Vittorio Giovannetti, Saikat Guha, Seth Lloyd, Lorenzo Maccone, Jeffrey H. Shapiro, Horace P. Yuen
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.
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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.
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.
Capacity Formulas for the Lossy Bosonic Compound Wiretap Channel
本文研究有损玻色复合窃听信道，在收发双方仅掌握信道部分状态信息下，旨在最大化传输消息并确保信息泄露渐近可忽略，并证明了两种信道状态信息情况下的容量公式。
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 pa…
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…
Joint Communication and Eavesdropper Detection on the Lossy Bosonic Channel
该研究从量子视角提出一种统一模型，用于在光纤上同时实现通信与窃听检测，并可与量子密钥分发等范式比较。
Classical modelling of a lossy Gaussian bosonic sampler
本文提出一种基于泰勒级数展开的经典算法，用于在特定压缩参数和损耗条件下高效近似模拟有损高斯玻色采样，并指出该算法可经典模拟近期声称实现量子优势的实验。
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…
Joint Communication and Sensing over the Lossy Bosonic Quantum Channel
研究有损玻色子量子信道上的联合通信与感知问题，使用最优量子仪器实现数据传输与环境参数估计，刻画通信与检测速率的最优权衡并量化量子优势。
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…
For a quantum channel of additive Gaussian noise with loss, in the general case of $n$ copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.
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.
Shannon's channel coding theorem describes the maximum possible rate of reliable information transfer through a classical noisy communication channel. It, together with the source coding theorem, characterizes lossless channel communication in the classical regime. Lossy compression scenarios require the additional description provided by rate-distortion theory, which characterizes the trade-off between compression rate and the distortion of the compressed signal. Even in this context, the capacity characterizes the usefulness of a channel -- a channel with more capacity will always outperform…
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 capacity analysis of finite-dimensional lossy channels
本文研究了四维多级幅度阻尼通道的量子容量，采用分析和半数值方法表征了通用d维MAD通道的抗退化和退化区域。
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 calculate numerically the capacity of a lossy photon channel assuming photon number resolving detection at the output. We consider scenarios of input Fock and coherent states ensembles and show that the latter always exhibits worse performance than the former. We obtain capacity of a discrete-time Poisson channel as a limiting behavior of the Fock states ensemble capacity. We show also that in the regime of a moderate number of photons and low losses the Fock states ensemble with direct detection is beneficial with respect to capacity limits achievable with quadrature detection.
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…
We consider a line with noise in the simplest case. Loss does not add noise. Amplification via phase insensitive amplifiers do add noise. A lower bound of this capacity is the quantum analog to the Shannon capacity of a linear channel with additive white Gaussian noise, namely the difference of the Von Neumann entropy of the signal plus noise at the output of the line and the entropy of the noise alone. We show that this expression is indeed the capacity for the case of an amplifier with infinitesimal gain $G = 1+ε$, and for a cascade of an amplifier with arbitrary gain and a large loss, such …
We prove an upper bound on the private capacity of the single-mode noiseless bosonic wiretap channel. Combined with a previous lower bound, we obtain the low photon-number asymptotic expression for the private capacity. We then show that the multiple-mode noiseless bosonic wiretap channel is equivalent to parallel single-mode channels, hence the single-mode bounds can be applied. Finally, we consider multiple-spatial-mode propagation through atmospheric turbulence, and derive a private-capacity lower bound that only requires second moments of the channel matrix.
We show that when coherent-state encoding is employed in conjunction with coherent detection, the Bosonic broadcast channel is equivalent to a classical degraded Gaussian broadcast channel whose capacity region is dual to that of the classical Gaussian multiple-access channel. We further show that if a minimum output-entropy conjecture holds true, then the ultimate classical information capacity of the Bosonic broadcast channel can be achieved by a coherent-state encoding. We provide some evidence in support of the conjecture.
We analyze the role of nonlinear Hamiltonians in bosonic channels. We show that the information capacity as a function of the channel energy is increased with respect to the corresponding linear case, although only when the energy used for driving the nonlinearity is not considered as part of the energetic cost and when dispersive effects are negligible.
We determine the ultimate classical information capacity of a linear time-invariant bosonic channel with additive phase-insensitive Gaussian noise. This channel can model fiber-optic communication at power levels below the threshold for significant nonlinear effects. We provide a general continuous-time result that gives the ultimate capacity for such a channel operating in the quasimonochromatic regime under an average power constraint. This ultimate capacity is compared with corresponding results for heterodyne and homodyne detection over the same channel.
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…
I show that classical capacity per unit cost of noisy bosonic Gaussian channels can be attained by employing generalized on-off keying modulation format and a projective measurement of individual output states. This means that neither complicated collective measurements nor phase-sensitive detection is required to communicate over optical channels at the ultimate limit imposed by laws of quantum mechanics in the limit of low average cost.
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.
Quantum Ring States
本文提出量子环态，通过相位调制高斯资源生成非高斯态，并给出其信息论量的紧致界，用于提升有损热玻色子信道的通信速率和隐蔽吞吐量。
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…
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 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.
