Applying the simplest Kochen-Specker set for quantum information processing

Abstract

Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists from using them for any application. The KS set requiring the smallest number of contexts has been recently found. Relying on this simple KS set, here we report an input state-independent experimental technique to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.

REVTeX4, 5 pages, 5 figures

References in corpus (31)

• Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• The Free Will Theorem
• Bell-Kochen-Specker theorem: A proof with 18 vectors
• Graph-Theoretic Approach to Quantum Correlations
• Device-independent tests of classical and quantum dimensions
• Generation of maximally entangled states of qudits using twin photons
• State-independent quantum contextuality with single photons
• Improving zero-error classical communication with entanglement
• Experimental estimation of the dimension of classical and quantum systems
• Quantum key distribution session with 16-dimensional photonic states
• Experimental Device-independent Tests of Classical and Quantum Dimensions
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• Experimental quantum tomography of photonic qudits via mutually unbiased basis
• Bounding the quantum dimension with contextuality
• Experimental implementation of a Kochen-Specker set of quantum tests
• Kochen-Specker theorem for 8-dimensional space
• Kochen-Specker Vectors
• Fully nonlocal quantum correlations
• Manipulating spatial qudit states with programmable optical devices
• Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality
• Kochen-Specker set with seven contexts
• Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator
• Device-independent certification of high-dimensional quantum systems
• Test of mutually unbiased bases for six-dimensional photonic quantum systems
• Experimental implementation of an eight-dimensional Kochen-Specker set and observation of its connection with the Greenberger-Horne-Zeilinger theorem
• A Generalization of Kochen-Specker Sets Relates Quantum Coloring to Entanglement-Assisted Channel Capacity
• Fast entanglement detection for unknown states of two spatial qutrits
• Kochen-Specker Sets and the Rank-1 Quantum Chromatic Number
• Measurement strategy for spatially encoded photonic qubits

Cited by in corpus (33)

• Quantum information processing with space-division multiplexing optical fibres
• Five measurement bases determine pure quantum states on any dimension
• Experimental minimum-error quantum-state discrimination in high dimensions
• Simple method for experimentally testing any form of quantum contextuality
• Sustained state-independent quantum contextual correlations from a single ion
• Necessary and sufficient condition for quantum state-independent contextuality
• Quantum state-independent contextuality requires 13 rays
• Multipartite entanglement generation and contextuality tests using non-destructive three-qubit parity measurements
• Axiomatic approach to contextuality and nonlocality
• Contextuality in phase space
• Quantum Contextuality
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• Experimental quantum tomography assisted by multiply symmetric states in higher dimensions
• Testing noncontextuality inequalities that are building blocks of quantum correlations
• A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
• Certifying sets of quantum observables with any full-rank state
• A set of $4d-3$ observables to determine any pure qudit state
• Automated generation of Kochen-Specker sets
• Experimental demonstration of the connection between quantum contextuality and graph theory
• Hypergraph Contextuality
• Experimental test of high-dimensional quantum contextuality based on contextuality concentration
• Kochen-Specker sets and Hadamard matrices
• Characterizing $d-$dimensional quantum channels by means of quantum process tomography
• Proposal for Automated Operations for Single-Photon Multipath Qudits
• Vector Generation of Contextual Sets
• Non-Kochen-Specker Contextuality
• Experimental characterization of quantum processes: a selective and efficient method in arbitrary finite dimension
• Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Determination of spatial quantum states by using Point Diffraction Interferometry
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
• Kochen-Specker sets in four-dimensional spaces