Exact solution for the quantum and private capacities of bosonic dephasing channels

Abstract

The capacities of noisy quantum channels capture the ultimate rates of information transmission across quantum communication lines, and the quantum capacity plays a key role in determining the overhead of fault-tolerant quantum computation platforms. In the case of bosonic systems, central to many applications, no closed formulas for these capacities were known for bosonic dephasing channels, a key class of non-Gaussian channels modelling, e.g., noise affecting superconducting circuits or fiber-optic communication channels. Here we provide the first exact calculation of the quantum, private, two-way assisted quantum, and secret-key agreement capacities of all bosonic dephasing channels. We prove that that they are equal to the relative entropy of the distribution underlying the channel to the uniform distribution. Our result solves a problem that has been open for over a decade, having been posed originally by [Jiang & Chen, Quantum and Nonlinear Optics 244, 2010].

10+20 pages, 6 figures. v2 is close to the published version

References in corpus (10)

• Quantum algorithm for solving linear systems of equations
• Distillation of secret key and entanglement from quantum states
• Reference frames, superselection rules, and quantum information
• A No-Go Theorem for Gaussian Quantum Error Correction
• Direct and Reverse Secret-Key Capacities of a Quantum Channel
• Trapped-ion quantum logic gates based on oscillating magnetic fields
• Quantum Capacities of Bosonic Channels
• Degenerate Quantum Codes for Pauli Channels
• Quantum capacity and codes for the bosonic loss-dephasing channel
• Efficient one- and two-qubit pulsed gates for an oscillator stabilized Josephson qubit

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