Oblivious communication game, self-testing of projective and non-projective measurements and certification of randomness

Abstract

We provide an interesting two-party parity oblivious communication game whose success probability is solely determined by the Bell expression. The parity-oblivious condition in an operational quantum theory implies the preparation non-contextuality in an ontological model of it. We find that the aforementioned Bell expression has two upper bounds in an ontological model; the usual local bound and a non-trivial preparation non-contextual bound arising from the non-trivial parity-oblivious condition, which is smaller that the local bound. We first demonstrate the communication game when both Alice and Bob perform three measurements of dichotomic observables in their respective sites. The optimal quantum value of the Bell expression in this scenario enables us to device-independently self-test the maximally entangled state and trine-set of observables, three-outcome qubit positive-operator-valued-measures (POVMs) and 1.58 bit of local randomness. Further, we generalize the above communication game in that both Alice and Bob perform the same but arbitrary (odd) number ($n>3$) of measurements. Based on the optimal quantum value of the relevant Bell expression for any arbitrary $n$, we have also demonstrated device-independent self-testing of state and measurements.

16 pages, 2 figures

References in corpus (11)

• Device-independent security of quantum cryptography against collective attacks
• The uncertainty principle determines the non-locality of quantum mechanics
• Robust Self Testing of the Singlet
• Preparation contextuality powers parity-oblivious multiplexing
• Sum-of-squares decompositions for a family of CHSH-like inequalities and their application to self-testing
• Quantum Random Access Codes using Single $d$-level Systems
• Sharing non-locality and non-trivial preparation contextuality using same family of Bell expressions
• Self-testing properties of Gisin's elegant Bell inequality
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
• Device-independent certification of two bits of randomness from one entangled bit and Gisin's elegant Bell inequality
• Semi-device independent randomness certification using Mermin's proof of Kochen-Specker contextuality

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• Sharing preparation contextuality in Bell experiment by arbitrary pair of sequential observers
• Self-testing of multiple unsharpness parameters through sequential violations of non-contextual inequality
• Optimal quantum violations of n-locality inequalities with conditional dependence on inputs
• SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness