Partially unbiased entangled bases

Abstract

In this contribution we group the operator basis for d2 -dimensional Hilbert space in a way that enables us to relate bases of entangled states with single-particle mutually unbiased state bases (MUB), each in dimensionality d. We utilize these sets of operators to show that an arbitrary density matrix for this d2 -dimensional Hilbert-space system is analyzed via d2 +d+1 measurements, d2 -d of which involve those entangled states that we associate with MUB of the d -dimensional single-particle constituents. The number d2 +d+1 lies in the middle of the number of measurements needed for bipartite state reconstruction with two-particle MUB (d2 +1) and those needed by single-particle MUB [(d2 +1) 2]. © 2009 The American Physical Society.