We study the problem of transmitting classical information on a quantum channel in the absence of a shared phase reference. This problem is relevant for long-distance communications in free space and optical fiber, where phase noise is typically considered as a limiting factor. Previous analyses considered phase noise that acts independently on each communication mode, thus completely decohering successive signals and making it impossible to establish a phase reference. In the present work we analyze instead the realistic case in which the phase reference is lost only after m uses of the transmission line, due to a finite decoherence time. In this setting, focusing on the simplest case m = 2, we analyze two communication strategies using coherent states of the electromagnetic field and show that it is not beneficial to employ the total energy to establish a reference frame but rather to spread out the energy on all the modes and directly transmit information using their relative degrees of freedom.
We study the problem of transmitting classical information on a quantum channel in the absence of a shared phase reference. This problem is relevant for long-distance communications in free space and optical fiber, where phase noise is typically considered as a limiting factor. Previous analyses considered phase noise that acts independently on each communication mode, thus completely decohering successive signals and making it impossible to establish a phase reference. In the present work we analyze instead the realistic case in which the phase reference is lost only after m uses of the transmission line, due to a finite decoherence time. In this setting, focusing on the simplest case m = 2, we analyze two communication strategies using coherent states of the electromagnetic field and show that it is not beneficial to employ the total energy to establish a reference frame but rather to spread out the energy on all the modes and directly transmit information using their relative degrees of freedom.
We study the problem of transmitting classical information using quantum Gaussian states in the absence of a shared phase reference. This problem is relevant for long-distance communication in free space and optical fiber, where phase noise is typically considered as a limiting factor. We consider a family of phase-noise channels with a finite decoherence time, such that the phase-reference is lost after m consecutive uses of the transmission line. The Holevo capacity of these channels is always attained with photon-number encodings, challenging with current technology. Restricting to Gaussian encodings, we show that an optimal encoding can always be generated by acting with a Haar-random passive interferometer on ensembles of product single-mode squeezed-coherent states. Hence for coherent-state encodings the optimal rate depends only on the total-energy distribution and we provide upper and lower bounds for all m, the latter attainable at low energies with on/off modulation and photodetection. We generalize this lower bound to squeezed-coherent encodings, exhibiting for the first time to our knowledge an unconditional advantage with respect to any coherent encoding for m=1 and a considerable advantage with respect to its direct coherent counterpart for m>1. Finally, we show that the use of part of the energy to establish a reference frame is sub-optimal even at large energies. Our results represent a key departure from the case of phase-covariant Gaussian channels and constitute a proof-of-principle of the advantages of using non-classical, squeezed light in a motivated communication setting.
We study the problem of transmitting classical information using quantum Gaussian states on a family of phase-noise channels with a finite decoherence time, such that the phase-reference is lost after m consecutive uses of the transmission line. This problem is relevant for long-distance communication in free space and optical fiber, where phase noise is typically considered as a limiting factor. The Holevo capacity of these channels is always attained with photon-number encodings, challenging with current technology. Hence for coherent-state encodings the optimal rate depends only on the total-energy distribution and we provide upper and lower bounds for all m , the latter attainable at low energies with on/off modulation and photodetection. We generalize this lower bound to squeezed-coherent encodings, exhibiting for the first time to our knowledge an unconditional advantage with respect to any coherent encoding for m=1 and a considerable advantage with respect to its direct coherent counterpart for m>1 . This advantage is robust with respect to moderate attenuation, and persists in a regime where Fock encodings with up to two-photon states are also suboptimal. Finally, we show that the use of part of the energy to establish a reference frame is sub-optimal even at large energies. Our results represent a key departure from the case of phase-covariant Gaussian channels and constitute a proof-of-principle of the advantages of using non-classical, squeezed light in a motivated communication setting.
