is a bosonic thermofield vacuum. This state leads to a parametric down conversion, generating an output of two excited photons. Following a thermofield dynamics scheme, the input state, initially in a bosonic thermofield vacuum, and the output states, initially in vacuum states, evolve under a Liouville–von Neumann equation.

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