Mean king's problem with mutually unbiased bases and orthogonal Latin squares

Abstract

The mean king's problem with maximal mutually unbiased bases (MUB's) in general dimension d is investigated. It is shown that a solution of the problem exists if and only if the maximal number (d+1) of orthogonal Latin squares exists. This implies that there is no solution in d=6 or d=10 dimensions even if the maximal number of MUB's exists in these dimensions.

5 pages, 1 figure, v2: typos corrected. journal version

References in corpus (1)

• Solution to the King's problem with observables being not mutually complementary

Cited by in corpus (30)

• Quantum Cloning Machines and the Applications
• Entanglement in mutually unbiased bases
• On the structure of the sets of mutually unbiased bases for N qubits
• Numerical evidence for the maximum number of mutually unbiased bases in dimension six
• On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Entangling Power of Permutations
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• Discrete phase-space structure of $n$-qubit mutually unbiased bases
• Mutually unbiased bases and discrete Wigner functions
• Classification of GHZ-type, W-type and GHZ-W-type multiqubit entanglements
• Solution to the Mean King's problem with mutually unbiased bases for arbitrary levels
• Digital Discovery of 100 diverse Quantum Experiments with PyTheus
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group
• The Frobenius formalism in Galois quantum systems
• A Meaner King uses Biased Bases
• Construction of general symmetric-informationally-complete-positive-operator-valued measures by using a complete orthogonal basis
• Generation of all sets of mutually unbiased bases for three-qubit systems
• Quantum combinatorial designs and $k$-uniform states
• Structure of the sets of mutually unbiased bases with cyclic symmetry
• SU(2) nonstandard bases: the case of mutually unbiased bases
• Mutually unbiased maximally entangled bases from difference matrices
• Solution to the mean king's problem using quantum error-correcting codes
• Experimental Solutions to the High-Dimensional Mean King's Problem
• The correspondence between mutually unbiased bases and mutually orthogonal extraordinary supersquares
• Retrodiction of measurement outcomes on a single quantum system reveals entanglement with its environment
• Matrix reduction and Lagrangian submodules
• Bases for spin systems and qudits from angular momentum theory
• Solutions to the mean king's problem: higher-dimensional quantum error-correcting codes
• Mutually disjoint, maximally commuting set of physical observables for optimum state determination