Maximal randomness from partially entangled states

Abstract

We investigate how much randomness can be extracted from a generic partially entangled pure state of two qubits in a device-independent setting, where a Bell test is used to certify the correct functioning of the apparatus. For any such state, we first show that two bits of randomness are always attainable both if projective measurements are used to generate the randomness globally or if a nonprojective measurement is used to generate the randomness locally. We then prove that the maximum amount of randomness that can be generated using nonprojective measurements globally is restricted to between approximately 3.58 and 3.96 bits. The upper limit rules out that a bound of four bits potentially obtainable with extremal qubit measurements can be attained. We point out this is a consequence of the fact that nonprojective qubit measurements with four outcomes can only be self-tested to a limited degree in a Bell experiment.

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• Implementation of quantum measurements using classical resources and only a single ancillary qubit
• Device-independent certification of maximal randomness from pure entangled two-qutrit states using non-projective measurements
• Quantifying the intrinsic randomness in sequential measurements
• Tight upper bound of the maximal quantum violation of Gisin's elegant Bell inequality and its application in randomness certification
• Scalable Bell inequalities for graph states of arbitrary prime local dimension and self-testing
• Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks
• Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
• All Real Projective Measurements Can be Self-tested
• Certification of unbounded randomness with arbitrary noise
• Randomness versus Nonlocality in Multi-input and Multi-output Quantum Scenario
• Generalized measurements on qubits in quantum randomness certification and expansion
• Self-testing quantum systems of arbitrary local dimension with minimal number of measurements
• A universal scheme to self-test any quantum state or measurement
• Model-independent inference of quantum interaction from statistics
• Self-testing composite measurements and bound entangled state in a single quantum network
• Certifying Temporal Correlations
• Quantum bounds and device-independent security with rank-one qubit measurements
• Tight analytic bound on the trade-off between device-independent randomness and nonlocality
• Any gate of a quantum computer can be certified device-independently
• Strategies for entanglement distribution in optical fiber networks