Achieving minimum-error discrimination of an arbitrary set of laser-light pulses

Laser light is widely used for communication and sensing applications, so the optimal discrimination of coherent states--the quantum states of light emitted by a laser--has immense practical importance. However, quantum mechanics imposes a fundamental limit on how well different coher- ent states can be distinguished, even with perfect detectors, and limits such discrimination to have a finite minimum probability of error. While conventional optical receivers lead to error rates well above this fundamental limit, Dolinar found an explicit receiver design involving optical feedback and photon counting that can achieve the minimum probability of error for discriminating any two given coherent states. The generalization of this construction to larger sets of coherent states has proven to be challenging, evidencing that there may be a limitation inherent to a linear-optics-based adaptive measurement strategy. In this Letter, we show how to achieve optimal discrimination of any set of coherent states using a resource-efficient quantum computer. Our construction leverages a recent result on discriminating multi-copy quantum hypotheses (arXiv:1201.6625) and properties of coherent states. Furthermore, our construction is reusable, composable, and applicable to designing quantum-limited processing of coherent-state signals to optimize any metric of choice. As illustrative examples, we analyze the performance of discriminating a ternary alphabet, and show how the quantum circuit of a receiver designed to discriminate a binary alphabet can be reused in discriminating multimode hypotheses. Finally, we show our result can be used to achieve the quantum limit on the rate of classical information transmission on a lossy optical channel, which is known to exceed the Shannon rate of all conventional optical receivers.Comment: 9 pages, 2 figures; v2 Minor correction

Optical codeword demodulation with error rates below standard quantum limit using a conditional nulling receiver

The quantum states of two laser pulses---coherent states---are never mutually orthogonal, making perfect discrimination impossible. Even so, coherent states can achieve the ultimate quantum limit for capacity of a classical channel, the Holevo capacity. Attaining this requires the receiver to make joint-detection measurements on long codeword blocks, optical implementations of which remain unknown. We report the first experimental demonstration of a joint-detection receiver, demodulating quaternary pulse-position-modulation (PPM) codewords at a word error rate of up to 40% (2.2 dB) below that attained with direct-detection, the largest error-rate improvement over the standard quantum limit reported to date. This is accomplished with a conditional nulling receiver, which uses optimized-amplitude coherent pulse nulling, single photon detection and quantum feedforward. We further show how this translates into coding complexity improvements for practical PPM systems, such as in deep-space communication. We anticipate our experiment to motivate future work towards building Holevo-capacity-achieving joint-detection receivers.Comment: 6 pages, 4 figure

