arXiv subjects

Paul Butterley

Publications and source records attributed to Paul Butterley.

2 recordsLinked to original sources

arXiv2007

Numerical evidence for the maximum number of mutually unbiased bases in dimension six

The question of determining the maximal number of mutually unbiased bases in dimension six has received much attention since their introduction to quantum information theory, but a definitive answer has still not been found. In this paper we move away from the traditional analytic approach and use a numerical approach to attempt to determine this number. We numerically minimise a non-negative function of a set of N+1 orthonormal bases in dimension d which only evaluates to zero if the bases are mutually unbiased. As a result we find strong evidence that (as has been conjectured elsewhere) there are no more than three mutually unbiased bases in dimension six.

quant-ph↗

arXiv2005

Compatibility of subsystem states

We examine the possible states of subsystems of a system of bits or qubits. In the classical case (bits), this means the possible marginal distributions of a probability distribution on a finite number of binary variables; we give necessary and sufficient conditions for a set of probability distributions on all proper subsets of the variables to be the marginals of a single distribution on the full set. In the quantum case (qubits), we consider mixed states of subsets of a set of qubits; in the case of three qubits, we find quantum Bell inequalities -- necessary conditions for a set of two-qubit states to be the reduced states of a single mixed state of three qubits. We conjecture that these conditions are also sufficient.

quant-ph↗