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 exchange information between a source and a destination by encoding such information into quantum states according to modulation techniques. The design of quantum modulation techniques, including quantum quadrature amplitude modulation (QAM), requires choosing and characterizing quantum states. This paper explores the use of non-Gaussian photon-added Gaussian states (PAGSs) for quantum QAM communications. First, we characterize pure PAGSs in the Fock space and derive a closed-form expression for their inner product. Then, we develop a quantum QAM technique employing PAGSs. In particular, we show how to construct quantum QAM constellations of PAGSs. Finally, we evaluate the performance of the developed quantum QAM technique with PAGSs, when a square root measurement (SRM) receiver is employed, and compare such performance with that of existing coherent states. Results show that PAGSs can provide a performance gain with respect to coherent states.
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.
Quantum state discrimination (QSD) is a key enabler in quantum sensing and networking, for which we envision the utility of non-coherent quantum states such as photon-added coherent states (PACSs). This paper addresses the problem of discriminating between two noisy PACSs. First, we provide representation of PACSs affected by thermal noise during state preparation in terms of Fock basis and quasi-probability distributions. Then, we demonstrate that the use of PACSs instead of coherent states can significantly reduce the error probability in QSD. Finally, we quantify the effects of phase diffusion and photon loss on QSD performance. The findings of this paper reveal the utility of PACSs in several applications involving QSD.
The problem of communication using optical coherent quantum states, in the presence of background radiation, is considered. Two modulation formats are studied, on-off keying (OOK) and M-ary pulse-position modulation (PPM). The bit-error-rate performance improvement due to low-density parity-check coding is reported. For OOK, it is assumed that the coherent state signal has a random phase. For an average number of noise photons N = 0.1, the required number of signal photons per information bit is six in the case of coded quantum OOK. For the same level of noise (N = 0.1) and assuming that signal phase is known, coded 16-ary PPM requires only 1.21 of signal photons per information bit.
Quantum sensing and metrology is the application of non-classical resources to the measurement of physical quantities with precision or accuracy beyond that allowed by classical physics. For many years non-classical resources such as atomic energy quantization, Josephson Effect, and Quantum Hall Effect have been used to define the fundamental units of time, voltage, and resistance, respectively. In recent years non-classical resources such as quantum squeezing and entanglement have been exploited to expand the range of physical phenomena measured with unprecedented precision or accuracy. We summarize some of the recent research on advanced quantum sensing and metrology and discuss our analyses of photon-added coherent states (PACS) of light. These analyses take into account imperfect photon addition and detection processes and show that PACS enable beyond-classical signal-to-noise ratio for photon counting even in cases where the probability of intended photon addition is 80%. We also show that there remains undiscovered fundamental properties of PACS related to their production and implementation.