Detecting entanglement of continuous variables with three mutually unbiased bases

Abstract

An uncertainty relation is introduced for a symmetric arrangement of three mutually unbiased bases in continuous variable phase space, and then used to derive a bipartite entanglement criterion based on the variance of global operators composed of these three phase space variables. We test this criterion using spatial variables of photon pairs, and show that the entangled photons are correlated in three pairs of bases.

References in corpus (6)

• Universal Quantum Computation with Continuous-Variable Cluster States
• Continuous variable quantum computation with spatial degrees of freedom of photons
• Propagation of transverse intensity correlations of a two-photon state
• Heisenberg Uncertainty Relation for Three Canonical Observables
• Mutually Unbiased Bases for Continuous Variables
• Detection of transverse entanglement in phase space

Cited by in corpus (13)

• Measurements in two bases are sufficient for certifying high-dimensional entanglement
• Quantifying measurement incompatibility of mutually unbiased bases
• Quantifying high dimensional entanglement with two mutually unbiased bases
• Variance uncertainty relations without covariances for three and four observables
• Mutual Unbiasedness in Coarse-grained Continuous Variables
• Majorization uncertainty relations for mixed quantum states
• Uncertainty Relations for coarse-grained measurements: an overview
• Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
• Universality in Uncertainty Relations for a Quantum Particle
• Preparational Uncertainty Relations for $N$ Continuous Variables
• Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
• Periodic discretized continuous observables are neither continuous nor discrete
• Choice of mutually unbiased bases and outcome labelling affects measurement outcome secrecy