We evaluate the information capacities of a lossy bosonic channel with correlated noise. The model generalizes the one recently discussed in [Phys. Rev. A 77, 052324 (2008)], where memory effects come from the interaction with correlated environments. Environmental correlations are quantified by a multimode squeezing parameter, which vanishes in the memoryless limit. We show that a global encoding/decoding scheme, which involves input entangled states among different channel uses, is always preferable with respect to a local one in the presence of memory. Moreover, in a certain range of the parameters, we provide an analytical expression for the classical capacity of the channel showing that a global encoding/decoding scheme allows to attain it. All the results can be applied to a broad class of bosonic Gaussian channels.
We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.
We study the security of the information transmission between two honest parties realized through a lossy bosonic memory channel when losses are captured by a dishonest party. We then show that entangled inputs can enhance the private information of such a channel, which however does never overcome that of unentangled inputs in absence of memory.
The classical capacity of the lossy bosonic channel is calculated exactly. It is shown that its Holevo information is not superadditive, and that a coherent-state encoding achieves capacity. The capacity of far-field, free-space optical communications is given as an example.
We present a study of the achievable rates for classical information transmission via a lossy bosonic channel with memory, using homodyne detection. A comparison with the memoryless case shows that the presence of memory enhances the bit rate if information is encoded in collective states, i.e. states which are entangled over different uses of the channel.
We provide a simple and realistic model to study memory effects in a lossy bosonic quantum channel over arbitrary number of uses. The noise correlation among different uses is introduced by contiguous modes interactions which results in an exponential decay of the correlations over channel uses (modes). This model allows us to characterize the asymptotic behavior of the channel for classical information transmission.
We study the information transmission through a quantum channel, defined over a continuous alphabet and losing its energy en route, in presence of correlated noise among different channel uses. We then show that entangled inputs improve the rate of transmission of such a channel.
We show how to compute or at least to estimate various capacity-related quantities for Bosonic Gaussian channels. Among these are the coherent information, the entanglement assisted classical capacity, the one-shot classical capacity, and a new quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation/amplification and classical noise.
A scheme for transferring classical information over a lossy bosonic channel is proposed by generalizing the proposal presented in Phys. Rev. Lett. 106, 240502 (2011) by Guha. It employs codewords formed by products of coherent states of fixed mean photon number with multiple phases which, through a passive unitary transformation, reduce to a Pulse-Position Modulation code with multiple pulse phases. The maximum information rate achievable with optimal, yet difficult to implement, detection schemes is computed and shown to saturate the classical capacity of the channel in the low energy regime…
We study the communication capacities of bosonic broadband channels in the presence of different sources of noise. In particular we analyze lossy channels in presence of white noise and thermal bath. In this context, we provide a numerical solution for the entanglement assisted capacity and upper and lower bounds for the classical and quantum capacities.
We investigate the capacity of bosonic quantum channels for the transmission of quantum information. Achievable rates are determined from measurable moments of the channel by showing that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. Along the way we provide a complete characterization of degradable Gaussian channels and those arising fr…
Upper bounds on the secret-key-agreement capacity of a quantum channel serve as a way to assess the performance of practical quantum-key-distribution protocols conducted over that channel. In particular, if a protocol employs a quantum repeater, achieving secret-key rates exceeding these upper bounds is a witness to having a working quantum repeater. In this paper, we extend a recent advance [Liuzzo-Scorpo et al., arXiv:1705.03017] in the theory of the teleportation simulation of single-mode phase-insensitive Gaussian channels such that it now applies to the relative entropy of entanglement me…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
We study quantum channels that vary on time in a deterministic way, that is, they change in an independent but not identical way from one to another use. We derive coding theorems for the classical entanglement assisted and unassisted capacities. We then specialize the theory to lossy bosonic quantum channels and show the existence of contrasting examples where capacities can or cannot be drawn from the limiting behavior of the lossy parameter.
We calculate the entanglement assisted capacity of a multimode bosonic channel with loss. As long as the efficiency of the channel is above 50%, the superdense coding effect can be used to transmit more bits than those that can be stored in the message sent down the channel. Bounds for the other capacities of the multimode channel are also provided.
