Capacity of trace decreasing quantum operations and superadditivity of coherent information for a generalized erasure channel

Abstract

Losses in quantum communication lines severely affect the rates of reliable information transmission and are usually considered to be state-independent. However, the loss probability does depend on the system state in general, with the polarization dependent losses being a prominent example. Here we analyze biased trace decreasing quantum operations that assign different loss probabilities to states and introduce the concept of a generalized erasure channel. We find lower and upper bounds for the classical and quantum capacities of the generalized erasure channel as well as characterize its degradability and antidegradability. We reveal superadditivity of coherent information in the case of the polarization dependent losses, with the difference between the two-letter quantum capacity and the single-letter quantum capacity exceeding $7.197\cdot 10^{-3}$ bit per qubit sent, the greatest value among qubit-input channels reported so far.

16 pages, 5 figures

References in corpus (8)

• The structure of degradable quantum channels
• Unbounded number of channel uses are required to see quantum capacity
• New lower bounds on the non-zero capacity of Pauli Channels
• Extending quantum operations
• Quantum evolution in the stroboscopic limit of repeated measurements
• Sequential measurements of conjugate observables
• Post-processing of quantum instruments
• Experimental observation of coherent-information superadditivity in a dephrasure channel

Cited by in corpus (8)

• Generic nonadditivity of quantum capacity in simple channels
• Exploring super-additivity of coherent information of noisy quantum channels through Genetic algorithms
• Trace decreasing quantum dynamical maps: Divisibility and entanglement dynamics
• Postselected communication over quantum channels
• Multipartite entanglement to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses
• The superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels
• Additivity of quantum capacities in simple non-degradable quantum channels
• Conditional Action and imperfect Erasure of Qubits