Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions (2402.07700v5)

Published 12 Feb 2024 in quant-ph, math-ph, and math.MP

Abstract: Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be non-zero. Surprizingly this value turns out to be approximately equal to $0.4$ in all dimensions. Finally we show that, in even dimension, this channel has a decomposition in terms of unitary operations. This is in contrast with the three dimensional case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (50)
  1. Maximal output purity and capacity for asymmetric unital qudit channels. Journal of Physics A: Mathematical and General, 38(45):9785–9802, October 2005.
  2. Graeme Smith. Quantum channel capacities, 2010.
  3. Peter W. Shor. Capacities of quantum channels and how to find them. Mathematical Programming, 97(1):311–335, July 2003.
  4. Quantum capacity analysis of multi-level amplitude damping channels. Communications Physics, 4(1), February 2021.
  5. Provably secure and high-rate quantum key distribution with time-bin qudits. Science Advances, 3(11), November 2017.
  6. Quantum key distribution ford-level systems with generalized bell states. Physical Review A, 65(5), May 2002.
  7. Qudits and high-dimensional quantum computing. Frontiers in Physics, 8, November 2020.
  8. Roadmap on structured light. Journal of Optics, 19(1):013001, nov 2016.
  9. Full spatial characterization of entangled structured photons. Physical Review Letters, 132(6), February 2024.
  10. Time-division multiplexing of the orbital angular momentum of light. Opt. Lett., 37(2):127–129, Jan 2012.
  11. Orbital angular momentum states enabling fiber-based high-dimensional quantum communication. Phys. Rev. Appl., 11:064058, Jun 2019.
  12. Katarzyna Siudzińska. Classical capacity of generalized pauli channels. Journal of Physics A: Mathematical and Theoretical, 53(44):445301, oct 2020.
  13. Quantum parameter estimation of a generalized pauli channel. Journal of Physics A: Mathematical and General, 36(29):8093, jul 2003.
  14. Counterexample to an additivity conjecture for output purity of quantum channels. Journal of Mathematical Physics, 43:4353, 2002.
  15. On birkhoff’s theorem for doubly stochastic completely positive maps of matrix algebras. Linear Algebra and its Applications, 193:107, 1993.
  16. Koenraad M R Audenaert and Stefan Scheel. On random unitary channels. New Journal of Physics, 10(2):023011, February 2008.
  17. Quantum informational properties of the Landau–Streater channel. Journal of Mathematical Physics, 60(4):042202, April 2019.
  18. Realization of the Werner–Holevo and Landau–Streater Quantum Channels for Qutrits on Quantum Computers. Journal of Russian Laser Research, 41(1):40–53, January 2020.
  19. On the mixed-unitary rank of quantum channels. Communications in Mathematical Physics, 394(2):919–951, June 2022.
  20. Additivity for transpose depolarizing channels, 2004.
  21. Thomas P. W. Cope and Stefano Pirandola. Adaptive estimation and discrimination of holevo-werner channels. Quantum Measurements and Quantum Metrology, 4(1), December 2017.
  22. Converse bounds for quantum and private communication over holevo–werner channels. Journal of Physics A: Mathematical and Theoretical, 51(49):494001, November 2018.
  23. The communication value of a quantum channel. IEEE Transactions on Information Theory, 69(3):1660–1679, March 2023.
  24. M M Wolf and J Eisert. Classical information capacity of a class of quantum channels. New Journal of Physics, 7:93–93, April 2005.
  25. Additivity of minimal entropy output for a class of covariant channels, 2004.
  26. KMR Audenaert and S Scheel. On random unitary channels. New Journal of Physics, 10(2):023011, 2008.
  27. Entanglement breaking channels. Reviews in Mathematical Physics, 15(06):629–641, August 2003.
  28. The noisy werner-holevo channel and its properties, 2023.
  29. Degradability of modified landau-streater type low-noise quantum channels in high dimensions, 2024.
  30. I. Devetak and P. W. Shor. The Capacity of a Quantum Channel for Simultaneous Transmission of Classical and Quantum Information. Communications in Mathematical Physics, 256(2):287–303, June 2005.
  31. The structure of degradable quantum channels. Journal of Mathematical Physics, 49(10):102104, October 2008.
  32. Approximate degradable quantum channels. IEEE Transactions on Information Theory, 63(12):7832–7844, December 2017.
  33. Dividing Quantum Channels. Communications in Mathematical Physics, 279(1):147–168, April 2008.
  34. W. Forrest Stinespring. Positive Functions on C * -Algebras. Proceedings of the American Mathematical Society, 6(2):211, April 1955.
  35. Complementarity and Additivity for Covariant Channels. Quantum Information Processing, 5(3):179–207, June 2006.
  36. Selfcomplementary Quantum Channels. Open Systems & Information Dynamics, 23(03):1650014, September 2016.
  37. A survey on quantum channel capacities. IEEE Communications Surveys and; Tutorials, 20(2):1149–1205, 2018.
  38. Quantum capacity of a bosonic dephasing channel. Physical Review A, 102(4):042413, October 2020.
  39. Seth Lloyd. Capacity of the noisy quantum channel. Physical Review A, 55(3):1613–1622, March 1997.
  40. Sending classical information via noisy quantum channels. Physical Review A, 56(1):131–138, July 1997.
  41. Information transmission through a noisy quantum channel. Physical Review A, 57(6):4153–4175, June 1998.
  42. I. Devetak. The private classical capacity and quantum capacity of a quantum channel. IEEE Transactions on Information Theory, 51(1):44–55, January 2005.
  43. Quantum computation and quantum information. Cambridge University Press, Cambridge ; New York, 10th anniversary ed edition, 2010.
  44. M. B. Hastings. Superadditivity of communication capacity using entangled inputs. Nature Physics, 5(4):255–257, April 2009.
  45. Entanglement-Assisted Classical Capacity of Noisy Quantum Channels. Physical Review Letters, 83(15):3081–3084, October 1999.
  46. Entanglement-assisted capacity of a quantum channel and the reverse Shannon theorem. IEEE Transactions on Information Theory, 48(10):2637–2655, October 2002.
  47. A. S. Holevo. Complementary Channels and the Additivity Problem. Theory of Probability & Its Applications, 51(1):92–100, January 2007.
  48. A. S. Holevo. Quantum systems, channels, information: a mathematical introduction. Number 16 in De Gruyter studies in mathematical physics. De Gruyter, Berlin, 2012.
  49. Peter Shor. Quantum error correction, 2002.
  50. William Gordon Ritter. Quantum channels and representation theory. Journal of Mathematical Physics, 46(8), August 2005.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets