Partially Unbiased Entangled Bases

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].

5 pages

References in corpus (6)

• On the structure of the sets of mutually unbiased bases for N qubits
• Multicomplementary operators via finite Fourier transform
• A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
• Mutually unbiased phase states, phase uncertainties, and Gauss sums
• Mutually unbiased bases and generalized Bell states
• MUBs, polytopes, and finite geometries

Cited by in corpus (6)

• Reference frame independent quantum key distribution
• Particle-wave duality: a dichotomy between symmetry and asymmetry
• Maximally Entangled States via Mutual Unbiased collective Bases
• Maximal Entanglement, Collective Coordinates and Tracking the King
• Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs
• Radon Transform in Finite Dimensional Hilbert Space