H. Bombin, M. A. Martin-Delgado
We construct a class of topological quantum codes to perform quantum entanglement distillation. These codes implement the whole Clifford group of unitary operations in a fully topological manner and without selective addressing of qubits. This allows us to extend their application also to quantum teleportation, dense coding and computation with magic states.
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It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the issues is the efficient placement of magic state distillation sub circuits, so-called distillation boxes, in the space-time volume that abstracts the computation's required resources. This work presents a general, systematic, online method for the synthesis of such circuits. Distillation box placement is controlled by so-called schedulers. The work introduc…
We present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi--Hubbard model on a quasi-1D ladder geometry. The term distillation refers to the dynamical, spatial separation of singlons and doublons in the sudden expansion of interacting particles in an optical lattice, i.e., the release of a cloud of atoms from a trapping potential. Remarkably, quantum distillation can lead to a contraction of the doublon cloud, resulting in an increased density of the doublons in the core region compared to the initial state. As a main res…
Enhancing Quantum Key Distribution with Entanglement Distillation and Classical Advantage Distillation
提出一种级联纠缠纯化与经典优势纯化的两阶段方案，通过枚举算法优化纠缠纯化协议，在高噪声区域实现有限密钥率并超越原有安全界，且无需额外量子资源。
We study several properties of distillation protocols to purify multilevel qubit states (qudits) when applied to a certain family of initial mixed bipartite states. We find that it is possible to use qudits states to increase the stability region obtained with the flow equations to distill qubits. In particular, for qutrits we get the phase diagram of the distillation process with a rich structure of fixed points. We investigate the large-$D$ limit of qudits protocols and find an analytical solution in the continuum limit. The general solution of the distillation recursion relations is present…
We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. We finally study the effect of the detector efficiency on the secret key r…
Threshold (Q, P) Quantum Distillation
该研究提出了一种阈值量子蒸馏方法，通过减少参与方数量来蒸馏完美量子相关性，并揭示了蒸馏与状态分离性之间的联系。
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. For an important class of protocols, which exploit tomographically complete measurements on entangled pairs of any dimension, we show that the noise threshold for classical advantage distillation is identical with the threshold for quantum entanglement distillation. As a consequence, the two distillation procedures are equivalent: neither offers a security advantage over the other.
All about quantum error correction: distillation, mitigation, self-correction and beyond
本文展示蒸馏、错误缓解和动态解耦等量子错误处理技术是量子纠错框架的特例，通过扩展至状态自适应、信道自适应及多阶段编码实现统一视角，并提出自纠正量子存储器模型。
We consider a hypothetical topological quantum computer where the qubits are comprised of either Ising or Fibonacci anyons. For each case, we calculate the time and number of qubits (space) necessary to execute the most computationally expensive step of Shor's algorithm, modular exponentiation. For Ising anyons, we apply Bravyi's distillation method [S. Bravyi, Phys. Rev. A 73, 042313 (2006)] which combines topological and non-topological operations to allow for universal quantum computation. With reasonable restrictions on the physical parameters we find that factoring a 128 bit number requir…
We report that, for the generation of a secure cryptographic key from correlations established through a noisy quantum channel, the quantum and classical advantage distillation procedures are not equivalent, when coherent eavesdropping attacks are duly taken into account. The quantum procedure can tolerate markedly more noise in the channel than the classical procedure.
PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.
Quantum low density parity check (QLDPC) codes are useful primitives for quantum information processing because they can be encoded and decoded efficiently. Besides, the error correcting capability of a few QLDPC codes exceeds the quantum Gilbert-Varshamov bound. Here, we report a numerical performance analysis of an adaptive entanglement distillation scheme using QLDPC codes. In particular, we find that the expected yield of our adaptive distillation scheme to combat depolarization errors exceed that of Leung and Shor whenever the error probability is less than about 0.07 or greater than abou…
This paper tries to probe the relation between the local distinguishability of orthogonal quantum states and the distillation of entanglement. An new interpretation for the distillation of entanglement and the distinguishability of orthogonal quantum states in terms of information is given, respectively. By constraining our discussion on a special protocol we give a necessary and sufficient condition for the local distinguishability of the orthogonal pure states, and gain the maximal yield of the distillable entanglement. It is shown that the information entropy, the locally distinguishability…
Probabilistic Entanglement Distillation: Error Exponents via Postselected Quantum Hypothesis Testing Against Separable States
本文研究了在近非纠缠操作下的概率纠缠纯化误差指数，通过后选择量子假设检验与分离态集的联系，推导了解析特征并建立了纠缠稀释与成本之间的关系。
Entanglement degradation in open quantum systems is reviewed in the Choi-Jamiołkowski representation of linear maps. In addition to physical processes of entanglement dissociation and entanglement annihilation, we consider quantum dynamics transforming arbitrary input states into those that remain positive under partial transpose (PPT-inducing channels). Such evolutions form a convex subset of distillation-prohibiting channels. A relation between the above channels and entanglement-binding ones is clarified. An example of the distillation-prohibiting map $Φ\otimesΦ$ is given, where $Φ$ is not …
We present a generalized tomographic quantum key distribution protocol in which the two parties share a Bell diagonal mixed state of two qubits. We show that if an eavesdropper performs a coherent measurement on many quantum ancilla states simultaneously, classical methods of secure key distillation are less effective than quantum entanglement distillation protocols. We also show that certain Bell diagonal states are resistant to any attempt of incoherent eavesdropping.