We consider quantum key distribution (QKD) and entanglement distribution using a single-sender multiple-receiver pure-loss bosonic broadcast channel. We determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. A practical implication of our result is that the capacity region demonstrated drastically improves upon rates achievable using a naive time-sharing strategy, which has been employed in previously demonstrated network QKD systems. We s…
Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coher…
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 the…
Experimental control over ultracold quantum gases has made it possible to investigate low-dimensional systems of both bosonic and fermionic atoms. In closed 1D systems there are a lot of similarities in the dynamics of local quantities for spinless fermions and strongly interacting "hard-core" bosons, which on a lattice can be formalised via a Jordan-Wigner transformation. In this study, we analyse the similarities and differences for spinless fermions and hard-core bosons on a lattice in the presence of particle loss. The removal of a single fermion causes differences in local quantities comp…
We discuss a Bosonic channel model with memory effects. It relies on a multi-mode squeezed (entangled) environment's state. The case of lossy Bosonic channels is analyzed in detail. We show that in the absence of input energy constraints the memory channels are equivalent to their memoryless counterparts. In the case of input energy constraint we provide lower and upper bounds for the memory channel capacity.
We present upper bounds on the quantum and private capacity of single-mode, phase-insentitive Bosonic Gaussian Channels based on degradable extensions. Our findings are state-of-the-art in the following parameter regions: low temperature and high transmissivity for the thermal attenuator, low temperature for additive Gaussian noise, high temperature and intermediate amplification for the thermal amplifier.
Information theory establishes the ultimate limits on performance for noisy communication systems [Shannon48]. An accurate model of a physical communication device must include quantum effects, but typically including these makes the theory intractable. As a result communication capacities are not known, even for transmission between two users connected by an electromagnetic waveguide subject to gaussian noise. Here we present an exactly solvable model of communications with a fully quantum electromagnetic field. This allows us to find explicit expressions for all the point-to-point capacities…
The minimum Renyi and Wehrl output entropies are found for bosonic channels in which the signal photons are either randomly displaced by a Gaussian distribution (classical-noise channel), or in which they are coupled to a thermal environment through lossy propagation (thermal-noise channel). It is shown that the Renyi output entropies of integer orders z>1 and the output Wehrl entropy are minimized when the channel input is a coherent state.
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a "forbidden interval". We show that it takes place in different settings: when transmitting classical messages through a lossy bosonic channel, when transmitting over an entanglement-assisted lossy bosonic channel, and when discriminating channels with different loss parameters. Moreover, we consider a setting in which stochastic resonance occurs in the transmission of a qub…
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon, accompanying the standard unitary Kerr transformation of the optical field, is described with high accuracy as Gaussian phase diffusion with parameters given by closed expressions in terms of the system properties. We show that the irreversibility of the nonlinear phase noise ultimately limits the ability to transmit classical information in the phase variable over a l…
Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is deal…
We establish several upper bounds on the energy-constrained quantum and private capacities of all single-mode phase-insensitive bosonic Gaussian channels. The first upper bound, which we call the "data-processing bound," is the simplest and is obtained by decomposing a phase-insensitive channel as a pure-loss channel followed by a quantum-limited amplifier channel. We prove that the data-processing bound can be at most 1.45 bits larger than a known lower bound on these capacities of the phase-insensitive Gaussian channel. We discuss another data-processing upper bound as well. Two other upper …
Recently, there have been considerable progresses on the bounds of various quantum channel capacities for bosonic Gaussian channels. Especially, several upper bounds for the classical capacity and the quantum capacity on the bosonic Gaussian channels, via a technique known as quantum entropy power inequality, have been shed light on understanding the mysterious quantum-channel-capacity problems. However, upper bounds for the private capacity on quantum channels are still missing for the study on certain universal upper bounds. Here, we derive upper bounds on the private capacity for bosonic Ga…
Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the lossy parameter, we study the energy-constrained quantum Fisher information (QFI) for generic temperature and lossy parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum…
One of the most sought-after goals in experimental quantum communication is the implementation of a quantum repeater. The performance of quantum repeaters can be assessed by comparing the attained rate with the quantum and private capacity of direct transmission, assisted by unlimited classical two-way communication. However, these quantities are hard to compute, motivating the search for upper bounds. Takeoka, Guha and Wilde found the squashed entanglement of a quantum channel to be an upper bound on both these capacities. In general it is still hard to find the exact value of the squashed en…
