Bell inequality violations with random mutually unbiased bases
arXiv:2205.04037 · doi:10.1103/PhysRevA.106.012209
Abstract
We examine the problem of exhibiting Bell nonlocality for a two-qudit entangled pure state using a randomly chosen set of mutually unbiased bases (MUBs). Interestingly, even if we employ only two-setting Bell inequalities, we find a significant chance of obtaining a Bell violation if the two parties are individually allowed to measure a sufficient number of MUBs. In particular, for the case of maximally entangled qutrits and ququarts, our numerical estimates indicate that we can obtain near-guaranteed Bell violation by considering only such Bell inequalities. The case of maximally entangled ququints is similar, albeit the chance of ending up with a successful trial decreases somewhat to approximately . Upon a closer inspection, we find that even all these no-violation instances violate some more-setting Bell inequalities. These results suggest that the experimental tests of Bell nonlocality for these higher-dimensional entangled states remain viable even if the two parties do not share a common reference frame.
arXiv comment10+1 pages, 9 figures, 6 tables. v2 is essentially the same as the published version
References in corpus (44)
- Quantum cryptography: Public key distribution and coin tossing
- Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
- Bell nonlocality
- Significant-loophole-free test of Bell's theorem with entangled photons
- Random Numbers Certified by Bell's Theorem
- A strong loophole-free test of local realism
- Security of quantum key distribution using d-level systems
- A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
- Bell inequalities for arbitrarily high dimensional systems
- Optimal eavesdropping in quantum cryptography with six states
- Quantum Error Correction and Orthogonal Geometry
- On mutually unbiased bases
- Non-local correlations as an information theoretic resource
- Event-Ready Bell Test Using Entangled Atoms Simultaneously Closing Detection and Locality Loopholes
- A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality
- Private Randomness Expansion With Untrusted Devices
- Entanglement detection via mutually unbiased bases
- Device-independent entanglement quantification and related applications
- Geometry of the set of quantum correlations
- Device-independent randomness expansion against quantum side information
- Lifting Bell inequalities
- Device-independent Randomness Expansion with Entangled Photons
- Bell inequalities tailored to maximally entangled states
- Guaranteed violation of a Bell inequality without aligned reference frames or calibrated devices
- Nonclassical correlations from randomly chosen local measurements
- Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments
- Reexamination of a multisetting Bell inequality for qudits
- There is no anomaly in the nonlocality of two entangled qutrits
- Linking Entanglement Detection and State Tomography via Quantum 2-Designs
- Multi-setting Bell inequality for qudits
- Concentration phenomena in the geometry of Bell correlations
- Generating nonclassical correlations without fully aligning measurements
- Observers can always generate nonlocal correlations without aligning measurements by covering all their bases
- Multipartite nonlocality and random measurements
- Closed sets of correlations: answers from the zoo
- Towards an equivalence between maximal entanglement and maximal quantum nonlocality
- Survey on the Bell nonlocality of a pair of entangled qudits
- Bell inequalities for three systems and arbitrarily many measurement outcomes
- Experimental comparison of tomography and self-testing in certifying entanglement
- Demonstrating genuine multipartite entanglement and nonseparability without shared reference frames
- Maximal Violation of a Broad Class of Bell Inequalities and Its Implications on Self-Testing
- Strength and typicality of nonlocality in multisetting and multipartite Bell scenarios
- Naturally restricted subsets of nonsignaling correlations: typicality and convergence
- Device-independent certification of multipartite entanglement using measurements performed in randomly chosen triads