This paper try to probe the relation of distinguishing locally and distillation of entanglement. The distinguishing information (DI) and the maximal distinguishing information (MDI) of a set of pure states are defined. The interpretation of distillation of entanglement in term of information is given. The relation between the maximal distinguishing information and distillable entanglement is gained. As a application of this relation the distillable entanglement of Bell-diagonal states is present.
Non-Hermitian Boundary State Distillation with Lossy Waveguides
提出并实验验证了一种利用有损波导等效非厄米哈密顿量，对通用输入光进行拓扑提纯以保留最长寿命边界态的方法，免除了精细微调需求。
Sources of entangled photon pairs using two parametric down-converters are capable of generating interchangeable entanglement in two different degrees of freedom. The connection between these two degrees of freedom allows the control of the entanglement properties of one, by acting on the other degree of freedom. We demonstrate experimentally, the quantum distillation of the position entanglement using polarization analyzers.
Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we develop the framework of the approximate coherence distillation under strictly incoherent operations. This protocol considers the situation that we cannot transform an initial state $ρ$ into a target state $ψ$ with certainty; instead, we aim to deterministically transform the initial state $ρ$ into an intermediate state $ϕ$ that is most approximate to the target state $ψ$ in terms of fidelity. We also present the explicit conversion strategy of the approximate coherence distillat…
Classical Autoencoder Distillation of Quantum Adversarial Manipulations
本文提出利用经典自编码器蒸馏量子操纵图像数据集，以提升量子分类器在对抗攻击下的鲁棒性。
The security of a cryptographic key that is generated by communication through a noisy quantum channel relies on the ability to distill a shorter secure key sequence from a longer insecure one. We show that -- for protocols that use quantum channels of any dimension and completely characterize them by state tomography -- the noise threshold for classical advantage distillation is substantially lower than the threshold for quantum entanglement distillation because the eavesdropper can perform powerful coherent attacks. The earlier claims that the two noise thresholds are identical, which were b…
Experimental virtual distillation of entanglement and coherence
本研究在光子量子系统上实验实现虚拟资源蒸馏协议，突破传统蒸馏限制，完成四维相干及单拷贝EPR对纠缠的虚拟蒸馏，提升了量子隐形传态保真度，为含噪硬件操控量子资源提供了可行路径。
Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that $1$D and $2$D quantum voids --faces of the nonlocal simplex set with no quantum realization-- can be…
Virtual quantum resource distillation: General framework and applications
本文提出虚拟资源蒸馏的一般框架，适用于量子态及动态量子对象，通过半定规划表征性能，并应用于纠缠、相干性、魔法及量子通信等资源理论。
We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [\textit{Phys. Rev. Lett. 102, 120401 (2009)}]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon coincidence measurements.
We suggest a way to quantify a type of macroscopic entanglement via distillation of Greenberger-Horne-Zeilinger states by local operations and classical communication. We analyze how this relates to an existing measure of quantum macroscopicity based on the quantum Fisher information in several examples. Both cluster states and Kitaev surface code states are found to not be macroscopically quantum but can be distilled into macroscopic superpositions. We look at these distillation protocols in more detail and ask whether they are robust to perturbations. One key result is that one-dimensional c…
We show theoretically and experimentally that single copy distillation of squeezing from continuous variable non-Gaussian states is possible using linear optics and conditional homodyne detection. A specific non-Gaussian noise source, corresponding to a random linear displacement, is investigated. Conditioning the signal on a tap measurement, we observe probabilistic recovery of squeezing.
