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Entropy 2014, 16(3), 1484-1492; doi:10.3390/e16031484

Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States

1
School of Physics, University of Sydney, Sydney, NSW 2006, Australia
2
University of Waterloo, 200 University Ave West, Waterloo, ON N2L 3G1, Canada
3
Quantum Information Processing Group, Raytheon BBN Technologies, 10 Moulton Street, Cambridge, MA 02138, USA
*
Author to whom correspondence should be addressed.
Received: 21 January 2014 / Revised: 4 February 2014 / Accepted: 5 March 2014 / Published: 14 March 2014
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Abstract

Recently there has been much effort in the quantum information community to prove (or disprove) the existence of symmetric informationally complete (SIC) sets of quantum states in arbitrary finite dimension. This paper strengthens the urgency of this question by showing that if SIC-sets exist: (1) by a natural measure of orthonormality, they are as close to being an orthonormal basis for the space of density operators as possible; and (2) in prime dimensions, the standard construction for complete sets of mutually unbiased bases and Weyl-Heisenberg covariant SIC-sets are intimately related: The latter represent minimum uncertainty states for the former in the sense of Wootters and Sussman. Finally, we contribute to the question of existence by conjecturing a quadratic redundancy in the equations for Weyl-Heisenberg SIC-sets. View Full-Text
Keywords: SIC-POVMs; minimum-uncertainty states SIC-POVMs; minimum-uncertainty states
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Appleby, D.M.; Dang, H.B.; Fuchs, C.A. Symmetric Informationally-Complete Quantum States as Analogues to Orthonormal Bases and Minimum-Uncertainty States. Entropy 2014, 16, 1484-1492.

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