Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Abstract

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families of Bell inequalities that are maximally violated by $d$-dimensional MUBs and SICs respectively, ii) proving device-independent certification of natural operational notions of MUBs and SICs, and iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device independent quantum key distribution and device-independent quantum random number generation respectively. Moreover, we also present the first example of an extremal point of the quantum set of correlations which admits physically inequivalent quantum realisations. Our results elaborately demonstrate the foundational and practical relevance of the two most important discrete Hilbert space structures to the field of quantum nonlocality.

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Cited by in corpus (51)

• Semidefinite programming relaxations for quantum correlations
• Quantum Correlations in the Minimal Scenario
• Analysing quantum systems with randomised measurements
• Resource-efficient high-dimensional entanglement detection via symmetric projections
• Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness
• Certification of a Nonprojective Qudit Measurement using Multiport Beamsplitters
• Nonlocality, steering and quantum state tomography in a single experiment
• Self-testing of any pure entangled state with minimal number of measurements and optimal randomness certification in one-sided device-independent scenario
• Classical Cost of Transmitting a Qubit
• Certification of incompatible measurements using quantum steering
• Device-independent quantification of measurement incompatibility
• How many mutually unbiased bases are needed to detect bound entangled states?
• Mutually unbiased frames
• Enhanced Schmidt number criteria based on correlation trace norms
• Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements
• Detecting the dimensionality of genuine multi-particle entanglement
• Three numerical approaches to find mutually unbiased bases using Bell inequalities
• Network quantum steering enables randomness certification without seed randomness
• Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Bell inequality violations with random mutually unbiased bases
• Mutually Unbiased Measurements, Hadamard Matrices, and Superdense Coding
• Certification of unbounded randomness with arbitrary noise
• Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
• An Operational Environment for Quantum Self-Testing
• Biased Random Access Codes
• A universal scheme to self-test any quantum state or measurement
• Entropic uncertainty relations for mutually unbiased periodic coarse-grained observables resemble their discrete counterparts
• Optimality of any pair of incompatible rank-one projective measurements for some non-trivial Bell inequality
• Self-testing composite measurements and bound entangled state in a single quantum network
• Quantum value for a family of $I_{3322}$-like Bell functionals
• Necessary and Sufficient Condition for Randomness Certification from Incompatibility
• Quantum Coherence and Distinguishability as Complementary Resources: A Resource-Theoretic Perspective from Wave-Particle Duality
• Periodic discretized continuous observables are neither continuous nor discrete
• Higher-dimensional symmetric informationally complete measurement via programmable photonic integrated optics
• Quantum bounds and device-independent security with rank-one qubit measurements
• General measurements with limited resources and their application to quantum unambiguous state discrimination
• Non-projective Bell state measurements
• Relating measurement disturbance, information and orthogonality
• Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
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• All classes of informationally complete symmetric measurements in finite dimensions
• Bounding Large-Scale Bell Inequalities
• Device-independent certification of degeneracy-breaking measurements
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