We develop a unified theory of ideal error rate performance and quantum limit sensitivities for a large variety of optical modulation formats under four detection schemes: optically pre-amplified direct detection, and coherent homodyne / (a)synchronous heterodyne.
Polarization-modulated optical signals can be demodulated via direct detection of Stokes vectors. In this article, we develop a quantum theory of noise in the Stokes vector receiver. Examining the conditions that enable simultaneous measurement of three elements of the Stokes vector, we demonstrate that an optical pre-amplifier in front of the Stokes vector receiver can reduce the power penalty associated with simultaneous measurements, down to the quantum limit of 3 dB. Then, the 3-D Gaussian noise model for the shot noise and optical pre-amplifier noise is discussed. Subsequently, based on the noise analyses, we derive bit error rate formulae for the cubic-lattice polarization modulation format and evaluate the sensitivity of the Stokes vector receiver.
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.
Since it was noted that quantum computers could break public key cryptosystems based on number theory, extensive studies have been undertaken on quantum cryptography, which offers unconditionally secure communication based on quantum mechanics. We investigate a quantum key distribution (QKD) scheme using macroscopic coherent light with optically pre-amplified direct differential detection. A transmitter “Alice” sends a series of two macroscopic nonorthogonal coherent states that partially overlap due to quantum noise. A receiver “Bob” amplifies and receives it with direct differential detection followed by a thresholding process. To avoid difficulties in detection, our scheme uses conventional direct differential photodetection, not single-photon detection or homodyne detection as in previous QKD protocols. System performance assuming some eavesdropping is evaluated, the results of which suggest that our scheme is usable for short or medium distance.