Operational characterization of quantumness of unsteerable bipartite states

Abstract

Recently, the quantumness of local correlations arising from separable states in the context of a Bell scenario has been studied and linked with superlocality [Phys. Rev. A {\bf 95}, 032120 (2017)]. Here we investigate the quantumness of unsteerable correlations in the context of a given steering scenario. Generalizing the concept of superlocality, we define as \textit{super-correlation}, the requirement for a larger dimension of the preshared randomness to simulate the correlations than that of the quantum states that generate them. Since unsteerable states form a subset of Bell local states, it is an interesting question whether certain unsteerable states can be super-correlated. Here, we answer this question in the affirmative. In particular, the quantumness of certain unsteerable correlations can be pointed out by the notion of \textit{super-unsteerability}, the requirement for a larger dimension of the classical variable that the steering party has to preshare with the trusted party for simulating the correlations than that of the quantum states which reproduce them. This provides a generalized approach to quantify the quantumness of unsteerable correlations in convex operational theories.

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References in corpus (15)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• No-local-broadcasting theorem for quantum correlations
• The Communication Cost of Simulating Bell Correlations
• Joint measurability of generalized measurements implies classicality
• Logical Bell Inequalities
• Einstein-Podolsky-Rosen steering and the steering ellipsoid
• Fine-grained EPR-steering inequalities
• Analog of the Clauser-Horne-Shimony-Holt inequality for steering
• Quantum steering ellipsoids, extremal physical states and monogamy
• Optimal Measurements for Tests of EPR-Steering with No Detection Loophole using Two-Qubit Werner States
• Cost of Einstein-Podolsky-Rosen steering in the context of extremal boxes
• Nonclassicality of local bipartite correlations

Cited by in corpus (9)

• Ability of unbounded pairs of observers to achieve quantum advantage in random access codes with a single pair of qubits
• Superunsteerability as a quantifiable resource for random access codes assisted by Bell-diagonal states
• Operational nonclassicality of local multipartite correlations in the limited-dimensional simulation scenario
• Asymmetric One-Sided Semi-Device-Independent Steerability of Quantum Discordant States
• Characterization of the quantumness of unsteerable tripartite correlations
• Certifying quantumness beyond steering and nonlocality and its implications on quantum information processing
• Local-hidden-state models for T-states using finite shared randomness
• Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
• Contextuality, superlocality and nonclassicality of supernoncontextuality