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Mutually unbiased bases containing a complex Hadamard matrix of Schmidt rank three.

ABSTRACT: Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank three. The CHM is equivalent to a controlled unitary operation on the qubit-qutrit system via local unitary transformation I 2???V and I 2???W. We show that V and W have no zero entry, and apply it to exclude constructed examples as members of MUBs. We further show that the maximum of entangling power of controlled unitary operation is log 2 3 ebits. We derive the condition under which the maximum is achieved, and construct concrete examples. Our results describe the phenomenon that if a CHM of Schmidt rank three belongs to an MUB then its entangling power may not reach the maximum.

SUBMITTER: Hu M

PROVIDER: S-EPMC7125992 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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Mutually unbiased bases containing a complex Hadamard matrix of Schmidt rank three.

Hu Mengyao M Chen Lin L Sun Yize Y

Proceedings. Mathematical, physical, and engineering sciences 20200325 2235

Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank three. The CHM is equivalent to a controlled unitary operation on the qubit-qutrit system via local unitary transformation I 2 ⊗ V and I 2 ⊗ W. We show that V and W have no zero entry, and apply it ...[more]

PMID: 32269490

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