Fundamental limits to quantum channel discrimination

Year: 2019

Authors: Pirandola S., Laurenza R., Lupo C., Pereira JL.

Autors Affiliation: MIT, Res Lab Elect, 77 Massachusetts Ave, Cambridge, MA 02139 USA; Univ York, Comp Sci, York YO10 5GH, N Yorkshire, England; Univ York, York Ctr Quantum Technol, York YO10 5GH, N Yorkshire, England; INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy; Univ Sheffield, Dept Phys & Astron, Sheffield S3 7RH, S Yorkshire, England

Abstract: What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation stretching. Then, we prove that the minimum error probability affecting the channel discrimination cannot beat a bound determined by the Choi matrices of the channels, establishing a general, yet computable formula for quantum hypothesis testing. As a consequence of this bound, we derive ultimate limits and no-go theorems for adaptive quantum illumination and single-photon quantum optical resolution. Finally, we show how the methodology can also be applied to other tasks, such as quantum metrology, quantum communication and secret key generation.


Volume: 5      Pages from: 3-1  to: 3-8

More Information: This work has been supported by the EPSRC via the ´UK Quantum Communications Hub´ (EP/M013472/1) and by the European Commission via ´Continuous Variable Quantum Communications´ (CiViQ, Project ID: 820466). The authors would like to thank Satoshi Ishizaka, Sam Braunstein, Seth Lloyd, Gaetana Spedalieri, and Zhi-Wei Wang for feedback.
DOI: 10.1038/s41534-019-0162-y

Citations: 82
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