Chistopher A. Fuchs
I demonstrate that, rather unexpectedly, there exist noisy quantum channels for which the optimal classical information transmission rate is achieved only by signaling alphabets consisting of nonorthogonal quantum states.
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Nonorthogonal coding in spectrally-entangled photons
本研究针对安全量子通信需求，提出在原子系综产生的多路复用光谱纠缠光子对中实现非正交编码及多通道架构，经二阶关联等量化验证其编解码能力优于正交编码，可支撑大规模多用户量子通信。
When classical information is sent through a quantum channel of nonorthogonal states, there is a possibility that transmittable classical information exceeds a channel capacity in a single use of the initial channel by extending it into multi-product channel. In this paper, it is shown that this remarkable feature of a quantum channel, so-called superadditivity, appears even in as low as the third extended coding of the simplest binary input channel. A physical implementation of this channel is indicated based on cavity QED techniques.
A general quantum noisy channel is analyzed, wherein the transmitted qubits may experience symmetry-breaking decoherence, along with memory effects. We find the optimal basis not to be fully entangled, but a combination of factorized and partially-entangled states in the presence of memory, asymmetry and the state-bias of the noise. Capacity-maximization is shown to be achievable by combining temporal shaping of the transmitted qubits and optimal basis selection.
We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold. It is noteworthy that the resulting channel capacity is a non-differentiable function of the memory parameter.
We obtain a maximizer for the quantum mutual information for classical information sent over the quantum qubit amplitude damping channel. This is achieved by limiting the ensemble of input states to antipodal states, in the calculation of the product-state capacity for the channel, the resulting maximizing ensemble consisting of just two non-orthogonal states. We also consider the product-state capacity of a convex combination of two memoryless channels and demonstrate in particular that it is in general not given by the minimum of the capacities of the respective memoryless channels.
We present a model of an N-qubit channel where consecutive qubits experience correlated random rotations. Our model is an extension to the standard decoherence-free subsystems approach (DFS) which assumes that all the qubits experience the same disturbance. The variation of rotations acting on consecutive qubits is modeled as diffusion on the SU(2) group. The model may be applied to spins traveling in a varying magnetic field, or to photons passing through a fiber whose birefringence fluctuates over the time separation between photons. We derive an explicit formula describing the action of the…
In the present paper we give proof that the information-transmission capacity of the approximate position measurement with the oscillator energy constraint, which underlies noisy Gaussian homodyning in quantum optics, is attained on Gaussian encoding. The proof is based on general principles of convex programming. Rather remarkably, for this particular model the method reduces the solution of the optimization problem to a generalization of the celebrated log-Sobolev inequality. We hope that this method should work also for other models lying out of the scope of the "threshold condition" ensuri…
Experimental demonstration of optimal measurement for unambiguously discriminating asymmetric qudit states
本研究通过光子轨道角动量态实验实现了对不对称四态的最优测量，为高维量子信息处理提供了新的方法。
Evaluating the quantum capacity of quantum channels is an important but difficult problem, even for channels of low input and output dimension. Smith and Smolin showed that the quantum capacity of the Clifford-twirl of a qubit amplitude damping channel (a qubit depolarizing channel) has a quantum capacity that is at most the coherent information of the qubit amplitude damping channel evaluated on the maximally mixed input state. We restrict our attention to obtaining upper bounds on the quantum capacity using a generalization of Smith and Smolin's degradable extension technique. Given a degrad…
Quantum networks entangle remote nodes by distributing quantum states, which inevitably suffer from decoherence while traversing quantum channels. Pertinent decoherence mechanisms govern the channel capacity, its reach, and the quality and rate of distributed entanglement. Hence recognizing, understanding, and modeling those mechanisms is a crucial step in building quantum networks. Here, we study practical fiber-optic quantum channels that partially filter individual modes of transmitted polarization entangled states and are capable of introducing dephasing. First, we theoretically model and …
Proof of the Gaussian maximizers conjecture for the communication capacity of noisy heterodyne measurements
本研究基于凸规划框架，证明了高斯编码是能量约束下广义外差接收机通信速率的最优编码，推广了此前需能量阈值条件的结论，揭示了阈值内外最优编码的结构差异，证明用到联系广义Wehrl熵与波函数梯度的新对数索伯列夫型不等式。
We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.
