Two-qubit symmetric informationally complete positive-operator-valued measures

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.82.042308· OSTI ID:21450726

Huangjun, Zhu; Teo, Yong Siah ^[1]; Englert, Berthold-Georg ^[1]

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1. Centre for Quantum Technologies, National University of Singapore, Singapore 117543 (Singapore)

In the four-dimensional Hilbert space, there exist 16 Heisenberg-Weyl (HW) covariant symmetric informationally complete positive-operator-valued measures (SIC POVMs) consisting of 256 fiducial states on a single orbit of the Clifford group. We explore the structure of these SIC POVMs by studying the symmetry transformations within a given SIC POVM and among different SIC POVMs. Furthermore, we find 16 additional SIC POVMs by a suitable regrouping of the 256 fiducial states, and show that they are unitarily equivalent to the original 16 SIC POVMs by establishing an explicit unitary transformation. We then reveal the additional structure of these SIC POVMs when the four-dimensional Hilbert space is taken as the tensor product of two-qubit Hilbert spaces. In particular, when either the standard product basis or the Bell basis are chosen as the defining basis of the HW group, in eight of the 16 HW covariant SIC POVMs, all fiducial states have the same concurrence of {radical}(2/5). These SIC POVMs are particularly appealing for an experimental implementation, since all fiducial states can be connected to each other with just local unitary transformations. In addition, we introduce a concise representation of the fiducial states with the aid of a suitable tabular arrangement of their parameters.

• OSTI ID: 21450726
• Journal Information: Physical Review. A, Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevA.82.042308; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

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