On the benefits of phase shift keying to optical telecommunication systems

Les avantages de la modulation de phase vis-à-vis la modulation d’intensité pour les réseaux optiques sont claires et accepté par la communauté scientifique des télécommunications optiques. Surtout, la modulation de phase montre une meilleure sensibilité au bruit, ainsi qu’une plus grande tolérance aux effets non-linéaires que la modulation d’intensité. Nous présentons dans cette thése un étude qui vise à développer les avantages de la modulation de phase. Nous attaquons d’abord la complexité du récepteur en détection directe, en proposant une nouvelle configuration dont la complexité est comparable à celle du récepteur pour la modulation d’intensité traditionnel, mais avec des meilleures performances. Cette solution pourrait convenir pour les réseaux métropolitains (et même d’accès) à haut débit binaire. Nous passons ensuite à l’examen de la possibilité d’utiliser des amplificateur à semi-conducteur (SOA) au lieu des amplificateurs à fibre dopée à l’erbium pour fournir amplification optique aux signaux modulés en phase. Les non-linéarité des SOA sont étudiées, et un compensateur simple et très efficace est proposé. Les avantages des amplificateurs à semi-conducteur par rapport à ceux à fibre sont bien connus. Surtout, la méthode que nous proposons permettrait l’integrabilité des SOA avec d’autres composants de réseau (par exemple, le récepteur nommé cidessus), menant à des solutions technologiques de petite taille et efficaces d’un point de vue énergétique. Il y a deux types de systèmes pour signaux modulés en phase: basé sur la détection directe, ou sur les récepteurs cohérents. Dans le dernière partie de ce travail, nous nous concentrons sur cette dernière catégorie, et nous comparons deux solutions possibles pour la mise à niveau des réseaux terrestres actuel. Nous comparons deux configurations dont les performances sont très comparables en termes de sensibilité au bruit, mais nous montrons comment la meilleure tolérance aux effets non linéaires (en particuliers dans les systèmes à débit mixte) fait que une solution soit bien plus efficace que l’autre.The advantages of phase modulation (PM) vis-à-vis intensity modulation for optical networks are accepted by the optical telecommunication community. PM exhibits a higher noise sensitivity than intensity modulation, and it is more tolerant to the effects of fiber nonlinearity. In this thesis we examine the challenges and the benefits of working with different aspects of phase modulation. Our first contribution tackles the complexity of the direct detection noncoherent receiver for differentially encoded quadrature phase shift keying. We examine a novel configuration whose complexity is comparable to that of traditional receivers for intensity modulation, yet outperforming it. We show that under severe nonlinear impairments, our proposed receiver works almost as well as the conventional receiver, with the advantage of being much less complex. We also show that the proposed receiver is tolerant to chromatic dispersion, and to detuning of the carrier frequency. This solution might be suitable for high-bit rates metro (and even access) networks. Our second contribution deals with the challenges of using semiconductor optical amplifiers (SOAs) instead of typical erbium doped fiber amplifiers (EDFAs) to provide amplification to phase modulated signals. SOAs nonlinearities are investigated, and we propose a simple and very effective feed-forward compensator. Above all, the method we propose would permit the integrability of SOAs with other network components (for example, the aforementioned receiver) achieving small size, power efficient sub-systems. Phase modulation paves the way to high spectral efficiency, especially when paired with digital coherent receivers. With the digital coherent receiver, the degree of freedom offered by polarization can be exploited to increase the channel bit rate without increasing its spectral occupancy. In the last part of this work we focus on polarization multiplexed signaling paired with coherent reception and digital signal processing. Our third contribution provides insight on the strategies for upgrading current terrestrial core networks to high bit rates. This is a particularly challenging scenario, as phase modulation has to coexist with previously installed intensity modulated channels. We compare two configurations which have received much attention in the literature. These solutions show comparable performance in terms of back-to-back noise sensitivity, and yet are not equivalent. We show how the superior tolerance to nonlinear fiber propagation (and particularly to cross phase modulation induced by the presence of intensity modulated channels) makes one of them much more effective than the other

Entanglement-enhanced testing of multiple quantum hypotheses

Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled photons at the input and a generalized form of conditional nulling receiver at the output, we may outperform any classical strategy. Our results can be applied to enhance a range of technological tasks, including the optical readout of sparse classical data, the spectroscopic analysis of a frequency spectrum, and the determination of the direction of a target at fixed range

Entanglement-Assisted Absorption Spectroscopy

Spectroscopy is an important tool for probing the properties of materials, chemicals and biological samples. We design a practical transmitter-receiver system that exploits entanglement to achieve a provable quantum advantage over all spectroscopic schemes based on classical sources. To probe the absorption spectra, modelled as pattern of transmissivities among different frequency modes, we employ broad-band signal-idler pairs in two-mode squeezed vacuum states. At the receiver side, we apply photodetection after optical parametric amplification. Finally, we perform a maximal-likehihood decision test on the measurement results, achieving orders-of-magnitude-lower error probability than the optimum classical systems in various examples, including `wine-tasting' and `drug-testing' where real molecules are considered. In detecting the presence of an absorption line, our quantum scheme achieves the optimum performance allowed by quantum mechanics. The quantum advantage in our system is robust against noise and loss, which makes near-term experimental demonstration possible

Single-Laser Multi-Terabit/s Systems

Optical communication systems carry the bulk of all data traffic worldwide. This book introduces multi-Terabit/s transmission systems and three key technologies for next generation networks. A software-defined multi-format transmitter, an optical comb source and an optical processing scheme for the fast Fourier transform for Tbit/s signals. Three world records demonstrate the potential: The first single laser 10 Tbit/s and 26 Tbit/s OFDM and the first 32.5 Tbit/s Nyquist WDM experiments