In this thesis we study the information transmission through Gaussian quantum channels. Gaussian quantum channels model physical communication links, such as free space communication or optical fibers and therefore, may be considered as the most relevant quantum channels. One of the central characteristics of any communication channel is its capacity. In this work we are interested in the classical capacity, which is the maximal number of bits that can be reliably transmitted per channel use. An important lower bound on the classical capacity is given by the Gaussian capacity, which is the maximal transmission rate with the restriction that only Gaussian encodings are allowed: input messages are encoded in so-called Gaussian states for which the mean field amplitudes are Gaussian distributed. We focus in this work mainly on the Gaussian capacity for the following reasons. First, Gaussian encodings are easily accessible experimentally. Second, the difficulty of studying the classical capacity, which arises due to an optimization problem in an infinite dimensional Hilbert space, is greatly reduced when considering only Gaussian input encodings. Third, the Gaussian capacity is conjectured to coincide with the classical capacity, even though this longstanding conjecture is unsolved until today. We start with the investigation of the capacities of the single-mode Gaussian channel. We show that the most general case can be reduced to a simple, fiducial Gaussian channel which depends only on three parameters: its transmissivity (or gain), the added noise variance and the squeezing of the noise. Above a certain input energy threshold, the optimal input variances are given by a quantum water-filling solution, which implies that the optimal modulated output state is a thermal state. This is a quantum extension (or generalization) of the well-known classical water-filling solution for parallel Gaussian channels. Below the energy threshold the solution is given by a transcendental equation and only the less noisy quadrature is modulated. We characterize in detail the dependence of the Gaussian capacity on its channel parameters. In particular, we show that the Gaussian capacity is a non-monotonous function of the noise squeezing and analytically specify the regions where it exhibits one maximum, a maximum and a minimum, a saddle point or no extrema. Then, we investigate the case of n-mode channels with noise correlations (i.e. memory), where we focus in particular on the classical additive noise channel. We consider memory models for which the noise correlations can be unraveled by a passive symplectic transformation. Therefore, we can simplify the problem to the study of the Gaussian capacity in an uncorrelated basis, which corresponds to the Gaussian capacity of n single-mode channels with a common input energy constraint. Above an input energy threshold the solutions is given by a global quantum water-filling solution, which implies that all modulated single-mode output states are thermal states with the same temperature. Below the threshold the channels are divided into three sets: i) those that are excluded from information transmission, ii) those for which only the less noisy quadrature is modulated, and iii) those for which the quantum water-filling solution is satisfied. As an example we consider a Gauss-Markov correlated noise, which in the uncorrelated basis corresponds to a collection of single-mode classical additive noise channels. When rotating the collection of optimal single-mode input states back to the original, correlated basis the optimal multi-mode input state becomes a highly entangled state. We then compare the performance of the optimal input state with a simple coherent state encoding and conclude that one gains up to 10% by using the optimal encoding. Since the preparation of the optimal input state may be very challenging we consider sub-optimal Gaussian-matrix product states (GMPS) as input states as well. GMPS have a known experimental setup and, though being heavily entangled, can be generated sequentially. We demonstrate that for the Markovian correlated noise as well as for a non-Markovian noise model in a wide range of channel parameters, a nearest-neighbor correlated GMPS achieves more than 99.9% of the Gaussian capacity. At last, we introduce a new noise model for which the GMPS is the exact optimal input state. Since GMPS are known to be ground states of quadratic Hamiltonians this suggests a starting point to develop links between optimization problems of quantum communication and many body physics.
Abstract Quantum communication is an important branch of quantum information science, promising unconditional security to classical communication and providing the building block of a future large-scale quantum network. Noise in realistic quantum communication channels imposes fundamental limits on the communication rates of various quantum communication tasks. It is therefore crucial to identify or bound the quantum capacities of a quantum channel. Here, we consider Gaussian channels that model energy loss and thermal noise errors in realistic optical and microwave communication channels and study their various quantum capacities in the energy-constrained scenario. We provide improved lower bounds to various energy-constrained quantum capacities of these fundamental channels and show that higher communication rates can be attained than previously believed. Specifically, we show that one can boost the transmission rates of quantum information and private classical information by using a correlated multi-mode thermal state instead of the single-mode thermal state of the same energy.
