Bipartite depolarizing channels

Abstract

We introduce a 3-parameter class of maps acting on a bipartite system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that alternatively determine a positive, completely positive, entanglement-breaking or entanglement-annihilating map. This model displays a much richer behaviour than the one shown by a simple depolarizing channel, yet it stays exactly solvable. As an example of this richness, PPT but not entanglement-breaking maps are found. A simple example of a positive yet indecomposable map is provided. Then, the study of the entanglement-annihilating property is fully addressed. Finally, we apply our results to solve the problem of the entanglement annihilation caused in a bipartite system by a tensor product of local depolarizing channels. In this context, a conjecture recently posed in the literature is proven, and many related open questions are answered. To arrive at this result we furthermore show how the Hadamard product between quantum states can be implemented via local operations.

18 pages, 3 figures

References in corpus (10)

• Entanglement detection
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Structural approximations to positive maps and entanglement breaking channels
• Purification of genuine multipartite entanglement
• Bound entanglement provides convertibility of pure entangled states
• Class of PPT bound entangled states associated to almost any set of pure entangled states
• Entanglement-annihilating and entanglement-breaking channels
• On multipartite invariant states I. Unitary symmetry
• Evaluating the geometric measure of multiparticle entanglement
• PPT-inducing, distillation-prohibiting, and entanglement-binding quantum channels

Cited by in corpus (17)

• Overcoming Noise in Entanglement Distribution
• Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation
• Genuine-multipartite entanglement criteria based on positive maps
• High-Dimensional Entanglement in States with Positive Partial Transposition
• When Do Composed Maps Become Entanglement Breaking?
• One-shot entanglement distillation beyond local operations and classical communication
• On contraction coefficients, partial orders and approximation of capacities for quantum channels
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• Bounding entanglement dimensionality from the covariance matrix
• Absolutely separating quantum maps and channels
• Positive tensor products of qubit maps and n-tensor-stable positive qubit maps
• Positive maps and trace polynomials from the symmetric group
• Eventually entanglement breaking Markovian dynamics: structure and characteristic times
• Entanglement Breaking Rank and the existence of SIC POVMs
• Quantum informational properties of the Landau-Streater channel
• Decomposability of Linear Maps under Tensor Products
• Superior resilience of non-Gaussian entanglement against local Gaussian noises