One-to-One Mapping between Steering and Joint Measurability Problems

Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it is known that for th...

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Bibliographic Details
Published in:Physical review letters 2015-12, Vol.115 (23), p.230402-230402, Article 230402
Main Authors: Uola, Roope, Budroni, Costantino, Gühne, Otfried, Pellonpää, Juha-Pekka
Format: Article
Language:English
Subjects:
Criteria
Equivalence
Incompatibility
Inequalities
Ingredients
Joints
Steering
Vices
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Summary:Quantum steering refers to the possibility for Alice to remotely steer Bob's state by performing local measurements on her half of a bipartite system. Two necessary ingredients for steering are entanglement and incompatibility of Alice's measurements. In particular, it is known that for the case of pure states of maximal Schmidt rank the problem of steerability for Bob's assemblage is equivalent to the problem of joint measurability for Alice's observables. We show that such an equivalence holds in general; namely, the steerability of any assemblage can always be formulated as a joint measurability problem, and vice versa. We use this connection to introduce steering inequalities from joint measurability criteria and develop quantifiers for the incompatibility of measurements.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.115.230402