Qubit channels with small correlations

Abstract

We introduce a class of quantum channels with correlations acting on pairs of qubits, where the correlation takes the form of a shift operator onto a maximally entangled state. We optimise the output purity and show that below a certain threshold the optimum is achieved by partially entangled states whose degree of entanglement increases monotonically with the correlation parameter. Above this threshold, the optimum is achieved by the maximally entangled state characterizing the shift. Although, a full analysis can only be done for the 2-norm, both numerical and heuristic arguments indicate that this behavior and the optimal inputs are independent of p>1 when the optimal output purity is measured using the p-norm.

11 pages, 4 figures, 2 tables

References in corpus (18)

• Mixed State Entanglement and Quantum Error Correction
• Entanglement-assisted local manipulation of pure quantum states
• Entanglement enhanced information transmission over a quantum channel with correlated noise
• Quantum Channels with Memory
• Additivity for a class of unital qubit channels
• Entangled states maximize the two qubit channel capacity for some Pauli channels with memory
• Quantum channels with a finite memory
• Quantum entanglement enhances the capacity of bosonic channels with memory
• The trumping relation and the structure of the bipartite entangled states
• Bosonic Memory Channels
• A dynamical model for quantum memory channels
• Entanglement enhanced classical capacity of quantum communication channels with correlated noise in arbitrary dimensions
• Entanglement-enhanced classical capacity of two-qubit quantum channels with memory: the exact solution
• Catalytic majorization and ${\ell }_p$ norms
• Information transmission through lossy bosonic memory channels
• Extending additivity from symmetric to asymmetric channels
• Multiplicativity of the maximal output 2-norm for depolarized Werner-Holevo channels
• Entanglement may enhance the channel capacity in arbitrary dimensions

Cited by in corpus (5)

• Quantum channels and memory effects
• Channel covariance, twirling, contraction, and some upper bounds on the quantum capacity
• On the transitional behavior of quantum Gaussian memory channels
• Spin chain model for correlated quantum channels
• Quantum Finite-Depth Memory Channels: Case Study