The geometry of the Einstein--Podolsky--Rosen correlations

Abstract

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications like quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalise their argument, Schrödinger subsequently introduced the notion of quantum steering. Still, the question which quantum states can be used for the EPR argument and which not remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-$\frac{1}{2}$ particles, this approach completely characterises the set of states leading to the EPR argument and consequently to a full description of the quantum correlations that can be used for steering. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question which observables in quantum mechanics are jointly measurable.

arXiv commentupdated to match the published version; comments are very welcome!

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Cited by in corpus (27)

• Quantum Steering
• Incompatible measurements in quantum information science
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• Operational nonclassicality in minimal autonomous thermal machines
• Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail to do so
• Reliable experimental certification of one-way Einstein-Podolsky-Rosen steering
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Contextuality as a Precondition for Quantum Entanglement
• Compatibility of Generalized Noisy Qubit Measurements
• One-way Einstein-Podolsky-Rosen steering beyond qubits
• Quantum steering of Bell-diagonal states with generalized measurements
• Shareability of steering in 2-producible states
• Necessary conditions for steerability of two qubits, from consideration of local operations
• Measuring network quantum steerability utilizing artificial neural networks
• On the power of one pure steered state for EPR-steering with a pair of qubits
• Assemblages and steering in general probabilistic theories
• Cost of Simulating Entanglement in Steering Scenario
• Scalable multiparty steering based on a single pair of entangled qubits
• Weak entanglement improves quantum communication using only product measurements
• Necessary and sufficient criterion of steering for two-qubit T states
• Demonstration that Einstein-Podolsky-Rosen steering requires more than one bit of faster-than-light information transmission
• Preparation of quantum correlations assisted by a steering Maxwell demon
• Certifying the activation of Bell nonlocality with finite data
• On compatibility of binary qubit measurements
• Protection of quantum steering ellipsoids in non-Markovian environments
• Asymmetric steerability of quantum equilibrium and nonequilibrium steady states through entanglement detection
• Cyclic Einstein-Podolsky-Rosen Steering