Simulating quantum correlations as a distributed sampling problem

Abstract

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, post-selection or non-local boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a non-local box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.

13 pages, 2 figures

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• Bell nonlocality
• Non-locality and Communication Complexity
• Bilocal versus non-bilocal correlations in entanglement swapping experiments
• Relaxed Bell inequalities and Kochen-Specker theorems
• Rethinking Superdeterminism
• Genuine hidden quantum nonlocality
• Local hidden--variable models for entangled quantum states
• Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics
• Bounds on Quantum Correlations in Bell Inequality Experiments
• On the local and non-local content of bipartite qubit and qutrit correlations
• Relaxed Bell Inequalities with Arbitrary Measurement Dependence for Each Observer
• On the power of non-local boxes
• Correlations of entangled quantum states cannot be classically simulated
• Simulation of bipartite qudit correlations
• Classical communication cost of quantum steering
• A formalism for steering with local quantum measurements
• Practical measurement-device-independent entanglement quantification
• Classical Cost of Transmitting a Qubit
• Measurement-dependence cost for Bell nonlocality: causal vs retrocausal models
• A Toy Model for Local and Deterministic Wave-function Collapse
• Bell inequalities, Counterfactual Definiteness and Falsifiability
• Quantum steering beyond instrumental causal networks
• Simulating Quantum Correlations with Finite Communication
• Lack of measurement independence can simulate quantum correlation even when signaling cannot
• On Dimension Bounds for Auxiliary Quantum Systems
• Bell-type inequalities for non-local resources
• Remote Sampling with Applications to General Entanglement Simulation
• Neural Network Approach to the Simulation of Entangled States with One Bit of Communication
• Local simulation of singlet statistics for restricted set of measurement
• Information Causality is a Special Point in the Dual of the Gray-Wyner Region
• The minimal communication cost for simulating entangled qubits
• Bell Correlations and the Common Future
• One Sided indeterminism alone is not a useful resource to simulate any nonlocal correlation
• Entanglement-swapping boxes and their communication properties
• Non-Local Box Complexity and Secure Function Evaluation
• Classical counterexample to Bell's theorem
• Leggett's theorem without inequalities
• Correlations, Bell Inequality Violation & Quantum Entanglement
• Entanglement-redistribution boxes
• Beating one bit of communication with quantum correlations in smaller dimensions
• High-performance parallel classical scheme for simulating shallow quantum circuits
• Maximal violation of Bell inequalities under local filtering
• Investigation of quantum entanglement simulation by random variables theories augmented by either classical communication or nonlocal effects
• Universal Bell Correlations Do Not Exist