Deep-space optical communication links operate under severely limited signal power, approaching the photon-starved regime that requires a receiver capable of measuring individual incoming photons. This makes the photon information efficiency (PIE), i.e., the number of bits that can be retrieved from a single received photon, a relevant figure of merit to characterize data rates achievable in deep-space scenarios. We review theoretical PIE limits assuming a scalable modulation format, such as pulse position modulation (PPM), combined with a photon counting direct detection receiver. For unrestricted signal bandwidth, the attainable PIE is effectively limited by the background noise acquired by the propagating optical signal. The actual PIE limit depends on the effectiveness of the noise rejection mechanism implemented at the receiver, which can be improved by the nonlinear optical technique of quantum pulse gating. Further enhancement is possible by resorting to photon number resolved detection, which improves discrimination of PPM pulses against weak background noise. The results are compared with the ultimate quantum mechanical PIE limit implied by the Gordon–Holevo capacity bound, which takes into account general modulation formats as well as any physically permitted measurement techniques.
We propose and analyze numerically concurrent intensity modulation/direct detection (IM/DD) optical key distribution (OKD) combined with conventional data transmission over a LEO-to-ground optical link. The idea is validated by numerical simulations which indicate that in a realistic scenario it is possible to generate simultaneously up to 200 Mbits of a secret key and downlink transmit up to 140 Gbits of data during a single nearly-zenithal pass of a LEO satellite. Such lengths of the secret key are three orders of magnitude higher in comparison to typical quantum key distribution systems, although they are generated under different security assumptions. The simplicity and robustness of IM/DD OKD protocols could make them an attractive and cost-effective option to provide security in the physical layer of space communication systems.
We show that utilizing pulse position modulation and photon number resolving detectors together with techniques such as quantum pulse gating allows to approach ultimate quantum limit on optical communication capacity in the presence of background noise in the weak output power regime. This shows that for communication over long distances by means of current existing technology it is possible to attain optimal performance, limited only by laws of quantum mechanics.
A method for photon-efficient quantum key distribution (QKD) is proposed and analyzed theoretically. The technique is based on nested encoding of multiple logical qubits into the discretized temporal degree of freedom of a single photon. The states of individual logical qubits are measured using a cascade of interferometric stages followed by time-resolved photon counting. The method may be useful in implementations of entanglement-based QKD protocols whose performance is limited by the brightness of onboard sources of nonclassical light, based e.g. on spontaneous parametric down-conversion. Numerical optimization taking into account the presence of background noise indicates the potential of multiqubit encoding for a nearly tenfold increase of the attainable key rate for entanglement-based LEO satellite QKD systems.
We discuss modulation formats that warrant high information efficiency of deep-space optical links under given power constraints. The discussion is framed using the theoretical concept of orthogonal optical modes occupying the available time-bandwidth space. With diminishing average signal power, the challenge is to concentrate the entire optical energy in very few of these modes. In the generic case of pulse position modulation (PPM), where optical modes occupy separate time bins, this results in increasing peak-to-average power ratio requirements for the transmitter light source. Equivalent information efficiency can be attained using frequency shift keying (FSK) employing modes that do not overlap in the spectral degree of freedom and have uniformly distributed instantaneous optical power in the temporal domain. Recently, efficient modulation formats have been proposed that use words composed from the binary phase shift keying (BPSK) alphabet. Such words can be converted after transmission into the PPM format with the help of structured optical receivers. Selected technical aspects of physical implementations of links based on different modulation formats are briefly reviewed.
The information capacity of an optical channel under power constraints is ultimately limited by the quantum nature of transmitted signals. We discuss currently available and emerging photonic technologies whose combination can be shown theoretically to enable nearly quantum-limited operation of a noisy optical communication link in the photon-starved regime, with the information rate scaling linearly in the detected signal power. The key ingredients are quantum pulse gating to facilitate mode selectivity, photon-number-resolved direct detection, and a photon-efficient high-order modulation format such as pulse position modulation, frequency shift keying, or binary phase shift keyed Hadamard words decoded optically using structured receivers.
