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Diagonal unitary entangling gates and contradiagonal quantum states


Diagonal unitary entangling gates and contradiagonal quantum states

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dc.contributor.author Lakshminarayan, Arul pl
dc.contributor.author Puchała, Zbigniew [SAP14010184] pl
dc.contributor.author Życzkowski, Karol [SAP11011566] pl
dc.date.accessioned 2015-02-09T11:53:43Z
dc.date.available 2015-02-09T11:53:43Z
dc.date.issued 2014 pl
dc.identifier.issn 1050-2947 pl
dc.identifier.uri http://ruj.uj.edu.pl/xmlui/handle/item/2914
dc.language eng pl
dc.rights Dodaję tylko opis bibliograficzny *
dc.rights.uri *
dc.title Diagonal unitary entangling gates and contradiagonal quantum states pl
dc.type JournalArticle pl
dc.abstract.en Nonlocal properties of an ensemble of diagonal random unitary matrices of order N 2 are investigated. The average Schmidt strength of such a bipartite diagonal quantum gate is shown to scale as log N, in contrast to the log N 2 behavior characteristic to random unitary gates. Entangling power of a diagonal gate U is related to the von Neumann entropy of an auxiliary quantum state ρ = AA† /N2 , where the square matrix A is obtained by reshaping the vector of diagonal elements of U of length N 2 into a square matrix of order N. This fact provides a motivation to study the ensemble of non-hermitian unimodular matrices A, with all entries of the same modulus and random phases and the ensemble of quantum states ρ, such that all their diagonal entries are equal to 1/N. Such a state is contradiagonal with respect to the computational basis, in sense that among all unitary equivalent states it maximizes the entropy copied to the environment due to the coarse graining process. The first four moments of the squared singular values of the unimodular ensemble are derived, based on which we conjecture a connection to a recently studied combinatorial object called the “Borel triangle”. This allows us to find exactly the mean von Neumann entropy for random phase density matrices and the average entanglement for the corresponding ensemble of bipartite pure states. pl
dc.description.volume 90 pl
dc.description.number 3 pl
dc.description.publication 1 pl
dc.identifier.doi 10.1103/PhysRevA.90.032303 pl
dc.identifier.eissn 1094-1622 pl
dc.identifier.eissn 1538-4446 pl
dc.title.journal Physical Review. A, Atomic, Molecular, and Optical Physics pl
dc.language.container eng pl
dc.affiliation Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego pl
dc.subtype Article pl
dc.identifier.articleid 032303 pl
dc.rights.original bez licencji pl
.pointsMNiSW [2014 A]: 35

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