Self-testing quantum systems of arbitrary local dimension with minimal number of measurements

Abstract

Bell nonlocality as a resource for device independent certification schemes has been studied extensively in recent years. The strongest form of device independent certification is referred to as self-testing, which given a device certifies the promised quantum state as well as quantum measurements performed on it without any knowledge of the internal workings of the device. In spite of various results on self-testing protocols, it remains a highly nontrivial problem to propose a certification scheme of qudit-qudit entangled states based on violation of a single $d$-outcome Bell inequality. Here we address this problem and propose a self-testing protocol for the maximally entangled state of any local dimension using the minimum number of measurements possible, i.e., two per subsystem. Our self-testing result can be used to establish unbounded randomness expansion, ${\log }_{2}d$ perfect random bits, while it requires only one random bit to encode the measurement choice.

arXiv comment20 pages, 1 figure, note the related work arXiv:1909.12759 appearing at the same time

References in corpus (24)

• Device-independent security of quantum cryptography against collective attacks
• Random Numbers Certified by Bell's Theorem
• Bell inequalities for arbitrarily high dimensional systems
• Multidimensional quantum entanglement with large-scale integrated optics
• Randomness vs Non Locality and Entanglement
• Testing the Hilbert space dimension
• Device-independent witnesses of genuine multipartite entanglement
• Robust Self Testing of the Singlet
• Maximally Non-Local and Monogamous Quantum Correlations
• No extension of quantum theory can have improved predictive power
• All Pure Bipartite Entangled States can be Self-Tested
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Optimal randomness certification from one entangled bit
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Bell inequalities tailored to maximally entangled states
• All the self-testings of the singlet for two binary measurements
• Device-independent parallel self-testing of two singlets
• Self-testing protocols based on the chained Bell inequalities
• Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
• Self-testing in parallel
• Maximal randomness from partially entangled states
• A generalization of the CHSH inequality self-testing maximally entangled states of any local dimension
• A two-player dimension witness based on embezzlement, and an elementary proof of the non-closure of the set of quantum correlations
• Device-independent certification of tensor products of quantum states using single-copy self-testing protocols

Cited by in corpus (4)

• Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices
• Device-independent certification of tensor products of quantum states using single-copy self-testing protocols
• Separation of quantum, spatial quantum, and approximate quantum correlations
• Practical parallel self-testing of Bell states via magic rectangles