Bounding the quantum capacity with flagged extensions

Farzad Kianvash; Marco Fanizza; Vittorio Giovannetti

doi:10.22331/q-2022-02-09-647

Bounding the quantum capacity with flagged extensions

Farzad Kianvash¹, Marco Fanizza^1,2, and Vittorio Giovannetti¹

¹NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
²Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) Spain

Published:	2022-02-09, volume 6, page 647
Eprint:	arXiv:2008.02461v2
Doi:	https://doi.org/10.22331/q-2022-02-09-647
Citation:	Quantum 6, 647 (2022).

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Abstract

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 application is a bound on the quantum $Q$ and private $P$ capacities of any channel being a mixture of a unitary map and another channel, with the probability associated to the unitary component being larger than $1/2$. We then specialize our sufficient conditions to flagged Pauli channels, obtaining a family of upper bounds on quantum and private capacities of Pauli channels. In particular, we establish new state-of-the-art upper bounds on the quantum and private capacities of the depolarizing channel, BB84 channel and generalized amplitude damping channel. Moreover, the flagged construction can be naturally applied to tensor powers of channels with less restricting degradability conditions, suggesting that better upper bounds could be found by considering a larger number of channel uses.

Popular summary

Quantum information can be protected from noise by encoding it in logical qubits. For several fundamental noise models in discrete variables, such as thermal attenuation and depolarizing noise, the optimal ratio of logical versus physical qubits (quantum capacity) is not known. We improve the upper bounds on the quantum capacity by constructing less noisy channels, where information on the noise acting is encoded in an auxiliary quantum register, and for which the quantum capacity can be computed.

► BibTeX data

@article{Kianvash2022boundingquantum,
  doi = {10.22331/q-2022-02-09-647},
  url = {https://doi.org/10.22331/q-2022-02-09-647},
  title = {Bounding the quantum capacity with flagged extensions},
  author = {Kianvash, Farzad and Fanizza, Marco and Giovannetti, Vittorio},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {647},
  month = feb,
  year = {2022}
}

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Cited by

[1] Felix Leditzky, Debbie Leung, Vikesh Siddhu, Graeme Smith, and John A. Smolin, "Generic Nonadditivity of Quantum Capacity in Simple Channels", Physical Review Letters 130 20, 200801 (2023).

[2] Stefano Chessa and Vittorio Giovannetti, "Resonant Multilevel Amplitude Damping Channels", Quantum 7, 902 (2023).

[3] Abbas Poshtvan and Vahid Karimipour, "Capacities of the covariant Pauli channel", Physical Review A 106 6, 062408 (2022).

[4] Shayan Roofeh and Vahid Karimipour, "Noisy Werner-Holevo channel and its properties", Physical Review A 109 5, 052620 (2024).

[5] Josu Etxezarreta Martinez, Antonio deMarti iOlius, and Pedro M. Crespo, "Superadditivity effects of quantum capacity decrease with the dimension for qudit depolarizing channels", Physical Review A 108 3, 032602 (2023).

[6] Chengkai Zhu, Chenghong Zhu, and Xin Wang, "Estimate Distillable Entanglement and Quantum Capacity by Squeezing Useless Entanglement", IEEE Journal on Selected Areas in Communications 42 7, 1850 (2024).

[7] Vahid Karimipour, "Noisy Landau-Streater and Werner-Holevo channels in arbitrary dimensions", Physical Review A 110 2, 022424 (2024).

[8] Marco Fanizza, Raffaele Salvia, and Vittorio Giovannetti, "Testing identity of collections of quantum states: sample complexity analysis", Quantum 7, 1105 (2023).

[9] Marco Fanizza, Farzad Kianvash, and Vittorio Giovannetti, "Estimating Quantum and Private Capacities of Gaussian Channels via Degradable Extensions", Physical Review Letters 127 21, 210501 (2021).

[10] Seid Koudia, Angela Sara Cacciapuoti, Kyrylo Simonov, and Marcello Caleffi, "How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation", arXiv:2108.07108, (2021).

[11] Mingrui Jing, Chengkai Zhu, and Xin Wang, "Circuit Knitting Faces Exponential Sampling Overhead Scaling Bounded by Entanglement Cost", arXiv:2404.03619, (2024).

[12] Shayan Roofeh and Vahid Karimipour, "Phase Transition in the Quantum Capacity of Quantum Channels", arXiv:2408.05733, (2024).

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