Mutually Unbiased Bases and Finite Projective Planes

Abstract

It is conjectured that the question of the existence of projective planes whose order is not a power of prime is intimately linked with the problem whether there exists a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space if d differs from a power of prime.

2 pages, no figures

References in corpus (8)

• Security of quantum key distribution using d-level systems
• A new proof for the existence of mutually unbiased bases
• Geometry of entangled states, Bloch spheres and Hopf fibrations
• Mutually unbiased binary observable sets on N qubits
• On SIC-POVMs and MUBs in Dimension 6
• Constructions of Mutually Unbiased Bases
• Aspects of mutually unbiased bases in odd prime power dimensions
• Geometry of the 3-Qubit State, Entanglement and Division Algebras

Cited by in corpus (38)

• On mutually unbiased bases
• Improving Quantum State Estimation with Mutually Unbiased Bases
• Genuinely multipartite entangled states and orthogonal arrays
• On the structure of the sets of mutually unbiased bases for N qubits
• Quantifying measurement incompatibility of mutually unbiased bases
• Symmetric Informationally Complete Measurements of Arbitrary Rank
• Multicomplementary operators via finite Fourier transform
• Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
• Quantum process reconstruction based on mutually unbiased basis
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• Hjelmslev Geometry of Mutually Unbiased Bases
• A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
• Mutually unbiased phase states, phase uncertainties, and Gauss sums
• The Lie Algebraic Significance of Symmetric Informationally Complete Measurements
• Mutually unbiased bases and discrete Wigner functions
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Angular Momentum and Mutually Unbiased Bases
• Mutually Unbiased Bases and Semi-definite Programming
• An operational link between MUBs and SICs
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group
• A unified approach to SIC-POVMs and MUBs
• On the connection between mutually unbiased bases and orthogonal Latin squares
• The Frobenius formalism in Galois quantum systems
• Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes?
• Maximal Entanglement, Collective Coordinates and Tracking the King
• A complementarity-based approach to phase in finite-dimensional quantum systems
• Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs
• Small sets of complementary observables
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• Radon Transform in Finite Dimensional Hilbert Space
• A family of Alltop functions that are EA-inequivalent to the cubic function
• Huyghens, Bohr, Riemann and Galois: Phase-Locking
• SU(2) nonstandard bases: the case of mutually unbiased bases
• Projective toric designs, quantum state designs, and mutually unbiased bases
• Cyclic Mutually Unbiased Bases and Quantum Public-Key Encryption
• Affine Constellations Without Mutually Unbiased Counterparts
• Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
• Construction of Structured Incoherent Unit Norm Tight Frames