Pulse position modulation (PPM) is widely adopted in free space optical transmission, and is a candidate for deep space transmission, also in quantum form. The change of signal photon number probability distribution is caused by thermal noise in quantum PPM format. We prove that squeezing improves state discrimination at fixed channel energy, and also in the presence of thermal noise. Then we compare the difference between coherent state and squeezed state in thermal noise and reveal that the squeezed state has better robustness. It is shown that for the fixed channel energy, the larger the squeezed parameter is not the better. For some given total channel energies, we further study and get the optimal squeezed parameter. Finally, combined with the actual situation, the simulation results show that, as a resource for noisy quantum communication channels, the squeezing operation can improve the quality of deep space quantum communication system with PPM.
The paper deals with quantum pulse position modulation (PPM), both in the absence (pure states) and in the presence (mixed states) of thermal noise, using the Glauber representation of coherent laser radiation. The objective is to find optimal (or suboptimal) measurement operators and to evaluate the corresponding error probability. For PPM, the correct formulation of quantum states is given by the tensorial product of m identical Hilbert spaces, where m is the PPM order. The presence of mixed states, due to thermal noise, generates an optimization problem involving matrices of huge dimensions, which already for 4-PPM, are of the order of ten thousand. To overcome this computational complexity, the currently available methods of quantum detection, which are based on explicit results, convex linear programming and square root measurement, are compared to find the computationally less expensive one. In this paper a fundamental role is played by the geometrically uniform symmetry of the quantum PPM format. The evaluation of error probability confirms the vast superiority of the quantum detection over its classical counterpart.
We introduce a squeezed-state pulse-position modulation (S-PPM) format, where the empty slots are squeezed vacuum states and the pulse slot is a displaced squeezed state. Based on this property, we propose an inverse-squeezing conditional pulse-nulling (IS-CPN) receiver. In the ideal case, inverse squeezing maps S-PPM into an equivalent coherent-state PPM signal with a large pulse energy, leading to a closed-form expression for the receiver error probability. We further analyze IS-CPN under common phase diffusion using a finite-path MAP formulation with phase-averaged likelihoods. Numerical results show that IS-CPN outperforms conventional CPN under the same energy constraint and remains advantageous under phase noise and finite photon-number resolution. These results demonstrate that combining squeezed-state modulation with inverse-squeezing conditional nulling can improve photon-efficient optical communication.
This paper introduces the use of photon-added squeezed states (PASSs) for quantum pulse position modulation (QPPM). It is shown that the use of PASSs in QPPM communication systems can reduce the symbol error probability (SEP) with respect to the use of different classes of quantum states with the same energy, including squeezed states and photon-added coherent states. The impact of thermal noise and phase diffusion on the SEP is also evaluated. The findings of this paper show the utility of PASSs in quantum communication systems.
Quantum communication systems exploit the quantum features of light to enhance the reliability of a classically described communication system. This paper proposes the use of photon-added coherent states (PACSs), instead of coherent states, for quantum pulse position modulation (PPM) systems. PACSs are the most simple example of non-classical non-Gaussian states of light, as they can not be described by the classical laws of physics. We show that employing PACS in a PPM communication system improves the reliability of the communication with respect to using a coherent state with the same energy.
Optical pulse position modulation (PPM) places a laser pulse, a.k.a. a coherent state of amplitude
αof mean photon number
N=∣α∣2, in one of
Mconsecutive time slots, Ideal photon detection on each slot achieves a mean probability of error
((M−1)/1M)e−Nof distinguishing the
iMPPM codewords, since
e−Nis the probability the pulse-containing slot does not produce a click, per Poisson-shot-noise photo-detection theory. The quantum (Helstrom) limit of the minimum probability of error is lower than above, has a closed-form expression, and scales as
∼e−2Nwhen
Me−N≪1. The optimal receiver must make a quantum joint measurement on all
Mslots. Even though receiver algorithms exist that achieve the
∼e−2Nscaling in the high
Nregime, none are known that bridge the classical-quantum gap for small
N, the primary regime of interest for optical PPM. It is also not known how close to the Helstrom limit can one get using LOCC. (local operations and classical communications), i.e., a receiver that slices each of the
Mslots into
ntiny slices, makes a measurement on the first slice, and based on the measurement result picks a measurement to apply to the next slice, etc., until all the
Mnslices have been measured. In this paper, we propose an LOCC receiver for demodulating PPM that uses semiclassical coherent feedback control and photon detection, which outperforms all known PPM receivers, including one that employed squeezing, a non-classical operation. To bridge the remaining gap to the Helstrom limit, one might need truly quantum operations within a joint (non-LOCC) receiver.