Complete classification of steerability under local filters and its relation with measurement incompatibility
arXiv:2201.07691 · doi:10.1038/s41467-022-32466-y
Abstract
Quantum steering is the central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another one via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables measurement assemblage (SEO), first proposed to connect the problem of steerability with measurement incompatibility. We provide an efficient method to compute the maximal extractable steerability via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples.
arXiv comment13 pages, 2 figures, comments welcome!
References in corpus (57)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- Three qubits can be entangled in two inequivalent ways
- Concentrating Partial Entanglement by Local Operations
- Bell nonlocality
- Steering, Entanglement, Nonlocality, and the EPR Paradox
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- One-sided Device-Independent Quantum Key Distribution: Security, feasibility, and the connection with steering
- Entanglement monotones
- Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
- Quantum Steering
- Robustness of entanglement
- Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
- Quantum steering: a review with focus on semidefinite programming
- Experimental EPR-Steering of Bell-local States
- Bell's inequalities and density matrices. Revealing hidden nonlocality.
- Observation of one-way Einstein-Podolsky-Rosen steering
- Quantifying Einstein-Podolsky-Rosen steering
- One-way Einstein-Podolsky-Rosen Steering
- Joint Measurability, Einstein-Podolsky-Rosen Steering, and Bell Nonlocality
- An Invitation to Quantum Incompatibility
- Joint measurability of generalized measurements implies classicality
- Inequivalence of entanglement, steering, and Bell nonlocality for general measurements
- Quantum root-mean-square error and measurement uncertainty relations
- Detection of entanglement in asymmetric quantum networks and multipartite quantum steering
- Measurements incompatible in Quantum Theory cannot be measured jointly in any other local theory
- Arbitrarily loss-tolerant Einstein-Podolsky-Rosen steering allowing a demonstration over 1 km of optical fiber with no detection loophole
- One-to-one mapping between steering and joint measurability problems
- How robust is a quantum gate in the presence of noise?
- Genuine hidden quantum nonlocality
- All sets of incompatible measurements give an advantage in quantum state discrimination
- Quantatitive relations between measurement incompatibility, quantum steering, and nonlocality
- Maximal randomness expansion from steering inequality violations using qudits
- Natural Framework for Device-Independent Quantification of Quantum Steerability, Measurement Incompatibility, and Self-Testing
- A Complete Resource Theory of Quantum Incompatibility as Quantum Programmability
- Demonstration of Einstein-Podolsky-Rosen Steering with Enhanced Subchannel Discrimination
- Verifying the quantumness of a channel with an untrusted device
- Robustness of incompatibility for quantum devices
- Experimental Measurement-Device-Independent Quantum Steering and Randomness Generation Beyond Qubits
- Measurement incompatibility and steering are necessary and sufficient for operational contextuality
- Network Quantum Steering
- Continuous variable steering and incompatibility via state-channel duality
- Most incompatible measurements for robust steering tests
- Experimental demonstration of measurement-device-independent measure of quantum steering
- Quantifying Quantumness of Channels Without Entanglement
- Computing secure key rates for quantum key distribution with untrusted devices
- Einstein-Podolsky-Rosen steering: Its geometric quantification and witness
- Quantum steerability: characterization, quantification, superactivation and unbounded amplification
- Super-Activation of Quantum Steering
- Necessary and sufficient condition for contextuality from incompatibility
- Revealing of hidden quantum steerability using local filtering operations
- Distillation of quantum steering
- Robust self-testing of steerable quantum assemblages and its applications on device-independent quantum certification
- Nonlocality, steering and quantum state tomography in a single experiment
- Classification of multipartite entanglement containing infinitely many kinds of states
- Device-independent quantification of measurement incompatibility
- Distillation of genuine tripartite Einstein-Podolsky-Rosen steering
Cited by in corpus (24)
- Quantifying Quantumness of Channels Without Entanglement
- Steering-enhanced quantum metrology using superpositions of noisy phase shifts
- Deep learning the hierarchy of steering measurement settings of qubit-pair states
- Device-independent verification of Einstein-Podolsky-Rosen steering
- Dynamical Landauer Principle: Quantifying Information Transmission by Thermodynamics
- Maxwell's two-demon engine under pure dephasing noise
- Resource Marginal Problems
- Thermodynamic Approach to Quantifying Incompatible Instruments
- Accelerating multipartite entanglement generation in non-Hermitian superconducting qubits
- Dynamical Landauer principle: Thermodynamic criteria of transmitting classical information
- Quantum thermodynamic advantage in work extraction from steerable quantum correlations
- Interplay of nonlocality and incompatibility breaking qubit channels
- Assemblages and steering in general probabilistic theories
- Experimental distillation of tripartite quantum steering with an optimal local filtering operation
- Experimentally ruling out joint reality based on operational completeness
- Locally inaccessible hidden quantum correlations
- Quantum steering ellipsoids and quantum obesity in critical systems
- Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
- Swapping of quantum correlations and the role of local filtering operations
- Resource theory of interactive quantum instruments
- Robustness of tripartite entangled states in passive PT-symmetric qubits
- Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
- General quantum resources providing advantages in work-extraction tasks
- Operational Coherent Measurements with Steering and Randomness