Keyring models: an approach to steerability

Abstract

If a measurement is made on one half of a bipartite system, then, conditioned on the outcome, the other half has a new reduced state. If these reduced states defy classical explanation -- that is, if shared randomness cannot produce these reduced states for all possible measurements -- the bipartite state is said to be steerable. Determining which states are steerable is a challenging problem even for low dimensions. In the case of two-qubit systems a criterion is known for T-states (that is, those with maximally mixed marginals) under projective measurements. In the current work we introduce the concept of keyring models -- a special class of local hidden state models. When the measurements made correspond to real projectors, these allow us to study steerability beyond T-states. Using keyring models, we completely solve the steering problem for real projective measurements when the state arises from mixing a pure two-qubit state with uniform noise. We also give a partial solution in the case when the uniform noise is replaced by independent depolarizing channels.

15(+4) pages, 5 figures. v2: references added, v3: minor changes

References in corpus (12)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Grothendieck's constant and local models for noisy entangled quantum states
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$
• Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
• Nonlocality of a single photon: paths to an EPR-steering experiment
• Most incompatible measurements for robust steering tests
• Adaptive strategy for joint measurements
• Non-separability and steerability of two-qubit states from the geometry of steering outcomes
• Convex separation from convex optimization for large-scale problems

Cited by in corpus (4)

• Quantum Steering
• Algorithmic construction of local models for entangled quantum states: optimization for two-qubit states
• Necessary conditions for steerability of two qubits, from consideration of local operations
• Eventually entanglement breaking divisible quantum dynamics