# Positivity and Nonadditivity of Quantum Capacities Using Generalized Erasure Channels

@article{Siddhu2021PositivityAN, title={Positivity and Nonadditivity of Quantum Capacities Using Generalized Erasure Channels}, author={Vikesh Siddhu and Robert B. Griffiths}, journal={IEEE Transactions on Information Theory}, year={2021}, volume={67}, pages={4533-4545} }

We consider various forms of a process, which we call <italic>gluing</italic>, for combining two or more complementary quantum channel pairs <inline-formula> <tex-math notation="LaTeX">$({\mathcal B}, {\mathcal C})$ </tex-math></inline-formula> to form a composite. One type of gluing combines a perfect channel with a second channel to produce a <italic>generalized erasure channel</italic> pair <inline-formula> <tex-math notation="LaTeX">$({\mathcal B}_{g}, {\mathcal C}_{g})$ </tex-math></inline…

## 9 Citations

Log-singularities for studying capacities of quantum channels.

- Computer Science
- 2020

A small linear increase from zero in some eigenvalue of a density operator makes the derivative of its von-Neumann entropy logarithmic, a $\log$-singularity, and methods for checking non-additivity and positivity of the coherent information of a noisy quantum channel are developed.

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

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2021

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 platypus of the quantum channel zoo

- Computer ScienceArXiv
- 2022

It is shown that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

Entropic singularities give rise to quantum transmission

- PhysicsNature communications
- 2021

This work shows non-additivity in a simple low-noise channel and proves a general theorem concerning positivity of a channel’s coherent information, and shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information.

Bounding quantum capacities via partial orders and complementarity

- Computer Science
- 2022

This work gives operationally motivated bounds on several capacities, including the quantum capacity and private capacity of a quantum channel and the one-way distillable entanglement and private key of a Quantum state, in terms of capacity quantities involving the complementary channel or state.

Multiletter codes to boost superadditivity of coherent information in quantum communication lines with polarization dependent losses

- Computer Science
- 2021

This work shows that in the asymptotic limit of the infinite code length the superadditivity phenomenon takes place whenever the communication channel is neither degradable nor antidegradable, and provides a method how to modify the proposed codes and get a higher quantum communication rate by doubling the code length.

Quantum capacity and codes for the bosonic loss-dephasing channel

- Physics
- 2022

Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source…

Leaking information to gain entanglement.

- Physics
- 2020

Entanglement lies at the root of quantum theory. It is a remarkable resource that is generally believed to diminish when entangled systems interact with their environment. On the contrary, we find…

Bounding the quantum capacity with flagged extensions

- MathematicsQuantum
- 2022

In this article we consider flagged extensions of convex combination of quantum channels, and find general sufficient conditions for the degradability of the flagged extension. An immediate…

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