scholarly journals Exact Minimum Eigenvalue Distribution of an Entangled Random Pure State

2008 ◽  
Vol 131 (1) ◽  
pp. 33-49 ◽  
Author(s):  
Satya N. Majumdar ◽  
Oriol Bohigas ◽  
Arul Lakshminarayan
Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 539 ◽  
Author(s):  
Lu Wei

The Tsallis entropy is a useful one-parameter generalization to the standard von Neumann entropy in quantum information theory. In this work, we study the variance of the Tsallis entropy of bipartite quantum systems in a random pure state. The main result is an exact variance formula of the Tsallis entropy that involves finite sums of some terminating hypergeometric functions. In the special cases of quadratic entropy and small subsystem dimensions, the main result is further simplified to explicit variance expressions. As a byproduct, we find an independent proof of the recently proven variance formula of the von Neumann entropy based on the derived moment relation to the Tsallis entropy.


2021 ◽  
Vol 820 ◽  
pp. 136600
Author(s):  
Kazumi Okuyama
Keyword(s):  

Author(s):  
Carlo W. J. Beenakker

This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.


1992 ◽  
Author(s):  
Beresford Parlett ◽  
Tzon-Tzer Lu
Keyword(s):  

Author(s):  
Moshe Blidstein
Keyword(s):  

Chapter 6 turns to the internal ordering of the community through purity discourse concerning sin. It discusses the regulation of sin inside the borders of the pure community, focusing on the eucharist and on the conceptualization of repentance and penance as purification. Though in the first two centuries the eucharist had already become the sacred ritual representing the community, and was therefore guarded by purity restrictions, there was as yet no ritual system through which sinners could purify themselves and thus approach the eucharist. Some texts, such as the Didache, describe the eucharist as a sacrifice and the communal cohesion it requires as a pure state.


Author(s):  
JingWei Wen ◽  
XiaoCong Qiu ◽  
XiangYu Kong ◽  
XinYu Chen ◽  
Fan Yang ◽  
...  

2016 ◽  
Vol 53 ◽  
pp. 66-71 ◽  
Author(s):  
Stephen T. Hedetniemi ◽  
David P. Jacobs ◽  
Vilmar Trevisan

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