Abstract
We study the problem of transmitting classical information using quantum Gaussian states on a family of phase-noise channels with a finite decoherence time, such that the phase-reference is lost after m consecutive uses of the transmission line. This problem is relevant for long-distance communication in free space and optical fiber, where phase noise is typically considered as a limiting factor. The Holevo capacity of these channels is always attained with photon-number encodings, challenging with current technology. Hence for coherent-state encodings the optimal rate depends only on the total-energy distribution and we provide upper and lower bounds for all m, the latter attainable at low energies with on/off modulation and photodetection. We generalize this lower bound to squeezed-coherent encodings, exhibiting for the first time to our knowledge an unconditional advantage with respect to any coherent encoding for m=1 and a considerable advantage with respect to its direct coherent counterpart for m>1. This advantage is robust with respect to moderate attenuation, and persists in a regime where Fock encodings with up to two-photon states are also suboptimal. Finally, we show that the use of part of the energy to establish a reference frame is sub-optimal even at large energies. Our results represent a key departure from the case of phase-covariant Gaussian channels and constitute a proof-of-principle of the advantages of using non-classical, squeezed light in a motivated communication setting.
Highlights
The ability to establish and maintain a shared reference frame [1] between the sender and receiver is often an implicit assumption in communication scenarios. This is the case, for example, in long-distance communication on optical fiber and in free space, where the information is encoded into quantum states of the
This can happen when the relative phase drifts during transmission due to a physical mechanism in the medium, e.g., Kerr non-linearities and temperature fluctuations in optical fiber [12–14] or turbulence effects in free space [15]; but it can be an effective result of other mechanisms, e.g., the use of a photodetector to measure the signals or the presence of a malicious eavesdropper [16, 17]
We show that the use of part of the signals to establish a common phase reference [1, 32, 33] on these channels is in general detrimental for the communication rate, even at large signal energies
Summary
The ability to establish and maintain a shared reference frame [1] between the sender and receiver is often an implicit assumption in communication scenarios.
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