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Diagonal unitary entangling gates and contradiagonal quantum states
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Diagonal unitary entangling gates and contradiagonal quantum states
Bibliographic description
| title: | Diagonal unitary entangling gates and contradiagonal quantum states |
| author: | Lakshminarayan Arul, Puchała Zbigniew  , Życzkowski Karol
|
| journal title: | Physical Review. A, Atomic, Molecular, and Optical Physics |
| volume: | 90 |
| issue: | 3 |
| date of publication : | 2014 |
| article ID: | 032303 |
| ISSN: |
1050-2947 |
| eISSN: |
1094-1622 1538-4446 |
| DOI: | |
| language: | English |
| journal language: | English |
| abstract in English: | 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. |
| number of pulisher's sheets: | 1 |
| affiliation: | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego |
| type: | journal article |
| subtype: | academic paper |
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