Optimal estimation and discrimination of excess noise in thermal and amplifier channels

Abstract

We determine a fundamental upper bound on the performance of any adaptive protocol for discrimination or estimation of a channel which has an unknown parameter encoded in the state of its environment. Since our approach relies on the principle of data processing, the bound applies to a variety of discrimination measures, including quantum relative entropy, hypothesis testing relative entropy, Rényi relative entropy, fidelity, and quantum Fisher information. We apply the upper bound to thermal (amplifier) channels with a known transmissivity (gain) but unknown excess noise. In these cases, we find that the upper bounds are achievable for several discrimination measures of interest, and the method for doing so is non-adaptive, employing a highly squeezed two-mode vacuum state at the input of each channel use. Estimating the excess noise of a thermal channel is of principal interest for the security of quantum key distribution, in the setting where a fiber-optic cable has a known transmissivity but a tampering eavesdropper alters the excess noise on the channel, so that estimating the excess noise as precisely as possible is desirable. Finally, we outline a practical strategy which can be used to achieve these limits.

arXiv comment11 pages, 1 figure

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Cited by in corpus (11)

• Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
• Asymptotic theory of quantum channel estimation
• Memory effects in quantum metrology
• Sub-Quantum Fisher Information
• Bounding the quantum limits of precision for phase estimation with loss and thermal noise
• Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
• Generalized Measure of Quantum Fisher Information
• New bounds on adaptive quantum metrology under Markovian noise
• Uniqueness and Optimality of Dynamical Extensions of Divergences
• Quantum rebound capacity
• Optimal gain sensing of quantum-limited phase-insensitive amplifiers