The Dynamics of the Pure State Density Matrix for Hamiltonian Systems

1987 ◽  
pp. 119-146
Author(s):  
E. R. Pike ◽  
Sarben Sarkar ◽  
J. S. Satchell
Keyword(s):  
Density Matrix ◽  
Hamiltonian Systems ◽  
Pure State ◽  
State Density

scholarly journals Classical Chaos Described by a Density Matrix

Physics ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 739-746
Author(s):  
Andres Mauricio Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
Temporal Evolution ◽  
Entropy Density ◽  
State Density ◽  
Unexpected Result ◽  
Semiclassical Model ◽  
Classical Chaos

In this paper, a reference to the semiclassical model, in which quantum degrees of freedom interact with classical ones, is considered. The classical limit of a maximum-entropy density matrix that describes the temporal evolution of such a system is analyzed. Here, it is analytically shown that, in the classical limit, it is possible to reproduce classical results. An example is classical chaos. This is done by means a pure-state density matrix, a rather unexpected result. It is shown that this is possible only if the quantum part of the system is in a special class of states.

scholarly journals Classical Chaos Described by a Density Matrix

2021 ◽  
Author(s):  
A.M. Kowalski ◽  
Angelo Plastino ◽  
Gaspar Gonzalez Acosta
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Classical Limit ◽  
Degrees Of Freedom ◽  
State Density ◽  
Semiclassical Model ◽  
Classical Chaos

We work with reference to a well-known semiclassical model, in which quantum degrees of freedom interact with classical ones. We show that, in the classical limit, it is possible to represent classical results (e.g., classical chaos) by means a pure-state density matrix.

scholarly journals Iterative solutions to the steady-state density matrix for optomechanical systems

2015 ◽  
Vol 91 (1) ◽  
Author(s):  
P. D. Nation ◽  
J. R. Johansson ◽  
M. P. Blencowe ◽  
A. J. Rimberg
Keyword(s):  
Steady State ◽  
Density Matrix ◽  
State Density ◽  
Optomechanical Systems ◽  
Iterative Solutions

scholarly journals Explicit constructions of all separable two-qubits density matrices and related problems for three-qubits systems

2015 ◽  
Vol 13 (08) ◽  
pp. 1550061 ◽  
Author(s):  
Y. Ben-Aryeh ◽  
A. Mann
Keyword(s):  
Pure State ◽  
State Density ◽  
Singular Value ◽  
High Order ◽  
Sufficient Condition ◽  
Lorentz Transformations ◽  
Density Matrices ◽  
Single Qubit ◽  
Pauli Matrices ◽  
Singular Value Decompositions

Explicitly separable density matrices are constructed for all separable two-qubits states based on Hilbert–Schmidt (HS) decompositions. For density matrices which include only two-qubits correlations the number of HS parameters is reduced to 3 by using local rotations, and for two-qubits states which include single qubit measurements, the number of parameters is reduced to 4 by local Lorentz transformations. For both cases, we related the absolute values of the HS parameters to probabilities, and the outer products of various Pauli matrices were transformed to pure state density matrices products. We discuss related problems for three-qubits. For n-qubits correlation systems ([Formula: see text]) the sufficient condition for separability may be improved by local transformations, related to high order singular value decompositions (SVDs).

A Note on the Ohya-Masuda Quantum Algorithm

2002 ◽  
Vol 09 (02) ◽  
pp. 115-123
Author(s):  
Miroljub Dugić
Keyword(s):  
Density Matrix ◽  
Complexity Theory ◽  
Quantum Measurement ◽  
Pure State ◽  
Quantum Algorithm ◽  
Satisfiability Problem ◽  
Second Step ◽  
Coherent Superposition ◽  
Complete Problem ◽  
Np Complete

We analyze the Ohya-Masuda quantum algorithm that solves the so-called “satisfiability” problem, which is an NP-complete problem of the complexity theory. We distinguish three steps in the algorithm, and analyze the second step, in which a coherent superposition of states (a “pure” state) transforms into an “incoherent” mixture presented by a density matrix. We show that, if “nonideal” (in analogy with “nonideal” quantum measurement), this transformation can make the algorithm to fail in some cases. On this basis we give some general notions on the physical implementation of the Ohya-Masuda algorithm.

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