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Square Root Statistics of Density Matrices and Their Applications

Journal Article · · Entropy
DOI:https://doi.org/10.3390/e26010068· OSTI ID:2281038
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To estimate the degree of quantum entanglement of random pure states, it is crucial to understand the statistical behavior of entanglement indicators such as the von Neumann entropy, quantum purity, and entanglement capacity. These entanglement metrics are functions of the spectrum of density matrices, and their statistical behavior over different generic state ensembles have been intensively studied in the literature. As an alternative metric, in this work, we study the sum of the square root spectrum of density matrices, which is relevant to negativity and fidelity in quantum information processing. In particular, we derive the finite-size mean and variance formulas of the sum of the square root spectrum over the Bures–Hall ensemble, extending known results obtained recently over the Hilbert–Schmidt ensemble.

Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States); Texas Tech University, Lubbock, TX (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-06CH11357; SC0024631
OSTI ID:
2281038
Alternate ID(s):
OSTI ID: 2337761
OSTI ID: 2474887
Journal Information:
Entropy, Journal Name: Entropy Journal Issue: 1 Vol. 26; ISSN ENTRFG; ISSN 1099-4300
Publisher:
MDPI AGCopyright Statement
Country of Publication:
Switzerland
Language:
English

References (17)

Cauchy–Laguerre Two-Matrix Model and the Meijer-G Random Point Field journal November 2013
Relating the Bures Measure to the Cauchy Two-Matrix Model journal October 2015
Random quantum correlations and density operator distributions journal May 1998
Geometry of Quantum States book January 2006
Entropy of an n ‐system from its correlation with a k ‐reservoir journal May 1978
Fidelity for Mixed Quantum States journal December 1994
Induced measures in the space of mixed quantum states journal August 2001
Bures volume of the set of mixed quantum states journal September 2003
Bures–Hall ensemble: spectral densities and average entropies journal June 2019
Proof of Sarkar–Kumar’s conjectures on average entanglement entropies over the Bures–Hall ensemble journal May 2020
Second-order statistics of fermionic Gaussian states journal February 2022
Computable measure of entanglement journal February 2002
Axiomatic and operational connections between the l1 -norm of coherence and negativity journal February 2018
Exact variance of von Neumann entanglement entropy over the Bures-Hall measure journal December 2020
Random density matrices: Analytical results for mean fidelity and variance of squared Bures distance journal March 2023
Entanglement Entropy and Entanglement Spectrum of the Kitaev Model journal August 2010
Average entropy of a subsystem journal August 1993

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Related Subjects

97 MATHEMATICS AND COMPUTING
Bures–Hall ensemble
fidelity
negativity
quantum entanglement
quantum entanglement
negativity
fidelity
Bures–Hall ensemble
random matrix theory
random matrix theory