scholarly journals Random matrices with prescribed eigenvalues and expectation values for random quantum states

2020 ◽  
Vol 373 (7) ◽  
pp. 5141-5170
Author(s):  
Elizabeth S. Meckes ◽  
Mark W. Meckes
Keyword(s):  
Random Matrices ◽  
Quantum States ◽  
Expectation Values ◽  
Random Quantum States

scholarly journals Signatures of Anderson localization and delocalized random quantum states

2018 ◽  
Vol 514 ◽  
pp. 141-149
Author(s):  
Giorgio J. Moro ◽  
Giulia Dall'Osto ◽  
Barbara Fresch
Keyword(s):  
Anderson Localization ◽  
Quantum States ◽  
Random Quantum States

scholarly journals Does the Equivalence between Gravitational Mass and Energy Survive for a Composite Quantum Body?

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
A. G. Lebed
Keyword(s):  
Hydrogen Atom ◽  
Mass Operator ◽  
Energy Operator ◽  
Quantum States ◽  
Gravitational Mass ◽  
Hydrogen Atoms ◽  
Expectation Values ◽  
Direct Experiment ◽  
Stationary Quantum ◽  
Passive Gravitational Mass

We define passive and active gravitational mass operators of the simplest composite quantum body—a hydrogen atom. Although they do not commute with its energy operator, the equivalence between the expectation values of passive and active gravitational masses and energy is shown to survive for stationary quantum states. In our calculations of passive gravitational mass operator, we take into account not only kinetic and Coulomb potential energies but also the so-called relativistic corrections to electron motion in a hydrogen atom. Inequivalence between passive and active gravitational masses and energy at a macroscopic level is demonstrated to reveal itself as time-dependent oscillations of the expectation values of the gravitational masses for superpositions of stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level reveals itself as unusual electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms, moved by small spacecraft with constant velocity in the Earth’s gravitational field. We suggest the corresponding experiment on the Earth’s orbit to detect this radiation, which would be the first direct experiment where quantum effects in general relativity are observed.

scholarly journals Quantum random state generation with predefined entanglement constraint

2014 ◽  
Vol 12 (05) ◽  
pp. 1450030 ◽  
Author(s):  
Anmer Daskin ◽  
Ananth Grama ◽  
Sabre Kais
Keyword(s):  
Error Correction ◽  
Weighted Graph ◽  
Quantum States ◽  
Von Neumann Entropy ◽  
Bipartite Entanglement ◽  
Von Neumann ◽  
Communication Algorithms ◽  
Equivalent Quantum ◽  
State Generation ◽  
Random Quantum States

Entanglement plays an important role in quantum communication, algorithms, and error correction. Schmidt coefficients are correlated to the eigenvalues of the reduced density matrix. These eigenvalues are used in von Neumann entropy to quantify the amount of the bipartite entanglement. In this paper, we map the Schmidt basis and the associated coefficients to quantum circuits to generate random quantum states. We also show that it is possible to adjust the entanglement between subsystems by changing the quantum gates corresponding to the Schmidt coefficients. In this manner, random quantum states with predefined bipartite entanglement amounts can be generated using random Schmidt basis. This provides a technique for generating equivalent quantum states for given weighted graph states, which are very useful in the study of entanglement, quantum computing, and quantum error correction.

scholarly journals Bending the Bruhat-Tits tree. Part I. Tensor network and emergent Einstein equations

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Lin Chen ◽  
Xirong Liu ◽  
Ling-Yan Hung
Keyword(s):  
Einstein Equation ◽  
Companion Paper ◽  
Quantum States ◽  
Einstein Equations ◽  
Higher Dimension ◽  
Expectation Values ◽  
Einstein Tensor ◽  
Geometric Information ◽  
Network Construction ◽  
Tensor Network

Abstract As an extended companion paper to [1], we elaborate in detail how the tensor network construction of a p-adic CFT encodes geometric information of a dual geometry even as we deform the CFT away from the fixed point by finding a way to assign distances to the tensor network. In fact we demonstrate that a unique (up to normalizations) emergent graph Einstein equation is satisfied by the geometric data encoded in the tensor network, and the graph Einstein tensor automatically recovers the known proposal in the mathematics literature, at least perturbatively order by order in the deformation away from the pure Bruhat-Tits Tree geometry dual to pure CFTs. Once the dust settles, it becomes apparent that the assigned distance indeed corresponds to some Fisher metric between quantum states encoding expectation values of bulk fields in one higher dimension. This is perhaps a first quantitative demonstration that a concrete Einstein equation can be extracted directly from the tensor network, albeit in the simplified setting of the p-adic AdS/CFT.

SU(1,1) LIE ALGEBRA APPLIED TO THE TIME-DEPENDENT QUADRATIC HAMILTONIAN SYSTEM PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (26) ◽  
pp. 3429-3441 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
SEONG SOO CHOI
Keyword(s):  
Hamiltonian System ◽  
Probability Density ◽  
Lie Algebra ◽  
Time Evolution ◽  
Coherent States ◽  
Classical Trajectory ◽  
Quantum States ◽  
Time Dependent ◽  
Expectation Values ◽  
Quadratic Hamiltonian

We realized SU (1,1) Lie algebra in terms of the appropriate SU (1,1) generators for the time-dependent quadratic Hamiltonian system perturbed by a singularity. Exact quantum states of the system are investigated using SU (1,1) Lie algebra. Various expectation values in two kinds of the generalized SU (1,1) coherent states, that is, BG coherent states and Perelomov coherent states are derived. We applied our study to the CKOPS (Caldirola–Kanai oscillator perturbed by a singularity). Due to the damping constant γ, the probability density of the SU (1,1) coherent states for the CKOPS converged to the center with time. The time evolution of the probability density in SU (1,1) coherent states for the CKOPS are very similar to the classical trajectory.

Random quantum states

1990 ◽  
Vol 20 (11) ◽  
pp. 1365-1378 ◽  
Author(s):  
William K. Wootters
Keyword(s):  
Quantum States ◽  
Random Quantum States
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