The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The standard coherent Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, information rates over the photon gas model essentially coincide with those over the Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable by using electromagnetic radiation affected by thermal noise and signal decoherence are studied. The classical coherent-state Gaussian model is compared with an alternative photon gas model which represents lack of a shared phase reference between transmitter and receiver. At any frequency, the information rates in the presence of decoherence essentially coincide with those over a Gaussian model when the signal-to-noise ratio is below a threshold. Only above the threshold does decoherence cause a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40 dB for radio frequencies and vanishes at optical frequencies.
The information rates achievable with a photon-gas model of electromagnetic radiation are studied. At any frequency, information rates over the photon-gas model essentially coincide with the Shannon capacity when the signal-to-noise ratio is below a threshold. Only above the threshold does the photon gas incur in a significant loss in information rates; the loss can amount to half of the capacity. The threshold exceeds 40dB for radio frequencies and vanishes at higher frequencies.
We consider a communication system consisting of an information source of electromagnetic radiation. It is assumed that the information source radiates an electromagnetic signal with an average power S, and the signal propagated through the electromagnetic channel is assumed to be perturbed by additive thermal noise at temperature T. For simplicity, we assume that the electromagnetic signal is one-dimensional (i.e., the photon fluctuation is restricted to only one polarized state), in which the propagation occurs in the same direction of the wave vectors. It is emphasized that the corresponding occupation number of the quantum levels can be fully described. Obviously, these occupation quantum levels correspond to the microsignal structure of the information source. It is therefore assumed that these occupation numbers can be uniquely determined for those representing an input signal ensemble. We further assume that an ideal receiver (an ideal photon counter) is used at the output end of the channel. That is, the receiver is able to detect the specified frequencies of the electromagnetic signal. It is also emphasized that in practice the interaction of the electromagnetic signal and the detector are strictly statistical, that is, a certain amount of information loss is expected at the output end of the receiver. The idealized model of the receiver we have proposed mainly simplifies the method by which the quantum effect on the communication channel can be easily calculated.
How does the shape of detector noise affect optical communication? Two receivers can have the same noise covariance yet support different communication rates. This work determines both the quantum noise floor and the photon scale for approaching the capacity ceiling of specified non-Gaussian optical measurements. The central distinction is between the size of a high-energy communication advantage and the finite signal energy needed to realize it. Exact quantum noise floor. The receiver is a displacement-covariant measurement with a fixed, unflagged ancillary state. For every vacuum–single-photon seed σt=(1−t)∣0⟩⟨0∣+t∣1⟩⟨1∣, with 0≤t≤1/2, the output Shannon entropy is minimized uniquely by coherent states over all normal quantum inputs, without an input energy or photon-number cutoff. A separate entropy theorem covers three-level seeds σ=p0∣0⟩⟨0∣+p1∣1⟩⟨1∣+p2∣2⟩⟨2∣ with p1≤0.1, p2≤0.001, and p0=1−p1−p2. A capacity decomposition with a matched thermal benchmark. Let E be the mean signal photon budget per use, μ the fixed mean ancillary photon number, k the coherent-input response, and G1+μ the circular Gaussian density with the same second moment. With natural logarithms, the unassisted classical capacity satisfies Cσ(E)=ln(1+1+μE)+D(k∥G1+μ)−Δσ(E). The first term is the exact capacity of the matched thermal receiver, allowing arbitrary quantum encoders. The relative entropy is the limiting high-energy capacity gain. The deficit Δσ(E)=Uσ(E)−Cσ(E), where Uσ(E)=1+ln(E+1+μ)−h(k), is the finite-energy shortfall from that gain. The converse permits mixed, non-Gaussian and entangled block codewords under an average total signal-photon constraint. Response zeros determine the sharp convergence rate. For each fixed nonvacuum seed in the stated families, write the coherent-response transform as k(ξ)=e−uP(u), where u=∣ξ∣2, P(u)=1−μu+vu2, and v=p2/2. Then limE→∞E−lnΔσ(E)=2minP(ζ)=0∣ζ∣. Positive classical modulation of coherent states attains this exponent with exact signal-energy accounting. In the nonvacuum two-level family, ordinary Gaussian modulation instead leaves an algebraic deficit. Uniform estimates cover compact three-level parameter families through the merger of two real zeros into a complex pair. Thus the response's relative entropy determines the high-energy gain, while its zeros determine the leading photon cost of approaching that gain. Finite-energy guarantees. Explicit bounds compare ordinary Gaussian modulation with a positive variance-mixture preparation and an upper bound valid for every quantum code. For t=1/2 and E=1, the capacity gain over the thermal receiver with the same ancillary mean photon number obeys 0.009742<Cσ1/2(1)−Cτ1/2(1)<0.010469nat/use. The better achievable bound depends on signal energy; no exact finite-energy optimizer is assumed. The matched-covariance noise comparison builds on classical additive-noise results of Ihara and Diggavi–Cover. The contribution here connects an exact all-input quantum noise floor to a sharp capacity remainder and positive, energy-accounted preparations. The results concern the stated receiver families and ideal measurement model; ancillary preparation and implementation overhead are separate resources. The integrated article includes complete proofs and five figures.
Two types of noise are discussed that may become important when light frequencies are used for communication purposes. At such high frequencies a quantum of energy is not negligible compared to the total transmitted energies (low number of quanta!). The fluctuations caused by the nonzero size of a quantum of energy will predominate over thermal noise, and the usual amplifier noise encountered at microwave (and lower) frequencies. The two types of processes producing quantum noise that we intend to discuss are shown in Pig. 1. They are: The radiative attenuation noise introduced when a signal, phase-and amplitude-control1ed at the high-power transmitter end, is highly attenuated through the inverse square law radiative attenuation. Such a process would take place in the use of optical frequencies for energy transmission over large distances. The noise introduced in linear amplification. objective of this paper is to show how these forms of noise can be analyzed using simple statistics and classical electromagnetic theory with the aid of only a few quantum-theoretical results that have a simple physical meaning.
Recovering complex optical signals with high sensitivity is central to coherent communication and sensing. Beyond conventional homodyne and heterodyne reception, phase-conjugate twin-wave encoding and phase-sensitive joint detection offer an alternative strategy with enhanced sensitivity. Extending this approach to long-distance transmission of high-order-modulated signals is challenging because optical phase coherence must be maintained at the receiver. Here we experimentally demonstrate injection-locking-assisted phase-conjugated twin-wave reception of 200-MBaud signals with modulation formats up to 256-QAM over 100 km of optical fiber. Optical injection locking regenerates the local oscillator (LO) from a reference transmitted through the 16 dB-loss link, while pilot-assisted optical feedback stabilizes the relative signal-LO phase, enabling coherent combining of the phase-conjugated twin waves at a single balanced photodetector. At equal received signal-photon number per quadrature in each data-carrying optical mode, the measured PCTW signal-to-noise ratio (SNR) exceeds the ideal single-mode homodyne standard quantum limit (SQL) benchmark. The SNR gains over the measured homodyne and conventional heterodyne results are about 3 dB and 6 dB, respectively. Constellation and bit-error-rate measurements show that this gain improves high-order data recovery relative to heterodyne reception. An ideal Gaussian-noise model predicts a photon information efficiency of 1.54 bits per received signal photon for uniform 16-QAM. These results establish an injection-locking-assisted coherent receiver architecture that implements joint detection of phase-conjugated twin waves over 100 km of fiber with enhanced sensitivity, providing a practical route for photon-efficient coherent communication.