We show that a collection of lossy multi-chromatically modulated qubits can be used to dissipatively engineer arbitrary Gaussian states of a set of bosonic modes. Our ideas are especially suited to superconducting-circuit architectures, where all the required ingredients are experimentally available. The generation of such multimode Gaussian states is necessary for many applications, most notably measurement-based quantum computation. We build upon some of our previous proposals, where we showed how to generate single-mode and two-mode squeezed states through cooling and lasing. Special care m…
Bosonic channels are important in practice as they form a simple model for free-space or fiber-optic communication. Here we consider a single-sender two-receiver pure-loss bosonic broadcast channel and determine the unconstrained capacity region for the distillation of bipartite entanglement and secret key between the sender and each receiver, whenever they are allowed arbitrary public classical communication. We show how the state merging protocol leads to achievable rates in this setting, giving an inner bound on the capacity region. We also evaluate an outer bound on the region by using the…
The bosonic quantum channels have recently attracted a growing interest, motivated by the hope that they open a tractable approach to the generally hard problem of evaluating quantum channel capacities. These studies, however, have always been restricted to memoryless channels. Here, it is shown that the classical capacity of a bosonic Gaussian channel with memory can be significantly enhanced if entangled symbols are used instead of product symbols. For example, the capacity of a photonic channel with 70%-correlated thermal noise of one third the shot noise is enhanced by about 11% when using…
We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also…
We investigate the quantum-secure covert-communication capabilities of lossy thermal-noise bosonic channels, the quantum-mechanical model for many practical channels. We determine the expressions for the covert capacity of these channels: $L_{\text{no-EA}}$, when Alice and Bob share only a classical secret, and $L_{\text{EA}}$, when they benefit from entanglement assistance. We find that entanglement assistance alters the fundamental scaling law for covert communication. Instead of $L_{\text{no-EA}}\sqrt{n}-r_{\text{no-EA}}(n)$, $r_{\text{no-EA}}(n)=o(\sqrt{n})$, entanglement assistance allows…
A new class of quantum channels called Grassmann channels is introduced and their classical and quantum capacity is calculated. The channel class appears in a study of the two-mode squeezing operator constructed from operators satisfying the fermionic algebra. We compare Grassmann channels with the channels induced by the bosonic two-mode squeezing operator. Among other results, we challenge the relevance of calculating entanglement measures to assess or compare the ability of bosonic and fermionic states to send quantum information to uniformly accelerated frames.
We study the problem of designing optical receivers to discriminate between multiple coherent states using coherent processing receivers---i.e., one that uses arbitrary coherent feedback control and quantum-noise-limited direct detection---which was shown by Dolinar to achieve the minimum error probability in discriminating any two coherent states. We first derive and re-interpret Dolinar's binary-hypothesis minimum-probability-of-error receiver as the one that optimizes the information efficiency at each time instant, based on recursive Bayesian updates within the receiver. Using this viewpoi…
Scuola Normale Superiore（比萨高等师范学院）；NEST-CNR（国家研究委员会纳米科学与技术创新研究所）；Inria（法国国家数字科学研究所）；Institut Polytechnique de Paris（巴黎理工学院）；Università di Bologna（博洛尼亚大学）
Previous work on the classical information capacities of bosonic channels has established the capacity of the single-user pure-loss channel, bounded the capacity of the single-user thermal-noise channel, and bounded the capacity region of the multiple-access channel. The latter is a multi-user scenario in which several transmitters seek to simultaneously and independently communicate to a single receiver. We study the capacity region of the bosonic broadcast channel, in which a single transmitter seeks to simultaneously and independently communicate to two different receivers. It is known that…
Communication over a noisy channel is often conducted in a setting in which different input symbols to the channel incur a certain cost. For example, for bosonic quantum channels, the cost associated with an input state is the number of photons, which is proportional to the energy consumed. In such a setting, it is often useful to know the maximum amount of information that can be reliably transmitted per cost incurred. This is known as the capacity per unit cost. In this paper, we generalize the capacity per unit cost to various communication tasks involving a quantum channel such as classica…
The generalized amplitude damping channel (GADC) is one of the sources of noise in superconducting-circuit-based quantum computing. It can be viewed as the qubit analogue of the bosonic thermal channel, and it thus can be used to model lossy processes in the presence of background noise for low-temperature systems. In this work, we provide an information-theoretic study of the GADC. We first determine the parameter range for which the GADC is entanglement breaking and the range for which it is anti-degradable. We then establish several upper bounds on its classical, quantum, and private capaci…
No advantage from classical assistance for energy-constrained bosonic dephasing channels
Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo（量子计算研究所与物理和天文学系，滑铁卢大学）；Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo（量子计算研究所与应用数学系，滑铁卢大学）
With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energy-constrained,…
As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist pairs of discrete memoryless quantum channels, each of zero quantum capacity, which acquire positive quantum capacity when used together. Here we show that this "superactivation" phenomenon also occurs in the more realistic setting of optical channels with attenuation and Gaussian noise. This paves the way for its experimental realization and applic…
