Upper bounds on the private capacity for bosonic Gaussian channels. (English) Zbl 1448.81183
Summary: Recently, there have been considerable progresses on the bounds of various quantum channel capacities for bosonic Gaussian channels. Especially, several upper bounds for the classical capacity and the quantum capacity on the bosonic Gaussian channels, via a technique known as quantum entropy power inequality, have been shed light on understanding the mysterious quantum-channel-capacity problems. However, upper bounds for the private capacity on quantum channels are still missing for the study on certain universal upper bounds. Here, we derive upper bounds on the private capacity for bosonic Gaussian channels involving a general Gaussian-noise case through the conditional quantum entropy power inequality.
MSC:
| 81P47 | Quantum channels, fidelity |
| 81P17 | Quantum entropies |
| 81P40 | Quantum coherence, entanglement, quantum correlations |
| 81P42 | Entanglement measures, concurrencies, separability criteria |
Keywords:
quantum channel capacity; bosonic Gaussian channel; private capacity; quantum entropy power inequalityReferences:
| [1] | Shannon, C. E., A mathematical theory of communication, Bell Syst. Tech. J., 27, 379 (1948) · Zbl 1154.94303 |
| [2] | Nielsen, M. A.; Chuang, I. L., Quantum Computation and Quantum Information (2000), Cambridge University Press · Zbl 1049.81015 |
| [3] | Hayashi, M., Quantum Information Theory: Mathematical Foundation (2016), Springer: Springer New York |
| [4] | Wilde, M. M., Quantum Information Theory (2017), Cambridge University Press · Zbl 1379.81005 |
| [5] | Watrous, J., The Theory of Quantum Information (2018), Cambridge University Press · Zbl 1393.81004 |
| [6] | Holevo, A. S.; Werner, R. F., Evaluating capacities of bosonic Gaussian channels, Phys. Rev. A, 63, Article 032312 pp. (2001) |
| [7] | Weedbrook, C.; Pirandola, S.; García-Patrón, R.; Cerf, N. J.; Ralph, T. C.; Shapiro, J. H.; Lloyd, S., Gaussian quantum information, Rev. Mod. Phys., 84, 621 (2012) |
| [8] | Serafini, A., Quantum Continuous Variables: A Primer of Theoretical Methods (2017), CRC Press: CRC Press London · Zbl 1386.81005 |
| [9] | Lloyd, S., Capacity of the noisy quantum channel, Phys. Rev. A, 55, 1613 (1996) |
| [10] | Devetak, I., The private classical capacity and quantum capacity of a quantum channel, IEEE Trans. Inf. Theory, 51, 44 (2005) · Zbl 1293.94063 |
| [11] | Smith, G.; Renes, J. M.; Smolin, J. A., Structured codes improve the Bennett-Brassard-84 quantum key rate, Phys. Rev. Lett., 100, Article 170502 pp. (2008) |
| [12] | Li, K.; Winter, A.; Zou, X. B.; Guo, G. C., Private capacity of quantum channels is not additive, Phys. Rev. Lett., 103, Article 120501 pp. (2009) |
| [13] | Pirandola, S.; Laurenza, R.; Ottaviani, C.; Banchi, L., Fundamental limits of repeaterless quantum communications, Nat. Commun., 8, Article 15043 pp. (2017) |
| [14] | Pirandola, S.; Braunstein, S. L.; Laurenza, R.; Ottaviani, C.; Cope, T. P.W.; Spedalieri, G.; Banchi, L., Theory of channel simulation and bounds for private communication, Quantum Sci. Technol., 3, Article 035009 pp. (2018) |
| [15] | Christandl, M.; Müller-Hermes, A., Relative entropy bounds on quantum, private and repeater capacities, Commun. Math. Phys., 353, 821 (2017) · Zbl 1366.81084 |
| [16] | Rosati, M.; Mari, A.; Giovannetti, V., Narrow bounds for the quantum capacity of thermal attenuators, Nat. Commun., 9, 4339 (2018) |
| [17] | Sharma, K.; Wilde, M. M.; Adhikari, S.; Takeoka, M., Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels, New J. Phys., 20, Article 063025 pp. (2018) |
| [18] | Noh, K.; Albert, V. V.; Jiang, L., Quantum capacity bounds of Gaussian thermal loss channels and achievable rates with Gottesman-Kitaev-Preskill codes, IEEE Trans. Inf. Theory, 65, 2563 (2019) · Zbl 1431.94100 |
