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Second-order coding rates for pure-loss bosonic channels

Mark M. Wilde, Joseph M. Renes, Saikat Guha
2015 Quantum Information Processing  
The goal of the present paper is to initiate the study of second-order coding rates for these channels, by beginning with the simplest one, the pure-loss bosonic channel.  ...  pure-loss bosonic channel.  ...  Conclusion The main results of this paper are a one-shot coding theorem for arbitrary pure-state classicalquantum channels and the application of this theorem to determine second-order coding rates for  ... 
doi:10.1007/s11128-015-0997-x fatcat:cmz335x255c3lpv3pom6o7lqoe

Strong converse for the classical capacity of the pure-loss bosonic channel

M. M. Wilde, A. Winter
2014 Problems of Information Transmission  
This paper strengthens the interpretation and understanding of the classical capacity of the pure-loss bosonic channel, first established in [Giovannetti et al., Physical Review Letters 92, 027902 (2004  ...  We then prove that a strong converse theorem holds for the classical capacity of this channel (that such a rate-error trade-off cannot occur) if one instead demands for a maximum photon number constraint  ...  MMW is grateful to the quantum information theory group at the Universitat Autònoma de Barcelona for hosting him for a research visit during April-May 2013, during which some of the work for this research  ... 
doi:10.1134/s003294601402001x fatcat:qp4oitiy7zexdacmm4ohuomlou

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Kyungjoo Noh, Victor V. Albert, Liang Jiang
2019 IEEE Transactions on Information Theory  
Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely.  ...  Gaussian loss channels are of particular importance since they model realistic optical communication channels.  ...  Flammia, Sekhar Tatikonda, Richard Kueng, Linshu Li and Mengzhen Zhang for fruitful discussions. We also thank Mark M. Wilde and Matteo Rosati for useful comments on our manuscript.  ... 
doi:10.1109/tit.2018.2873764 fatcat:nw3h7ttya5d2zerdm6j4vgb7fi

Strong converse rates for classical communication over thermal and additive noise bosonic channels

Bhaskar Roy Bardhan, Mark M. Wilde
2014 Physical Review A. Atomic, Molecular, and Optical Physics  
decomposition of a thermal channel into a pure-loss channel followed by an amplifier channel.  ...  In order for these theorems to hold, we need to impose a maximum photon number constraint on the states input to the channel (the strong converse property need not hold if there is only a mean photon number  ...  Recently, a strong converse theorem has been proved to hold for the classical capacity of the pure-loss bosonic channel [33] .  ... 
doi:10.1103/physreva.89.022302 fatcat:t553drjs6zgstkbhxsemsrxrki

Quantum Computation and Communication in Bosonic Systems [article]

Kyungjoo Noh
2021 arXiv   pre-print
Specifically, I present the benchmark and optimization results of various single-mode bosonic codes against practically relevant excitation loss errors.  ...  I also demonstrate that fault-tolerant bosonic QEC is possible by concatenating a single-mode bosonic code with a multi-qubit error-correcting code.  ...  of bosonic pure-loss channels and First, we show that a bosonic pure-loss channel is degradable or anti-degradable  ... 
arXiv:2103.09445v1 fatcat:x3ldfdikdjcxphgeiyzlviuk3m

Bosonic Dirty Paper Coding [article]

Uzi Pereg
2021 arXiv   pre-print
Furthermore, considering the special case of a pure-loss bosonic channel, we demonstrate that the optimal coefficient for dirty paper coding is not necessarily the MMSE estimator coefficient as in the  ...  Then, we consider the bosonic channel with joint detection, for which the classical results do not apply, and derive a dirty-paper coding lower bound.  ...  For a lossy channel, the noise modê e is in a thermal state τ (N E ), and for a pure-loss channel, in the vacuum state.  ... 
arXiv:2101.00595v3 fatcat:37cj77qswned5ndn6xrw4ura4u

Quantum trade-off coding for bosonic communication

Mark M. Wilde, Patrick Hayden, Saikat Guha
2012 Physical Review A. Atomic, Molecular, and Optical Physics  
Lett. 108, 140501 (2012)], we identified these trade-off rate regions for the pure-loss bosonic channel and proved that they are optimal provided that a longstanding minimum output entropy conjecture is  ...  We also derive a "rule of thumb" for trade-off coding, which determines how to allocate photons in a coding strategy if a large mean photon number is available at the channel input.  ...  Shapiro for reminding us of relevant results [23] . MMW acknowledges the MDEIE (Québec) PSR-SIIRI international collaboration grant.  ... 
doi:10.1103/physreva.86.062306 fatcat:l2mla6p22fgklg52y72tb5i2lu

Majorization Theory Approach to the Gaussian Channel Minimum Entropy Conjecture

Raúl García-Patrón, Carlos Navarrete-Benlloch, Seth Lloyd, Jeffrey H. Shapiro, Nicolas J. Cerf
2012 Physical Review Letters  
A longstanding open problem in quantum information theory is to find the classical capacity of an optical communication link, modeled as a Gaussian bosonic channel.  ...  It has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic Gaussian distribution in phase space.  ...  Unfortunately, both conjectures have escaped a proof for all phase-insensitive channels but the pure-loss one.  ... 
doi:10.1103/physrevlett.108.110505 pmid:22540448 fatcat:ynef73cyfzdujfne4nt7ggrhmi

