Device independent state estimation based on Bell's inequalities
arXiv:0907.2170 · doi:10.1103/PhysRevA.80.062327
Abstract
The only information available about an alleged source of entangled quantum states is the amount by which the Clauser-Horne-Shimony-Holt (CHSH) inequality is violated: nothing is known about the nature of the system or the measurements that are performed. We discuss how the quality of the source can be assessed in this black-box scenario, as compared to an ideal source that would produce maximally entangled states (more precisely, any state for which ). To this end, we introduce several inequivalent notions of fidelity, each one related to the use one can make of the source after having assessed it; and we derive quantitative bounds for each of them in terms of the violation . We also derive a lower bound on the entanglement of the source as a function of only.
8 pages, 2 figures. Added appendices containing proofs
References in corpus (4)
Cited by in corpus (82)
- Bell nonlocality
- Self-testing of quantum systems: a review
- Closing the detection loophole in Bell experiments using qudits
- Robust Self Testing of the Singlet
- Experimentally faking the violation of Bell's inequalities
- Guess your neighbour's input: a multipartite non-local game with no quantum advantage
- Security of practical private randomness generation
- Maximal violation of the I3322 inequality using infinite dimensional quantum systems
- Quantum randomness extraction for various levels of characterization of the devices
- Analytic and nearly optimal self-testing bounds for the Clauser-Horne-Shimony-Holt and Mermin inequalities
- Experimental estimation of the dimension of classical and quantum systems
- Robust Self Testing of Unknown Quantum Systems into Any Entangled Two-Qubit States
- Quantum networks reveal quantum nonlocality
- Physical characterization of quantum devices from nonlocal correlations
- Self-testing quantum states and measurements in the prepare-and-measure scenario
- Device-independent certification of entangled measurements
- Self-testing of binary observables based on commutation
- Device-independent bounds for Hardy's experiment
- Interactive proofs for BQP via self-tested graph states
- Self-testing mutually unbiased bases in the prepare-and-measure scenario
- Semi-device-independent bounds on entanglement
- Asymptotically optimal data analysis for rejecting local realism
- Certifying the building blocks of quantum computers from Bell's theorem
- Self-testing entangled measurements in quantum networks
- Device-independent tomography of multipartite quantum states
- Detection Loophole in Bell experiments: How post-selected local correlations can look non-local
- Nonlocality and entanglement in qubit systems
- Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems
- Bell tests with min-entropy sources
- Device-independent quantum key distribution secure against adversaries with no long-term quantum memory
- Device-Independent Certification of a Nonprojective Qubit Measurement
- Activation of Non-Local Quantum Resources
- Device-Independent Randomness Generation in the Presence of Weak Cross-Talk
- Fully Distrustful Quantum Cryptography
- A framework for the study of symmetric full-correlation Bell-like inequalities
- Bound non-locality and activation
- Self-testing in parallel
- Multipartite fully-nonlocal quantum states
- How device-independent approaches change the meaning of physical theory
- Device-Independent Certification of Genuinely Entangled Subspaces
- Sample-efficient device-independent quantum state verification and certification
- Experimentally Robust Self-testing for Bipartite and Tripartite Entangled States
- Robust self-testing of two-qubit states
- Device-independent quantum key distribution with arbitrarily small nonlocality
- Chained Bell Inequality Experiment with High-Efficiency Measurements
- Certifying entangled measurements in known Hilbert spaces
- Device-independent tests of quantum channels
- Semi-device-independent certification of indefinite causal order
- Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
- Bell tests for continuous variable systems using hybrid measurements and heralded amplifiers
- Bell inequalities for three systems and arbitrarily many measurement outcomes
- A weak form of self-testing
- Realistic loophole-free Bell test with atom-photon entanglement
- Robust Self-Testing of Multiparticle Entanglement
- Self-testing with finite statistics enabling the certification of a quantum network link
- Maximal CHSH violations with low efficiency photodetection and homodyne measurements
- Device-Independent Bit Commitment based on the CHSH Inequality
- Nonlocality of three-qubit Greenberger-Horne-Zeilinger-symmetric states
- Quantum coherence fraction
- Certifying the Topology of Quantum Networks: Theory and Experiment
- Classical command of quantum systems via rigidity of CHSH games
- Multipartite Nonlocality as a Resource and Quantum Correlations Having Indefinite Causal Order
- Device and semi-device independent random numbers based on non-inequality paradox
- Quantum Information Processing with Adversarial Devices
- Revealing Quantum Advantage in a Quantum Network
- Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
- Trade-offs in multi-party Bell inequality violations in qubit networks
- On the inequivalence of the CH and CHSH inequalities due to finite statistics
- Revealing Hidden Genuine Tripartite Nonlocality
- Self-testing two-qubit maximally entangled states from generalized CHSH tests
- What is the minimum CHSH score certifying that a state resembles the singlet?
- Interplay among entanglement, measurement incompatibility, and nonlocality
- Entanglement versus Bell nonlocality of quantum nonequilibrium steady states
- Analysis of a proposal for a realistic loophole-free Bell test with atom-light entanglement
- Analytic Semi-device-independent Entanglement Quantification for Bipartite Quantum States
- Self-testing high dimensional states using the generalized magic square game
- A self-guide method to search maximal Bell violation for unknown quantum states
- Interactive proofs for BQP via self-tested graph states (extended abstract)
- Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
- Composable framework for device-independent state certification
- Tight analytic bound on the trade-off between device-independent randomness and nonlocality
- Maximal device-independent randomness in every dimension