Abstract
The state of a quantum system is a density matrix with several parameters. The concern herein is how to recover the parameters. Several possibilities exist for the optimal recovery method, and we consider some special cases. We assume that a few parameters are known and that the others are to be recovered. The optimal positive-operator-valued measure (POVM) for recovering unknown parameters with an additional condition is called a conditional symmetric informationally complete POVM (SIC-POVM). In this paper, we study the existence or nonexistence of conditional SIC-POVMs. We provide a necessary condition for existence and some examples.
Highlights
Positive-operator-valued measures (POVMs) are motivated by quantum information theory
K ≥ n2 must hold for the POVM
We show some examples of nonexistence of conditional SIC-POVMs
Summary
Positive-operator-valued measures (POVMs) are motivated by quantum information theory. Pi comprise a symmetric informationally complete POVM (SIC-POVM), known as an equiangular tight frame [8,25,26,27,28,29]. This currently popular idea [1,2,4,10,20,33] was defined by Zauner [31,32]. If some of the n2 − 1 parameters of a density matrix ρ are known, a SIC-POVM is not the optimal POVM for linear quantum state tomography for such ρ. A conditional SIC-POVM is the optimal POVM for linear quantum state tomography in this case.
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