Quantum reservoir computing is a class of quantum machine learning algorithms involving a reservoir of an echo state network based on a register of qubits, but the dependence of its memory capacity on the hyperparameters is still rather unclear. In order to maximize its accuracy in time--series predictive tasks, we investigate the relation between the memory of the network and the reset rate of the evolution of the quantum reservoir. We benchmark the network performance by three non--linear maps with fading memory on IBM quantum hardware. The memory capacity of the quantum reservoir is maximiz…
An example is given of a qubit quantum channel which requires four inputs to maximize the Holevo capacity. The example is one of a family of channels which are related to 3-state channels. The capacity of the product channel is studied and numerical evidence presented which strongly suggests additivity. The numerical evidence also supports a conjecture about the concavity of output entropy as a function of entanglement parameters. However, an example is presented which shows that for some channels this conjecture does not hold for all input states. A numerical algorithm for finding the capacit…
We construct a class of quantum channels in arbitrary dimensions for which entanglement improves the performance of the channel. The channels have correlated noise and when the level of correlation passes a critical value we see a sharp transition in the optimal input states (states which minimize the output entropy) from separable to maximally entangled states. We show that for a subclass of channels with some extra conditions, including the examples which we consider, the states which minimize the output entropy are the ones which maximize the mutual information.
SeCQC is an open-source program code which implements a Numerical Search for the classical Capacity of Quantum Channels (SeCQC) by using an iterative method. Given a quantum channel, SeCQC finds the statistical operators and POVM outcomes that maximize the accessible information, and thus determines the classical capacity of the quantum channel. The optimization procedure is realized by using a steepest-ascent method that fol- lows the gradient in the POVM space, and also uses conjugate gradients for speed-up.
Classical messages can be sent via a noisy quantum channel in various ways, corresponding to various choices of signal states of the channel. Previous work by Holevo and by Schumacher and Westmoreland relates the capacity of the channel to the properties of the signal ensemble. Here we describe some properties characterizing the ensemble that maximizes the capacity, using the relative entropy "distance" between density operators to give the results a geometric flavor.
We consider the additivity of the minimal output entropy and the classical information capacity of a class of quantum channels. For this class of channels the norm of the output is maximized for the output being a normalized projection. We prove the additivity of the minimal output Renyi entropies with entropic parameters contained in [0, 2], generalizing an argument by Alicki and Fannes, and present a number of examples in detail. In order to relate these results to the classical information capacity, we introduce a weak form of covariance of a channel. We then identify several instances of w…
Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide improved upper bounds of Gaussian loss channel capacity, both in the energy-constrained and unconstrained scenarios. We briefly review the Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energy-unconstrained case, that the GKP codes achieve the quantum capacity of Gaussian loss channels up to at most a co…
We consider a setting where qubits are processed sequentially, and derive fundamental limits on the rate at which classical information can be transmitted using quantum states that decohere in time. Specifically, we model the sequential processing of qubits using a single server queue, and derive explicit expressions for the capacity of such a `queue-channel.' We also demonstrate a sweet-spot phenomenon with respect to the arrival rate to the queue, i.e., we show that there exists a value of the arrival rate of the qubits at which the rate of information transmission (in bits/sec) through the …
We study the performance of a partially correlated amplitude damping channel acting on two qubits. We derive lower bounds for the single-shot classical capacity by studying two kinds of quantum ensembles, one which allows to maximize the Holevo quantity for the memoryless channel and the other allowing the same task but for the full-memory channel. In these two cases, we also show the amount of entanglement which is involved in achieving the maximum of the Holevo quantity. For the single-shot quantum capacity we discuss both a lower and an upper bound, achieving a good estimate for high values…
Static classical-quantum-entanglement trade-offs: an entropic converse and single-letter characterizations
本文给出二分量子态静态容量区域的统一熵反命题，通过支撑超平面刻画容量公式，并针对纯态擦除、对称可扩展态等情形获得完整单字母刻画，揭示非正交丢弃存储器的优势。
The present paper is devoted to investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities are computed explicitly for multimode Gaussian measurement channels. For this we establish a fundamental property of the entropy reduction of a measurement: under a restriction on the second moments of the input state it is maximized by a Gaussian state (providing an analytical expression for the maximum). In the case of one mode, the gain of entanglement assistance is investigated in detail.
We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for t…
We study the fundamental limits of classical communication using quantum states that decohere as they traverse through a network of queues. We consider a network of Markovian queues, known as a Jackson network, with a single source or multiple sources and a single destination. Qubits are communicated through this network with inevitable buffering at intermediate nodes. We model each node as a `queue-channel,' wherein as the qubits wait in buffer, they continue to interact with the environment and suffer a waiting time-dependent noise. Focusing on erasures, we first obtain explicit classical ca…
Algorithms for Computing the Petz-Augustin Capacity
本文提出计算Petz-Augustin容量的算法，通过两层方法结合熵镜像下降和固定点算法，实现非渐近收敛保证。
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