We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing ra…
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structu…
We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit…
We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schäfer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these opti…
Lower Bounding the Secret Key Capacity of Bosonic Gaussian Channels via Optimal Gaussian Measurements
通过最优高斯测量确定玻色高斯信道秘密密钥容量的下界，优化了热损耗和热放大信道的协议并简化了性能评估。
Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
本文研究了能量约束下玻色退相位信道的LOCC辅助量子容量，通过推导能量约束压扁纠缠的上界并证明最优输入态和压扁信道的性质，给出了该容量的紧密上下界估计。
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…
Low-ground/High ground capacity regions analysis for Bosonic Gaussian Channels
本文全面表征了信道级联导致的单模相位不敏感Gaussian Bosonic Channels间的联系，在其参数空间识别出低地和高地两个容量区域，并系统给出了结合已知上界与组合规则的量子和私有容量显式上界，改进了现有结果。
The additivity problem asks if the use of entanglement can boost the information-carrying capacity of a given channel beyond what is achievable by coding with simple product states only. This has recently been shown not to be the case for phase-insensitive one-mode Gaussian channels, but remains unresolved in general. Here we consider two general classes of bosonic noise channels, which include phase-insensitive Gaussian channels as special cases: these are beamsplitters with general, potentially non-Gaussian environment states and classical noise channels with general probabilistic noise. We …
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…
Data Transmission over a Bosonic Arbitrarily Varying Quantum Channel
本文研究受半经典攻击的有损玻色任意变化信道，建立显式容量公式，并将其与新近猜想的量子熵功率不等式联系起来。
Non-asymptotic quantum communication on lossy transmission lines with memory
本文将无记忆玻色 Gaussian 信道的非渐近容量下界推广到描述光纤记忆效应的非 Markov 模型，并借助 Toeplitz 矩阵奇异值新界给出有限次数下传输量子信息、纠缠和密钥的资源估计。
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…
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…
Central Limit Theorem for Bosonic Quantum Channels
本文发展了中心极限定理到玻色量子通道的设置，通过该扩展深入理解了高斯玻色通道作为极值对象的本质，并通过该定理恢复了经典中心极限定理和玻色量子态的中心极限定理，从而提供了将经典概率理论与连续变量量子系统联系起来的统一视角。此外，利用该结果，我们能够提供物理系统（可能非高斯）的玻色量子通道必须满足的必要不确定性关系。作为我们极限定理的另一个应用，我们通过将其与关联的高斯玻色通道容量联系起来，推导了线性玻色通道在能量约束下的量子容量的紧下界，进一步强化了高斯通道作为极值对象的作用。
We prove that several known upper bounds on the classical capacity of thermal and additive noise bosonic channels are actually strong converse rates. Our results strengthen the interpretation of these upper bounds, in the sense that we now know that the probability of correctly decoding a classical message rapidly converges to zero in the limit of many channel uses if the communication rate exceeds these upper bounds. In order for these theorems to hold, we need to impose a maximum photon number constraint on the states input to the channel (the strong converse property need not hold if there …
Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in …
No advantage from classical assistance for energy-constrained bosonic dephasing channels
研究证明能量受限下，单模玻色子退相位信道的四种容量一致，经典辅助无优势，推导了相关相对熵链规则并给出自适应协议速率上界，且链规则可由规范纯化态达到。
Heralded optical entanglement distribution via lossy quantum channels: A comparative study
本研究针对有损量子信道的纠缠分发损耗问题，提出三种基于不同光子源与探测器结构的多粒子GHZ态预告式分发方案，对比发现各方案在不同场景下各有优势，为相关电路设计提供参考。
The most natural way to describe an information-carrying system containing a specific noise is an additive white Gaussian-noise (AWGN) channel. In bosonic quantum systems (especially the Gaussian case), although the classical information capacity for a phase-insensitive and thermal-noise channel is additive based on a proof of the minimum output entropy conjecture, several open questions remain. By generalizing the Gaussian noise model from thermal noise to general Gaussian noise, we rigorously revisit and calculate these strong upper bounds on the information capacity for single-mode with gen…
In this paper, using the notion of nonlinear coherent states, we define a deformed bosonic dephasing channel modelling the impact of a Kerr medium on a quantum state, as it occurs, for instance, in quantum communication based on optical fibers. We show that, in certain regimes, the Kerr nonlinearity is able to compensate the dephasing. In addition, our studies reveal that the quantum capacity of the deformed bosonic dephasing channel can be greater than that of the undeformed, standard bosonic dephasing channel for certain nonlinearity parameters.
Quantum technologies able to manipulating single quantum systems, are presently developing. Among the dowries of the quantum realm, entanglement is one of the basic resources for the novel quantum revolution. Within this context, one is faced with the problem of protecting the entanglement when a system state is manipulated. In this paper, we investigate the effect of the classical driving field on the generation entanglement between two qubits interacting with a bosonic environment. We discuss the effect of the classical field on the generation of entanglement between two (different) qubits a…
Quantum channels can be activated by a kind of channels whose quantum capacity is zero. This activation effect might be useful to overcome noise of channels by attaching other channels which can enhance the capacity of a given channel. In this work, we show that such an activation is possible by specific positive-partial-transpose channels for Gaussian lossy channels whose quantum capacities are known. We also test more general case involving Gaussian thermal attenuator whose the exact value of quantum capacity has been unknown so far. For a recently suggested narrow upper bound on quantum cap…
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.
Dissipative stabilization of entangled qubit pairs in quantum arrays with a single localized dissipative channel
该研究针对含单个局域耗散通道的量子阵列，通过调控耗散与局域相互作用，实现了多对远距离无直接相互作用量子比特的稳态纠缠，为量子纠缠的耗散稳定制备提供了可行方案。
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…
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