Device-independent characterizations of a shared quantum state independent of any Bell inequalities

Abstract

In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out {that} a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two device-independent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to {bound} the underlying Hilbert space dimension. Second, when the {Hilbert space dimension bound} is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.

arXiv comment5 pages, 1 figure

References in corpus (16)

• No Signalling and Quantum Key Distribution
• From Bell's Theorem to Secure Quantum Key Distribution
• Testing the Hilbert space dimension
• Device-independent tests of classical and quantum dimensions
• A self-testing quantum random number generator
• Device-independent entanglement quantification and related applications
• Maximal violation of the I3322 inequality using infinite dimensional quantum systems
• Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
• Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
• Interconversion of Nonlocal Correlations
• Continuity bounds for entanglement
• Device-independent parallel self-testing of two singlets
• Device-Independent Tests of Entropy
• Minimum Dimension of a Hilbert Space Needed to Generate a Quantum Correlation
• Measurement-device-independent quantification of entanglement for given Hilbert space dimension
• Device-independent dimension tests in the prepare-and-measure scenario

Cited by in corpus (5)

• Nonclassicality of local bipartite correlations
• Operational characterization of quantumness of unsteerable bipartite states
• Family of Bell inequalities violated by higher-dimensional bound entangled states
• Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
• Device-independent dimension test in a multiparty Bell experiment