scholarly journals Convergence of a Reconstructed Density Matrix to a Pure State Using the Maximal Entropy Approach

2021 ◽  
Author(s):  
Rishabh Gupta ◽  
Raphael D. Levine ◽  
Sabre Kais
Keyword(s):  
Density Matrix ◽  
Pure State ◽  
Maximal Entropy

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.

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.

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 A Classical Interpretation of the Scrooge Distribution

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 619 ◽  
Author(s):  
William Wootters
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Distribution ◽  
Density Matrix ◽  
Pure State ◽  
Quantum Mechanical ◽  
Classical Probability ◽  
Pure States ◽  
Probability Simplex ◽  
Shed Light

The Scrooge distribution is a probability distribution over the set of pure states of a quantum system. Specifically, it is the distribution that, upon measurement, gives up the least information about the identity of the pure state compared with all other distributions that have the same density matrix. The Scrooge distribution has normally been regarded as a purely quantum mechanical concept with no natural classical interpretation. In this paper, we offer a classical interpretation of the Scrooge distribution viewed as a probability distribution over the probability simplex. We begin by considering a real-amplitude version of the Scrooge distribution for which we find that there is a non-trivial but natural classical interpretation. The transition to the complex-amplitude case requires a step that is not particularly natural but that may shed light on the relation between quantum mechanics and classical probability theory.

scholarly journals Compacting the density matrix in quantum dynamics: Singular value decomposition of the surprisal and the dominant constraints for anharmonic systems

2021 ◽  
Author(s):  
Ksenia Komarova ◽  
Francoise Remacle ◽  
Raphael D. Levine
Keyword(s):  
Singular Value Decomposition ◽  
Density Matrix ◽  
Quantum Dynamics ◽  
Radiative Decay ◽  
Electronic States ◽  
Singular Value ◽  
Time Dependent ◽  
Maximal Entropy ◽  
Value Decomposition ◽  
Time Point

We introduce a practical method for compacting the time evolution of the quantum state of a closed physical system. The density matrix is specified as a function of a few time-independent observables where their coefficients are time-dependent. The key mathematical step is the vectorization of the surprisal, the logarithm of the density matrix, at each time point of interest. The time span used depends on the required spectral resolution. The entire course of the system evolution is represented as a matrix where each column is the vectorized surprisal at the given time point. Using singular value decomposition, SVD, of this matrix we generate realistic approximations for the time-independent observables and their respective time dependent coefficients. This allows a simplification of the algebraic procedure for determining the dominant constraints (the time-independent observables) in the sense of the maximal entropy approach. A nonstationary coherent initial state of a Morse oscillator is used to introduce the approach. We derive analytical exact expression for the surprisal as a function of time and this offers a benchmark for comparison with the accurate but approximate SVD results. We discuss two examples of a Morse potential of different anharmonicities, the H2 and I2 molecules. We further demonstrate the approach for a two coupled electronic states problem, the well studied non radiative decay of pyrazine from its bright state. Five constraints are found to be enough to capture the ultrafast electronic population exchange and to recover the dynamics of the wave packet in both electronic states.

Sign in / Sign up

Export Citation Format

Share Document