The classical capacity of a noisy optical channel is the maximum rate at which information can be transmitted reliably, given a constraint on the mean input energy. For the ubiquitous bosonic Gaussian channels, which include standard models of loss and noise in fibre and free-space optical links, determining this rate requires addressing whether entanglement between channel uses or non-Gaussian signals can outperform Gaussian encodings. More precisely, the question is whether the energy-constrained Holevo information is additive across arbitrarily many channel uses and coincides with its Gaussian counterpart. We answer these fundamental questions in the affirmative for every single-mode bosonic Gaussian channel at every input energy. Namely, we prove that independently prepared Gaussian states with Gaussian-distributed random displacements achieve the capacity, including in the low-energy regime where squeezing the signals competes with encoding information in their displacement. Our proof connects an entanglement inequality to a sharp, additive lower bound on output entropy. We then characterise communication above capacity: under a strict total photon-number cutoff, the probability of correct decoding decreases exponentially with the number of channel uses, and we derive explicit bounds on the decay exponent. When only the mean photon number is constrained, a simple energy-rescaling formula determines exactly the entire asymptotic rate--error trade-off: the capacity at mean photon number N and allowed average decoding error ε equals the vanishing-error capacity at mean photon number N/(1−ε). Together, these results identify the ultimate limits of classical communication for some of the most fundamental models of optical communication.
In previous research on quantum information the- ory, channel capacity of the lossy bosonic channel that is a model of free space or an ideal optical fiber was shown. However, in the optical space communication, the influence of temporal and spatial change in the propagation path on the quantum communication has not been clarified. In order to clarify them, we have studied properties of quantum communications via channels with various fluctuations. We consider phase noise since phase fluctuates by a slight drift of the receiver and it has not been considered well compared to amplitude fluctuation. In this paper, we compute the error probability of the optimum quantum receiver in the presence of phase noise and compare with that of homodyne receiver when BPSK coherent-state signals are used. Then we consider the robustness of the optimum receiver against phase fluctuations. I. INTRODUCTION In order to increase the communication rate, higher fre- quency signals should be used. Light wave has a very high frequency in particular, optical communication systems using this were realized by the invention of the laser. Currently, optical fiber communication systems which consist of laser light source, optical fiber, and photodetector have come to be generally used. Moreover, light is also a promising carrier for wireless or space communications with high capacity. However, the performance of communication systems of this scheme has been approached to the theoretical limit. The factor is due to quantum mechanical effects of light, called quantum noise. Quantum noise increases in proportion to the frequency of the electromagnetic wave. Therefore, it cannot be ignored in the high frequency band, such as optical frequency. In addition, quantum noise is essentially different from the classical noise such as thermal noise. Therefore, it is not possible to suppress quantum noise using information theory which is the basis of current communication technology. That is, in order to realize higher communication rate, a theory which can describe accurately the quantum mechanical nature of light is required. For this reason, we should study quantum information theory which had been introduced axioms of quantum mechanics into the conventional information theory (2), (3), (4). As a previous study, the channel capacity of the lossy bosonic channel which is a model of free space and optical fiber communications was shown (5). That is, performance of ideal quantum communication was clarified. Therefore, as the next step, a study aiming at the actual use is required. As an example, the study on communication model that takes account of the propagation path environment will be needed. In classical communication, such models have been studied as a theory for realizing mobile communications, etc. However, in quantum communication, there are few such results of study now. This study is intended to clarify the influence of temporal and spatial change of the propagation path environment for the quantum communication. We consider phase noise since phase fluctuates by a slight drift of the receiver and it has not been considered well compared to amplitude fluctuation.