| [19] | Laurenza, R.; Tserkis, S.; Banchi, L.; Braunstein, S. L.; Ralph, T. C.; Pirandola, S., Tight bounds for private communication over bosonic Gaussian channels based on teleportation simulation with optimal finite resources, Phys. Rev. A, 100, Article 042301 pp. (2019) |
| [20] | Noh, K.; Pirandola, S.; Jiang, L., Enhanced energy-constrained quantum communication over bosonic Gaussian channels, Nat. Commun., 11, 457 (2020) |
| [21] | König, R.; Smith, G., The entropy power inequality for quantum systems, IEEE Trans. Inf. Theory, 60, 1536 (2014) · Zbl 1360.81094 |
| [22] | König, R.; Smith, G., Limits on classical communication from quantum entropy power inequalities, Nat. Photon., 7, 142 (2013) |
| [23] | König, R.; Smith, G., Classical capacity of quantum thermal noise channels to within 1.45 Bits, Phys. Rev. Lett., 110, Article 040501 pp. (2013) |
| [24] | De Palma, G.; Mari, A.; Giovannetti, V., A generalization of the entropy power inequality to bosonic quantum systems, Nat. Photon., 8, 958 (2014) |
| [25] | Audenaert, K.; Datta, N.; Ozols, M., Entropy power inequalities for qudits, J. Math. Phys., 57, Article 052202 pp. (2016) · Zbl 1347.81033 |
| [26] | Koenig, R., The conditional entropy power inequality for Gaussian quantum states, J. Math. Phys., 56, Article 022201 pp. (2015) · Zbl 1310.81038 |
| [27] | Jeong, K.; Lee, S.; Jeong, H., Conditional quantum entropy power inequality for d-level quantum systems, J. Phys. A, Math. Theor., 51, Article 145303 pp. (2018) · Zbl 1388.81092 |
| [28] | De Palma, G.; Trevisan, D., The conditional entropy power inequality for bosonic quantum systems, Commun. Math. Phys., 360, 639 (2018) · Zbl 1393.81038 |
| [29] | De Palma, G.; Huber, S., The conditional entropy power inequality for quantum additive noise channels, J. Math. Phys., 59, Article 122201 pp. (2018) · Zbl 1404.81058 |
| [30] | Huber, S.; König, R., Coherent state coding approaches the capacity of non-Gaussian bosonic channels, J. Phys. A, Math. Theor., 51, Article 184001 pp. (2018) · Zbl 1390.81099 |
| [31] | Jeong, K.; Lee, H. H.; Lim, Y., Universal upper bounds for Gaussian information capacity, Ann. Phys., 407, 46 (2019) |
| [32] | Lim, Y.; Lee, S.; Kim, J.; Jeong, K., Upper bounds on the quantum capacity for a general attenuator and amplifier, Phys. Rev. A, 99, Article 052326 pp. (2019) |
| [33] | Jozsa, R., Fidelity for mixed quantum states, J. Mod. Opt., 41, 2315 (1994) · Zbl 0941.81508 |
| [34] | Jeong, K.; Lim, Y., Purification of Gaussian maximally mixed states, Phys. Lett. A, 380, 3607 (2016) |
| [35] | Caruso, F.; Giovannetti, V.; Holevo, A. S., One-mode bosonic Gaussian channels: a full weak-degradability classification, New J. Phys., 8, 310 (2006) |
| [36] | Holevo, A. S., One-mode quantum Gaussian channels: structure and quantum capacity, Probl. Inf. Transm., 43, 1 (2007) · Zbl 1237.94036 |
| [37] | Holevo, A. S., The capacity of the quantum channel with general signal states, IEEE Trans. Inf. Theory, 44, 269 (1998) · Zbl 0897.94008 |
| [38] | Schumacher, B.; Westmoreland, M. D., Sending classical information via noisy quantum channels, Phys. Rev. A, 56, 131 (1997) |
| [39] | Wolf, M. M.; Giedke, G.; Cirac, J. I., Extremality of Gaussian quantum states, Phys. Rev. Lett., 96, Article 080502 pp. (2006) |
| [40] | Giovannetti, V.; Guha, S.; Lloyd, S.; Maccone, L.; Shapiro, J. H., Minimal output entropy of bosonic channels: a conjecture, Phys. Rev. A, 70, Article 032315 pp. (2004) |
| [41] | Giovannetti, V.; Guha, S.; Lloyd, S.; Maccone, L.; Shapiro, J. H.; Yuen, H. P., Classical capacity of the lossy bosonic channel: the exact solution, Phys. Rev. Lett., 92, Article 027902 pp. (2004) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
