| Einstein–Podolsky–Rosen steering | |
|---|---|
| Name | Einstein–Podolsky–Rosen steering |
| Discovered | 1935 (conceptual), formalized 2007 (modern criteria) |
| Discoverer | Einstein, Podolsky, Rosen (EPR paradox); formalization by Howard Wiseman, Stephen Jones and Andrew Doherty |
| Field | quantum mechanics |
Einstein–Podolsky–Rosen steering
Einstein–Podolsky–Rosen steering (commonly abbreviated EPR steering or simply steering) is a form of quantum nonlocality in which one party, by performing local measurements on their subsystem of an entangled state, can nonclassically affect the set of conditional states of another distant party. It occupies an intermediate position between quantum entanglement and Bell nonlocality, with operational significance for asymmetric tasks such as one-sided device-independent quantum cryptography. Steering matters because it formalizes the original EPR paradox concerns about completeness of quantum theory while providing practical resources for secure quantum protocols.
The term "steering" traces to the 1935 EPR paper by Einstein, Podolsky and Rosen and later discussion by Schrödinger who used the verb "steer" to describe remote state preparation via entanglement. For decades steering remained largely conceptual until rigorous criteria and operational definitions were introduced in the 2000s. The modern formalization due to Howard Wiseman, Stephen Jones and Andrew Doherty (2007) established steering as a distinct class of nonlocal correlations, prompting experimental tests in photonic systems by groups at institutions such as the University of Queensland, University of Waterloo, and NIST. Steering connects foundational debates on locality and realism with contemporary developments in quantum information science and quantum technologies.
Formally, steering is defined with respect to two parties, traditionally named Alice and Bob, who share a bipartite quantum state ρ_AB on Hilbert spaces H_A ⊗ H_B. Alice's choice of measurement x yielding outcome a produces an unnormalized conditional state (an assemblage) σ_{a|x} = Tr_A[(M_{a|x} ⊗ I) ρ_AB], where {M_{a|x}} are Alice's measurement operators. A state is unsteerable from Alice to Bob if the assemblage admits a local-hidden-state (LHS) model: σ_{a|x} = ∑_λ p(λ) p(a|x,λ) ρ_λ, with classical variable λ and local quantum states ρ_λ on Bob's side. Violation of any LHS decomposition indicates steerability. Mathematical tools used include semidefinite programming (SDP), convex geometry, and entropic or variance-based inequalities. Steering can be asymmetric: ρ_AB may be steerable from Alice to Bob but not vice versa, a feature linked to mixedness and local dimensions.
EPR steering sits between entanglement and Bell nonlocality in the hierarchy of quantum correlations: Bell nonlocal states are steerable, and steerable states are entangled, but converses do not hold in general. The hierarchy was clarified in the formal work of Wiseman et al. and has been illustrated by families of states such as Werner states introduced by Werner. Entanglement criteria (e.g., the PPT criterion by Peres and Horodecki family) detect separability but do not directly certify steering. Conversely, violation of a steering inequality implies entanglement even when Bell inequalities are not violated. Steering is also conceptually tied to quantum steering ellipsoids, measures such as steerable weight, and steering robustness, which quantify the degree of steerability.
Experimental demonstrations began with optical implementations using SPDC sources of entangled photons and homodyne detection in continuous-variable systems. Notable experiments were reported by groups led by Paul Kwiat, Nicolas Gisin, and teams at the Vienna and various institutions. Detection criteria used in experiments include linear steering inequalities, Reid’s criterion for continuous-variable quadratures (following Reid), and steering witnesses based on semidefinite programs. Recent platforms extend to trapped ions, superconducting qubits, and atomic ensembles, enabling tests of asymmetric steering, multipartite steering, and steering in noisy or lossy channels relevant for realistic quantum networks.
Steering has operational roles in quantum information tasks that exploit asymmetric trust. In one-sided device-independent quantum key distribution (1sDI-QKD), only one party's devices are trusted, and steering correlations provide security proofs against certain attacks, linking to work by Acín and collaborators. Steering is also applied in entanglement certification with untrusted devices, subchannel discrimination, randomness generation, and quantum metrology where remotely prepared states improve sensitivity. Integration with quantum networks implicates institutions like ESA and programs in quantum communication satellites, where steering resilience to loss is an active engineering concern.
Open theoretical directions include tight characterization of steerability for general mixed states and high-dimensional systems, resource theories of steering, and relations to quantum channel discrimination. Challenges remain in deriving complete sets of steering inequalities for multipartite scenarios and studying dynamics of steering under decoherence and non-Markovian noise. Connections between steering and quantum causal models, as well as potential thermodynamic signatures of steerability, are under investigation. Ongoing experimental development focuses on loophole-free steering demonstrations, integration into scalable quantum networks, and leveraging steering for practical cryptographic systems in collaboration among universities, national labs, and industry partners.
Category:Quantum mechanics Category:Quantum information theory Category:Foundations of quantum mechanics