Fiber-optic communications are moving to coherent detection in order to increase their spectral efficiency, i.e., their channel capacity per unit bandwidth. At power levels below the threshold for significant nonlinear effects, the channel model for such operation a linear time-invariant filter followed by additive Gaussian noise is one whose channel capacity is well known from Shannon's noisy channel coding theorem. The fiber channel, however, is really a bosonic channel, meaning that its ultimate classical information capacity must be determined from quantum-mechanical analysis, viz. from the Holevo-Schumacher-Westmoreland (HSW) theorem. Based on recent results establishing the HSW capacity of a linear (lossy or amplifying) channel with additive Gaussian noise, we provide a general continuous-time result, namely the HSW capacity of a linear time-invariant (LTI) bosonic channel with additive Gaussian noise arising from a thermal environment. In particular, we treat quasi-monochromatic communication under an average power constraint through a channel comprised of a stable LTI filter that may be attenuating at all frequencies or amplifying at some frequencies and attenuating at others. Phase-insensitive additive Gaussian noise-associated with the continuous-time Langevin noise operator needed to preserve free-field commutator brackets is included at the filter output. We compare the resulting spectral efficiencies with corresponding results for heterodyne and homodyne detection over the same channel to assess the increased spectral efficiency that might be realized with optimum quantum reception.
The Holevo limit bounds the channel capacity of a communication channel in which information is encoded in quantum states in a Hilbert space at the transmitter and decoded using quantum measurements at the receiver. Saturating the Holevo limit requires quantum-limited transceivers that either generate quantum states of light or employ quantum-limited measurements. Here, we demonstrate an integrated photonic-electronic quantum-limited coherent receiver (QRX) achieving 14.0 dB shot noise clearance (SNC), 520
μW knee power, 2.57 GHz 3-dB bandwidth, 3.50 GHz shot-noise-limited bandwidth, and 90.2 dB common-mode rejection ratio (
CMRR). We scale this design to a 32-channel QRX array with median 26.6 dB
SNC, and automatic
CMRR correction yielding a median 76.8 dB
CMRR at minimum. Using the integrated QRX and fiber-optic transmitter, we measure
0.15±0.01 dB of squeezing below the shot noise limit, limited by off-chip losses. We propose a squeezed light communication scheme that can surpass the Shannon limit, with a path toward the Holevo limit.
We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore, the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [F. E. Becerra et al., Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.