Key Assistance, Key Agreement, and Layered Secrecy for Bosonic Broadcast Channels [article]

Uzi Pereg, Roberto Ferrara, Matthieu R. Bloch
2021 arXiv   pre-print
We derive an achievable layered-secrecy region for a pure-loss bosonic channel that is formed by the concatenation of two beam splitters.  ...  The confidential capacity region of the pure-loss bosonic broadcast channel is determined, both with and without key assistance, and an achievable region is established for the lossy bosonic broadcast  ...  Then, in the next subsections, we will use those results in order to address the lossy and the pure-loss bosonic broadcast channels.  ... 
arXiv:2105.04033v2 fatcat:2mnk4ka35fg3pf62oldagz4dcq

Hardware-efficient bosonic quantum error-correcting codes based on symmetry operators

Murphy Yuezhen Niu, Isaac L. Chuang, Jeffrey H. Shapiro
2018 Physical Review A  
The χ^(2) binomial code is of special interest because, with m< N identified from channel monitoring, it can correct m-photon loss errors, m-photon gain errors, and (m-1)th-order dephasing errors using  ...  We develop quantum Hamming bounds for photon-loss errors in the code subspaces associated with the χ^(2) parity-check code and the χ^(2) embedded error-correcting code, and we prove that these codes saturate  ...  BC has the lowest code rate, 1/ log 2 (2N ), of our three codes. With channel monitoring that identifies m N, it can correct m-photon loss or gain errors or (m − 1)th-order dephasing errors.  ... 
doi:10.1103/physreva.97.032323 fatcat:csotagu5qfbyrhgzl7t4rcwdem

Performance and structure of single-mode bosonic codes

Victor V. Albert, Kyungjoo Noh, Kasper Duivenvoorden, Dylan J. Young, R. T. Brierley, Philip Reinhold, Christophe Vuillot, Linshu Li, Chao Shen, S. M. Girvin, Barbara M. Terhal, Liang Jiang
2018 Physical Review A  
Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate.  ...  These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon  ...  V.V.A. thanks Misha Guy and the Yale Center for Research Computing for resources and support and acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech.  ... 
doi:10.1103/physreva.97.032346 fatcat:wmhevtsj2zbtrbvhg3mfaf7mfu

Strong Converse for the Classical Capacity of Optical Quantum Communication Channels

Bhaskar Roy Bardhan, Raul Garcia-Patron, Mark M. Wilde, Andreas Winter
2015 IEEE Transactions on Information Theory  
This result is obtained by proving a strong converse theorem for the classical capacity of all phase-insensitive bosonic Gaussian channels, a well-established model of optical quantum communication channels  ...  We establish the classical capacity of optical quantum channels as a sharp transition between two regimes---one which is an error-free regime for communication rates below the capacity, and the other in  ...  [7] , for all entanglementbreaking and Hadamard channels [8] , as well as for pure-loss bosonic channels [9] .  ... 
doi:10.1109/tit.2015.2403840 fatcat:hcczqszo5jaobcfa5ktzva45yq

Trade-offs on number and phase shift resilience in bosonic quantum codes [article]

Yingkai Ouyang, Earl Campbell
2020 arXiv   pre-print
We show that by using arbitrarily many modes, g-gapped multi-mode codes can yield good approximate quantum error correction codes for any finite magnitude of Gaussian dephasing errors.  ...  We revisit rotation-invariant bosonic codes, which are supported on Fock states that are gapped by an integer g apart, and the gap g imparts number shift resilience to these codes.  ...  ACKNOWLEDGEMENTS The authors are grateful to Robert Koenig, Lisa Hänggli, Margret Heinze, and Barbara Terhal for fruitful discussions. YO and EC acknowledge support from the EPSRC (Grant No.  ... 
arXiv:2008.12576v2 fatcat:kj35kkl2rbf2bckeuzhjbw7ab4

Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [article]

Timo Hillmann, Fernando Quijandría, Arne L. Grimsmo, Giulia Ferrini
2021 arXiv   pre-print
Bosonic quantum error-correcting codes offer a viable direction towards reducing the hardware overhead required for fault-tolerant quantum information processing.  ...  A broad class of bosonic codes, namely rotation-symmetric codes, can be characterized by their phase-space rotation symmetry.  ...  An earlier study has shown a theoretical performance advantage of GKP codes over codes that belong to the RSB class [49] for the case of a pure loss noise channel.  ... 
arXiv:2108.01009v1 fatcat:epfjafhpingtzbw7bxv3rdynle

Identification Over Quantum Broadcast Channels [article]

Uzi Pereg, Johannes Rosenberger, Christian Deppe
2022 arXiv   pre-print
Furthermore, the identification capacity region of the single-mode pure-loss bosonic broadcast channel is obtained as a consequence.  ...  This relaxation allows for a double-exponential code size.  ...  Acknowledgments The authors wish to thank Roberto Ferrara (Technical University of Munich) for useful discussions.  ... 
arXiv:2201.11056v2 fatcat:75xfg6mf5bbdla4ukdzx6nzdbe
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