Quantum trade-off coding for bosonic communication

Abstract

The trade-off capacity region of a quantum channel characterizes the optimal net rates at which a sender can communicate classical, quantum, and entangled bits to a receiver by exploiting many independent uses of the channel, along with the help of the same resources. Similarly, one can consider a trade-off capacity region when the noiseless resources are public, private, and secret key bits. In [Phys. Rev. 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 true. Additionally, we showed that the performance gains of a trade-off coding strategy when compared to a time-sharing strategy can be quite significant. In the present paper, we provide detailed derivations of the results announced there, and we extend the application of these ideas to thermalizing and amplifying bosonic channels. 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. Our results on the amplifying bosonic channel also apply to the "Unruh channel" considered in the context of relativistic quantum information theory.

20 pages, 7 figures, v2 has a new figure and a proof that the regions are optimal for the lossy bosonic channel if the entropy photon-number inequality is true; v3, submission to Physical Review A (see related work at http://link.aps.org/doi/10.1103/PhysRevLett.108.140501); v4, final version accepted into Physical Review A

References in corpus (13)

• Gaussian Quantum Information
• Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits
• Coding Theorem and Strong Converse for Quantum Channels
• Experimental Demonstration of Blind Quantum Computing
• The Unruh effect in quantum information beyond the single-mode approximation
• Quantum Capacities of Bosonic Channels
• Optical codeword demodulation with error rates below standard quantum limit using a conditional nulling receiver
• Classical capacity of bosonic broadcast communication and a new minimum output entropy conjecture
• Private information via the Unruh effect
• Quantum Communication in Rindler Spacetime
• Information trade-offs for optical quantum communication
• Public and private communication with a quantum channel and a secret key
• Trade-off coding for universal qudit cloners motivated by the Unruh effect

Cited by in corpus (30)

• Performance and structure of single-mode bosonic codes
• Improved quantum capacity bounds of Gaussian loss channels and achievable rates with Gottesman-Kitaev-Preskill codes
• Quantum information processing with bosonic qubits in circuit QED
• Encoding an oscillator into many oscillators
• Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels
• Energy-constrained private and quantum capacities of quantum channels
• Entropy of a quantum channel
• Information trade-offs for optical quantum communication
• Passive states optimize the output of bosonic Gaussian quantum channels
• Gaussian states minimize the output entropy of one-mode quantum Gaussian channels
• Gaussian States Minimize the Output Entropy of the One-Mode Quantum Attenuator
• Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
• Gaussian optimizers for entropic inequalities in quantum information
• Enhanced energy-constrained quantum communication over bosonic Gaussian channels
• Quantum enigma machines and the locking capacity of a quantum channel
• Entanglement-assisted capacity regions and protocol designs for quantum multiple-access channels
• Information gap for classical and quantum communication in a Schwarzschild spacetime
• Approximate reversal of quantum Gaussian dynamics
• Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
• Capacities of Quantum Amplifier Channels
• Restoring quantum communication efficiency over high loss optical fibres
• Bosonic quantum communication across arbitrarily high loss channels
• Magic Resource Can Enhance the Quantum Capacity of Channels
• Quantum communication on the bosonic loss-dephasing channel
• Quantum Fisher and Skew information for Unruh accelerated Dirac qubit
• Quantum Optical Communication in the presence of strong attenuation noise
• New lower bounds to the output entropy of multi-mode quantum Gaussian channels
• Entanglement cost for infinite-dimensional physical systems
• Semantic Security with Infinite Dimensional Quantum Eavesdropping Channel
• Relativistic Quantum Communication