Super-Activation of Quantum Steering

Abstract

We consider Einstein-Podolsky-Rosen steering in the regime where the parties can perform collective measurements on many copies of a given shared entangled state. We derive a simple and efficient condition for guaranteeing that an entangled state is $k$-copy steerable. In particular we show that any two-qubit and qubit-qutrit entangled states is $k$-copy steerable. This allows us to discuss the effect of super-activation of steering, whereby an entangled state that is unsteerable (i.e., admits a local hidden state model) in the one-copy regime becomes $k$-copy steerable. We provide examples with few copies and low dimensions. Our results give evidence that entanglement and steering could become equivalent in the multi-copy regime.

8 pages, 1 figure

References in corpus (16)

• Entanglement detection
• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Distillation of secret key and entanglement from quantum states
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Disproving the Peres conjecture: Bell nonlocality from bipartite bound entanglement
• Noise robustness of the nonlocality of entangled quantum states
• Non-locality distillation and post-quantum theories with trivial communication complexity
• Steering bound entangled states: A counterexample to the stronger Peres conjecture
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Local hidden--variable models for entangled quantum states
• Distilling Non-Locality
• All quantum states useful for teleportation are nonlocal resources
• Bound non-locality and activation
• Quantum steerability: characterization, quantification, superactivation and unbounded amplification
• Better Bell Inequality Violation by Collective Measurements

Cited by in corpus (13)

• Network Quantum Steering
• Semi-device-independent certification of entanglement in superdense coding
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Work extraction and fully entangled fraction
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• Estimating many properties of a quantum state via quantum reservoir processing
• Witnessing network steerability of every bipartite entangled state without inputs
• On fully entangled fraction and quantum conditional entropies for states with maximally mixed marginals
• General quantum resources providing advantages in work-extraction tasks
• Entanglement Superactivation in Multiphoton Distillation Networks
• Certifying the activation of Bell nonlocality with finite data
• Static and dynamic coherence fraction in the Bernstein-Vazirani algorithm