Structural approximations to positive maps and entanglement breaking channels

Abstract

Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.

18 pages, 3 figures

References in corpus (42)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Separability criterion and inseparable mixed states with positive partial transposition
• Scalable multi-particle entanglement of trapped ions
• Bell Inequalities and the Separability Criterion
• Unextendible Product Bases and Bound Entanglement
• Optimization of entanglement witnesses
• General Entanglement Breaking Channels
• Witnessing multipartite entanglement
• Entanglement Measures under Symmetry
• Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
• Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
• Detection of entanglement with few local measurements
• Direct detection of quantum entanglement
• Schmidt number witnesses and bound entanglement
• Optimal spin squeezing inequalities detect bound entanglement in spin models
• Distillability and partial transposition in bipartite systems
• Entropic uncertainty relations and entanglement
• Spin squeezing inequalities and entanglement of $N$ qubit states
• Experimental Detection of Entanglement with Polarized Photons
• Four Photon Entanglement from Down Conversion
• Optimal entanglement criterion for mixed quantum states
• Characterization of separable states and entanglement witnesses
• An observable entanglement measure for unknown mixed quantum states
• Estimating the spectrum of a density operator
• "Interaction-Free" Imaging
• Noise robustness of the nonlocality of entangled quantum states
• Nonlinear entanglement witnesses
• Measuring Multipartite Concurrence with a Single Factorizable Observable
• Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment
• Genuine three-partite entangled states with a local hidden variable model
• Measuring the entanglement of bipartite pure states
• Entanglement in SO(3)-invariant bipartite quantum systems
• Optimal estimation of two-qubit pure-state entanglement
• On multipartite invariant states I. Unitary symmetry
• Structural physical approximations of unphysical maps and generalized quantum measurements
• A class of positive atomic maps
• Separability, entanglement and full families of commuting normal matrices
• SLOCC Convertibility between Two-Qubit States
• On multipartite invariant states II. Orthogonal symmetry
• A general scheme for construction of scalar separability criteria from positive maps
• Entanglement of positive definite functions on compact groups

Cited by in corpus (57)

• Entanglement detection
• Entanglement witnesses: construction, analysis and classification
• Cones of positive maps and their duality relations
• Bipartite depolarizing channels
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Constructing new optimal entanglement witnesses
• A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces
• Facial structures for various notions of positivity and applications to the theory of entanglement
• Free versus Bound Entanglement: Machine learning tackling a NP-hard problem
• Realizing Physical Approximation of the Partial Transpose
• One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps
• Optimality for indecomposable entanglement witnesses
• Public and private resource trade-offs for a quantum channel
• Constructing optimal entanglement witnesses. II
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• Entanglement Witness $2.0$: Compressed/Mirrored Entanglement Witnesses
• A characterization of optimal entanglement witnesses
• Optimal decomposable witnesses without the spanning property
• Optimal entanglement witnesses from generalized reduction and Robertson maps
• Optimal approximate transpose map via quantum designs and its applications to entanglement detection
• On structural physical approximations and entanglement breaking maps
• Designing Quantum Information Processing via Structural Physical Approximation
• A class of exposed indecomposable positive maps
• Non-classical correlations in quantum mechanics and beyond
• The structural physical approximations and optimal entanglement witnesses
• Sufficient separability criteria and linear maps
• Positive maps and trace polynomials from the symmetric group
• Experimental Implementation of the Universal Transpose Operation
• Geometric representation of two-qubit entanglement witnesses
• Entanglement witnesses arising from Choi type positive linear maps
• Structural physical approximations and entanglement witnesses
• Exposedness of Choi type entanglement witnesses and applications to lengths of separable states
• Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts
• Separability in terms of a single entanglement witness
• Norms and Cones in the Theory of Quantum Entanglement
• Checking the optimality of entanglement witnesses: an application to structural physical approximations
• Almost complete solution for the NP-hard separability problem of Bell diagonal qutrits
• Analysis of complete positivity conditions for quantum qutrit channels
• Disproving the conjecture on structural physical approximation to optimal decomposable entanglement witnesses
• Structural Physical Approximation make possible to realize the optimal singlet fraction with two measurements
• From Entanglement Witness to Generalized Catalan Numbers
• On the structure of mirrored operators obtained from optimal entanglement witnesses
• Constructing all entanglement witnesses from density matrices
• Recurrent construction of optimal entanglement witnesses for 2N qubit systems
• Geometry of entanglement witnesses parameterized by SO(3) group
• Physical realization of realignment criteria using structural physical approximation
• Bipartite Bound Entanglement
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Experimental Virtual Quantum Broadcasting
• Structured Negativity: A physically realizable measure of entanglement based on structural physical approximation
• A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist
• Extremal entanglement witnesses
• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Guaranteeing Completely Positive Quantum Evolution
• Agnostic Process Tomography
• The Origin of Separable States and Separability Criteria from Entanglement-breaking Channels
• Entanglement Meter: Estimation of entanglement with single copy in Interferometer