We present a scheme for generation and characterization of entangled spatial qubits based on type-II spontaneous parametric down-conversion (SPDC) in a periodically poled titanyl phosphate (PPKTP) multimode nonlinear waveguide [1]. Our scheme exploits intermodal dispersion which has been hitherto successfully employed to produce spatially pure SPDC photon pairs from a multimode waveguide without spatial filtering [2]. Production of discrete
entanglement relies on driving simultaneously two SPDC processes that involve different combinations of transverse spatial modes for which phase matching bandwidths significantly overlap. We propose a procedure for experimental identification of the spatial qubit subspace based on a scan of the spatial Wigner function via the displaced parity measurement using an inverting Sagnac interferometer and photon counting. We numerically verified the robustness
of the mode reconstruction procedure against experimental imperfections. We also propose an experimental method for detecting spatial entanglement in the position-wave vector phase space. Numerical simulations indicate that waveguide parameters required for experimental demonstrations are compatible with current manufacturing capabilities. Using simulated mode profiles we calculate the maximum attainable Clauser-Horne- Shimony-Holt combination value reaching 2.12, which clearly violates the classical limit and confirms the feasibility of observing non-classical features of the generated state.
[1] M. Jachura et al. Physical Review A, 95, 032322 (2017).
[2] M. Jachura, M. Karpiński, C. Radzewicz, K. Banaszek, Optics Express, 22, 8624-8632 (2014).
We investigate theoretically the efficiency of deep-space optical communication in the presence of background noise. With decreasing average signal power spectral density, a scaling gap opens up between optimized simple-decoded pulse position modulation and generalized on-off keying with direct detection. The scaling of the latter follows the quantum mechanical capacity of an optical channel with additive Gaussian noise. Efficient communication is found to require a highly imbalanced distribution of instantaneous signal power. This condition can be alleviated through the use of structured receivers which exploit optical interference over multiple time bins to concentrate the signal power before the detection stage.
Spectral-temporal manipulation of optical pulses has enabled numerous developments within a broad range of research topics, ranging from fundamental science to practical applications. Within quantum optics spectral-temporal degree of freedom of light offers a promising platform for integrated photonic quantum information processing. An important challenge in experimentally realizing spectral-temporal manipulation of quantum states of light is the need for highly efficient manipulation tools. In this context the intrinsically deterministic electro-optic methods show great promise for quantum applications.
We experimentally demonstrate application of electro-optic platform for spectral-temporal manipulation of ultrashort pulsed quantum light. Using techniques analogous to serrodyne frequency shifting we show active spectral translation of few-picosecond single photon pulses by up to 0.5 THz. By employing an approach based on an electro-optic time lens we demonstrate up to 6-fold spectral compression of heralded single photon pulses with efficiency that enables us to significantly increase single photon flux through a narrow bandpass filter.
We realize the required temporal phase manipulation by driving a lithium niobate waveguided electrooptic modulator with 33 dBm sinusoidal RF field at the frequency of either 10 GHz or 40 GHz. We use a phase lock loop to temporally lock the RF field to the 80 MHz repetition rate of approximately 1 ps long optical pulses. Heralded single photon wavepackets are generated by means of spontaneous parametric down-conversion in potassium dihydrogen phosphate (KDP) crystal, which enables preparation of spectrally pure single photon wavepackets without the need for spectral filtering. Spectral shifting is achieved by locking single-photon pulses to the linear slope of sinusoidal 40 GHz RF phase modulation. We verify the spectral shift by performing spectrally resolved heralded single photon counting, using frequency-to-time conversion by means of a highly dispersive chirped fiber Bragg grating. We verify the non-classicality of spectrally shifted single photons by measuring high-visibility Hong-Ou-Mandel interference using a reference single photon pulse.
Spectral compression is based on the time lens principle, which requires locking optical pulses to approximately quadratic region of sinusoidal phase modulation. We utilize both 10 GHz and 40 GHz RF driving frequencies. Bandwidth compression is achieved by chirping the single photon pulse using an appropriate length of single-mode fibre and subsequently subjecting it to the action of the time lens. We verify spectral compression directly using the aforementioned spectrally-resolved heralded single photon counting method. We achieve 3-fold spectral compression of 2 nm bandwidth single photon pulses using 40 GHZ modulation frequency, and 6-fold spectral compression of 0.9 nm bandwidth single photon pulses using 10 GHz modulation frequency. Overall transmission of our set-up exceeding 30% enables practical usability of our spectral compression method which we demonstrate experimentally by showing an increased photon flux through a narrowband filter.
Our results present an important contribution towards implementing quantum information processing in the spectral-temporal degree of freedom of a photon. In the context of quantum networks they present an enabling tool towards efficient photonic interfacing of different quantum information processing platforms.
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