arXiv:quant-ph/0507103 · Physical Review A

Matrix-element distributions as a signature of entanglement generation

Yaakov S. Weinstein, C. Stephen Hellberg

Published Aug 23, 2005• 20 citations

Abstract

We explore connections between an operator's matrix-element distribution and its entanglement generation. Operators with matrix-element distributions similar to those of random matrices generate states of high multipartite entanglement. This occurs even when other statistical properties of the operators do not coincide with random matrices. Similarly, operators with some statistical properties of random matrices may not exhibit random matrix element distributions and will not produce states with high levels of multipartite entanglement. Finally, we show that operators with similar matrix-element distributions generate similar amounts of entanglement.

DOI: 10.1103/physreva.72.022331

Related papers

Matrix Element Randomness, Entanglement, and Quantum Chaos

Yaakov S. Weinstein, C. Stephen Hellberg

We demonstrate the connection between an operator's matrix element distribution and entangling power via numerical simulations of random, pseudo-random, and quantum chaotic operators. Creating operators with a random distribution of matrix elements is more difficult than creating operators that reproduce other statistical properties of random matrices. Thus, operators that fulfill many random matrix statistical properties may not generate states of high multi-partite entanglement. To quantify the randomness of various statistical distributions and, by extension, entangling power, we use properties of interpolating ensembles that transition between integrable and random matrix ensembles.

arXiv:quant-ph/0405053May 11, 20040 citations

Entanglement Generation of Nearly Random Operators

Yaakov S. Weinstein, C. Stephen Hellberg

We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random parameters are restricted, pseudorandom operators, where there are far fewer random parameters than required for random matrices, and quantum chaotic evolution. Restricting randomness in different ways allows us to probe connections between entanglement and randomness. We comment on which properties affect entanglement generation and discuss ways of efficiently producing random states on a quantum computer.

arXiv:quant-ph/0502110Physical Review LettersJul 12, 200550 citations

Quantum Entanglement-Based Random Matrix Generation

Jincheng Zhang

Quantum entanglement, a peculiar phenomenon in quantum mechanics, presents a unique opportunity for generating highly complex and statistically diverse random matrices. This paper explores the development of a novel random matrix generation algorithm leveraging quantum entanglement to produce matrices suitable for machine learning training and optimization. We detail the core mechanism, focusing on the instantaneous nature of entanglement and its application to matrix manipulation, demonstrating a potential paradigm shift in this field. Quantum entanglement offers a novel approach to randomness, potentially surpassing traditional methods in generating matrices with enhanced statistical properties.

Sep 2, 20260 citations

基于量子纠缠的随机矩阵生成

Jincheng Zhang

This paper presents a novel random matrix generation algorithm based on quantum entanglement. The algorithm leverages the unique properties of quantum entanglement to generate complex matrix structures with adaptive probability distributions, offering enhanced simulation capabilities for intricate systems. Traditional random matrix generation methods often lack the depth of quantum entanglement integration, resulting in a significant improvement in the algorithm's ability to produce robust and statistically diverse matrices. The core mechanism involves carefully manipulating entangled quantum states to influence the matrix generation process, leading to a substantially increased level of complexity and adaptability. We demonstrate the effectiveness of this approach through simulations of complex systems, showcasing the algorithm's capacity to generate matrices exhibiting intricate entanglement topologies.

Sep 5, 20260 citations

Distribution of matrix elements of random operators

Mahir Saleh Hussein, Mauricio Porto Pato

It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the key quantity that determines these distribution is the commutator of the operator with the Hamiltonian. Application to symmetry breaking in quantum many-body systems is discussed.

arXiv:nucl-th/9907063Jul 15, 19990 citations

Quantum Entanglement-Based Random Matrix Generation Algorithm (QEMGA)

Jincheng Zhang

This paper introduces the Quantum Entanglement-Based Random Matrix Generation Algorithm (QEMGA), a novel approach to generating high-dimensional random matrices. Traditional matrix generation methods are often complex and lack the ability to produce high-quality random matrices. QEMGA leverages the unique properties of quantum entanglement to facilitate the creation of these matrices, offering a fundamentally new method for random matrix creation. We detail the algorithm's design, explain the underlying quantum mechanics, and present preliminary results demonstrating its effectiveness in generating complex random matrices. The research explores the potential of QEMGA to push the boundaries of randomness and offer a robust solution for applications requiring high-quality random matrix generation.

Aug 31, 20260 citations