Optical direct detection usually operates far above the quantum limit, due to the high thermal noise level of PIN photodiodes. For signal energy at the quantum level, the thermal effects in photon counters are also a strong limitation. The optical amplification or the heterodyne detection of the 2 quadratures of the field, widely used in high bit rate and long haul optical systems, overcome this limitation at the expense of a minimum 3db noise figure. By allowing a noise free mixing gain, as well as single quadrature measurements, the balanced homodyne receiver is allowed to reach quantum noise limited operation. The aim of this paper is to review the different quantum receiver implementations and to compare the minimum signal energy required to achieve a given bit error rate, or a given bit erasure rate, in high bit rate communications and quantum communications. Application to quantum cryptography will be also addressed.
Optical direct detection usually operates far above the quantum limit, due to the high thermal noise level of PIN photodiodes. For signal energy at the quantum level, the thermal effects in photon counters are also a strong limitation. The optical amplification or the heterodyne detection of the 2 quadratures of the field, widely used in high bit rate and long haul optical systems, overcome this limitation at the expense of a minimum 3db noise figure. By allowing a noise free mixing gain, as well as single quadrature measurements, the balanced homodyne receiver is allowed to reach quantum noise limited operation. The aim of this paper is to review the different quantum receiver implementations and to compare the minimum signal energy required to achieve a given bit error rate, or a given bit erasure rate, in high bit rate communications and quantum communications. Application to quantum cryptography will be also addressed.
A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary quantum-state signal. The effect of the quantum efficiency η of a photodetector used in the receiver is taken into account. Which quantum states have been received is determined by comparing the read-out of the receiver with a certain decision level; so the dependences of the detection operators and average probability of error on a decision level are also considered. As a quantum-state signal, the binary phaseshift keyed signal including thermal noise is investigated in detail, and the condition necessary for the average probability of error of the homodyne-direct receiver to be smaller than the standard quantum limit (the short noise limit) of the signal detection is obtained.
We present an application of coherent homodyne detection to the problem of low photon number communications and cryptography. As the coherent demodulation of an optical field requires the measurement of its (non commutating) inphase and quadrature components, we present the structure and operation of an 8-port optical hybrid comprising 2 balanced homodyne detection structures, for the simultaneous measurement of the 2 quadratures. We analyze this receiver operating with a strong local oscillator field, when the received field is in weak coherent states, with digital phase modulation: we obtain the homodyne statistics and the uncertainty product in the presence of vacuum noises from the input signal port and unused ports and discuss the increase in uncertainty due to the simultaneous measurements of the quadratures. We obtain the signal to noise ratio as well of the bit error rate performance for binary phase shift keying and discuss the departure from the standard quantum limit.
Abstract Coherent detection (homodyne detection/heterodyne detection) and single photon detection are commonly applied in classical communication and quantum communication/receiver respectively. In this paper, we firstly propose a quantum-enhanced receiver based on conjugated homodyne detection, which is consisted of two classical balanced homodyne detectors, for discrimination among quadrature-phase-modulated weak coherent states. Our detection part works as a photon counter in every single-shot measurement during the process of detection and feedback, which could help our quantum-enhanced receiver surpass the standard quantum limit when an optimized detection threshold τ=0.3 is selected. Moreover, our proposed quantum-enhanced receiver with conjugated homodyne detectors can obtain the same low error probability as conventional quantum-enhanced receivers (with its superconducting nanowire single photon detectors' detection efficiency 75% for pulse separation M=8 and 85% for M=12 under the same adaptive feedback countermeasures.) Meanwhile, our scheme of the quantum-enhanced receiver gains its incomparable advantages on room-temperature working condition and low cost due to the application of conjugated homodyne detectors. As far as we concerned, this is the first time to explore the performance of the quantum-enhanced receiver with commercial homodyne detectors. And the analysis in this paper may pave the way to reduce the cost of the quantum-enhanced receiver and make it more adaptable for long-distance optical communication systems.
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.
The minimum average optical signal power, Pmin., in optical communications is limited by the photodetector quantum efficiency and by noise. In this paper, the effect of thermal photons irradiated by all materials at absolute temperatures T>0 on optical information detection in communication lines is quantitatively considered. Usually, only the thermal current fluctuations in the photodetector are taken into account. Basing on the negentropy principle of information, assuming the Planck's blackbody radiation spectral distribution of photons, and describing the optical communication channel as non-symmetric noisy binary channel we have calculated the minimum energy required for the detection of one bit of information, ε= 6.5kT/bit, k =1.38×10-23 J/K being the Boltzmann constant. This ε value corresponds to the large error probability q = 0.20. At T = 20°C ε=4.05×10-21 J/bit and for the bit rate of R = 1010 bits/s one finds Pmin = Rε2.63×10-7 mW. In the case of more realistic value of q=10-9 ε=26kT/bit=1.05×10-19 J/bit, Pmin = 1.05×10-6 mW. This is only about 10 times lower than the quantum photodetection limit of conventional photodetectors. For more sensitive photodetectors the thermal photon noise can become important. It is shown that the minimum signal energy estimate ε≈10-19 J/bit is applicable also in a wider error probability range of q=10-3-10-15.
In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.