Bell tests with min-entropy sources

Abstract

Device independent protocols rely on the violation of Bell inequalities to certify properties of the resources available. The violation of the inequalities are meaningless without a few well-known assumptions. One of these is measurement independence, the property that the source of the states measured in an inequality is uncorrelated from the measurements selected. Since this assumption cannot be confirmed, we consider the consequences of relaxing it and find that the definition chosen is critically important to the observed behavior. Considering a definition that is a bound on the min-entropy of the measurement settings, we find lower bounds on the min-entropy of the seed used to choose the inputs required to deduce any quantum or non-local behavior from a Bell inequality violation. These bounds are significantly more restrictive than the ones obtained by endowing the seed with the further structure of a Santha-Vazirani source. We also outline a procedure for finding tight bounds and study the set of probabilities that can result from relaxing measurement dependence.

12 pages, 3 figures; similar to published version; comments are welcomed

References in corpus (10)

• Device-independent security of quantum cryptography against collective attacks
• Private Randomness Expansion With Untrusted Devices
• Robust Self Testing of the Singlet
• Relaxed Bell inequalities and Kochen-Specker theorems
• Hidden variable models for quantum theory cannot have any local part
• Device-independent certification of entangled measurements
• The effects of reduced "free will" on Bell-based randomness expansion
• Device-Independent Randomness Generation in the Presence of Weak Cross-Talk
• Mermin inequalities for perfect correlations
• A tight Tsirelson inequality for infinitely many outcomes

Cited by in corpus (23)

• Quantum Random Number Generators
• Cosmic Bell Test: Measurement Settings from Milky Way Stars
• A unifying framework for relaxations of the causal assumptions in Bell's theorem
• Arbitrarily small amount of measurement independence is sufficient to manifest quantum nonlocality
• Robust Device-Independent Randomness Amplification with Few Devices
• Maximally nonlocal theories cannot be maximally random
• Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer
• Device-independent randomness extraction for arbitrarily weak min-entropy source
• Measurement-dependent locality beyond i.i.d
• Randomness Requirement on CHSH Bell Test in the Multiple Run Scenario
• Demonstration of Quantum Nonlocality in presence of Measurement Dependence
• Measurement dependent locality
• Limited measurement dependence in multiple runs of a Bell test
• Measurement-dependence cost for Bell nonlocality: causal vs retrocausal models
• Superdeterministic hidden-variables models I: nonequilibrium and signalling
• Device-independent randomness amplification with a single device
• Robust Device Independent Randomness Amplification
• Clauser-Horne Bell test with imperfect random inputs
• Quantum nonlocality in presence of strong measurement dependence
• Explaining quantum correlations through evolution of causal models
• Robust Randomness Amplifiers: Upper and Lower Bounds
• Tight Bound on Randomness for Violating the CHSH Inequality
• Seedless extractors for device-independent quantum cryptography