Partially Unbiased Entangled Bases

TL;DR

This paper introduces a method to analyze bipartite quantum states using a minimal set of measurements related to mutually unbiased bases, connecting entangled and single-particle bases for efficient state reconstruction.

Contribution

It presents a novel grouping of operator bases that links entangled states with single-particle MUB, reducing the measurements needed for bipartite state analysis.

Findings

Requires d^2+d+1 measurements for state analysis

Uses d^2-d entangled state measurements related to MUB

Offers a measurement scheme between two-particle MUB and single-particle MUB

Abstract

In this contribution we group the operator basis for d^2 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 d^2 dimensional Hilbert space system is analyzed by via d^2+d+1 measurements, d^2-d of which involve those entangled states that we associate with MUB of the d-dimensional single particle constituents. The number $d^2+d+1$ lies in the middle of the number of measurements needed for bipartite state reconstruction with two-particle MUB (d^2+1) and those needed by single-particle MUB [(d^2+1)^2].