Structural physical approximations of unphysical maps and generalized quantum measurements

Abstract

We investigate properties of the structural physical approximation (SPA) of the partial transposition map recently introduced by Horodecki and Ekert [quant-ph/0111064]. We focus on the case of two-qubit states and show that in this case the map has the structure of a generalized quantum measurement followed by preparation of a suitable output state. We also introduce SPA for map that transforms two copies of density matrix of a single qubit onto a square of that matrix. We prove that also this map is essentially a generalized quantum measurement.

4 pages, RevTeX 4

References in corpus (9)

• Tomography of Quantum Operations
• Direct detection of quantum entanglement
• The no-signaling condition and quantum dynamics
• A fidelity measure for quantum channels
• Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
• Continuous-variable Werner state: separability, nonlocality, squeezing and teleportation
• Extremal equation for optimal completely-positive maps
• Quantum Operations, State Transformations and Probabilities
• Enhanced Estimation of a Noisy Quantum Channel Using Entanglement

Cited by in corpus (22)

• Quantum entanglement
• Generation and control of Greenberger-Horne-Zeilinger entanglement in superconducting circuits
• Universal observable detecting all two-qubit entanglement and determinant based separability tests
• Structural approximations to positive maps and entanglement breaking channels
• Noiseless Quantum Circuits for the Peres Separability Criterion
• Physical Implementability of Linear Maps and Its Application in Error Mitigation
• Deep learning of quantum entanglement from incomplete measurements
• Realizing Physical Approximation of the Partial Transpose
• Designing Quantum Information Processing via Structural Physical Approximation
• On structural physical approximations and entanglement breaking maps
• The structural physical approximations and optimal entanglement witnesses
• Sufficient separability criteria and linear maps
• Experimental Implementation of the Universal Transpose Operation
• Structural physical approximations and entanglement witnesses
• Structural Physical Approximation make possible to realize the optimal singlet fraction with two measurements
• Inferring superposition and entanglement from measurements in a single basis
• Physical realization of realignment criteria using structural physical approximation
• Experimental Virtual Quantum Broadcasting
• Linear maps as sufficient criteria for entanglement depth and compatibility in many-body systems
• Guaranteeing Completely Positive Quantum Evolution
• Agnostic Process Tomography
• Can Quantum Entanglement Detection Schemes Improve Search?