Entanglement distribution between distant parties is an essential component to most quantum communication protocols. Unfortunately, decoherence effects such as phase noise in optical fibers are known to demolish entanglement. Iterative (multistep) entanglement distillation protocols have long been proposed to overcome decoherence, but their probabilistic nature makes them inefficient since the success probability decays exponentially with the number of steps. Quantum memories have been contemplated to make entanglement distillation practical, but suitable quantum memories are not realised to d…
Even though entanglement is very vulnerable to interactions with the environment, it can be created by purely dissipative processes. Yet, the attainable degree of entanglement is profoundly limited in the presence of noise sources. We show that distillation can also be realized dissipatively, such that a highly entanglement steady state is obtained. The schemes put forward here display counterintuitive phenomena, such as improved performance if noise is added to the system. We also show how dissipative distillation can be employed in a continuous quantum repeater architecture, in which the res…
Quantum Conference Key Agreement with Classical Advantage Distillation
本研究证明了结合经典优势提取的量子会议密钥协商协议在有限密钥场景下对通用相干攻击的安全性，推导了安全密钥率界定方法，且该方案在部分场景中可提升协议噪声容忍度。
Quantum Relational Knowledge Distillation
本文提出量子关系知识蒸馏（QRKD），通过将经典特征映射为量子态并利用量子核捕获样本间关系来指导蒸馏，在多个视觉和语言基准上一致超越经典RKD，同时保持模型部署完全经典化。
Quantum Repeater Protocol using Quantum Error Correction for Distillation
本文提出利用量子纠错码实现确定性纠缠提纯，通过全局链路状态知识优化中继器的提纯和贝尔态测量调度，以提高端到端纠缠质量。
The distribution and processing of quantum entanglement form the basis of quantum communication and quantum computing. The realization of the two is difficult because quantum information inherently has a high susceptibility to decoherence, i.e. to uncontrollable information loss to the environment. For entanglement distribution, a proposed solution to this problem is capable of fully eliminating decoherence; namely iterative entanglement distillation. This approach builds on a large number of distillation steps each of which extracts a number of weakly decohered entangled states from a larger …
Fourier states are multi-qubit registers that facilitate phase rotations in fault-tolerant quantum computing. We propose distillation protocols for constructing the fundamental, $n$-qubit Fourier state with error $O(2^{-n})$ at a cost of $O(n \log n)$ Toffoli gates and Clifford gates, or any arbitrary Fourier state using $O(n^2)$ gates. We analyze these protocols with methods from digital signal processing. These results suggest that phase kickback, which uses Fourier states, could be the current lowest-overhead method for generating arbitrary phase rotations.
The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements h…
Probabilistic Channel Distillation via Indefinite Causal Order
研究高阶量子开关在量子信道蒸馏中的优势，证明其能以非零概率蒸馏任意量子比特泡利信道，并刻画渐近速率及多量子比特推广的不可行性。
How to surpass no-go limits in Gaussian quantum error correction and entangled Gaussian state distillation?
本文提出仅依赖局域高斯资源的高斯量子纠错协议，利用纠缠高斯态门隐形传态实现部分转置，从两个含噪高斯信道构造双模噪声极化信道，并扩展为非局域高斯态蒸馏协议，从而超越高斯量子信息处理中的不可行极限。
Quantum entanglement plays crucial roles in quantum information processing. Quantum entangled states have become the key ingredient in the rapidly expanding field of quantum information science. Although the nonclassical nature of entanglement has been recognized for many years, considerable efforts have been taken to understand and characterize its properties recently. In this review, we introduce some recent results in the theory of quantum entanglement. In particular separability criteria based on the Bloch representation, covariance matrix, normal form and entanglement witness; lower bound…
A new systematic strategy for steering the distillation process for a quantum system, that utilizes the so-called "pulsed" and "continuous" measurements on another quantum system in interaction with the former, is proposed. The distillation process characterized by the specific interaction between the two systems and the "pulsed" measurements is shown to be controllable through the "continuous" measurements, i.e., the quantum Zeno dynamics, providing an effective recipe to prefix the target.
Fast quantum interconnects via constant-rate entanglement distillation
针对大规模容错分布式量子计算中量子互连的保真度与速率瓶颈，提出基于量子错误检测码和容错技术的恒定速率纠缠提纯方法，经数值优化后性能较现有方案提升一个数量级，直接加速分布式量子算法执行。
Advantages of Global Entanglement-Distillation Policies in Quantum Repeater Chains
本研究通过模拟等距量子中继器链，比较局部与全局确定性纠缠蒸馏策略，发现全局策略在通信速率上始终更优，尤其在大型链中显著提升密钥率，表明局部决策可能非最优。
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic state distillation', a process based on stabilizer codes from quantum error correction. We define quantum weight enumerators that take into account the sign of the stabilizer operators. These enumerators completely describe the magic state distillation behavior when distilling T-type magic states. While it is straightforward to calculate them directly by co…
Entanglement distillation is a key primitive for distributing high-quality entanglement between remote locations. Probabilistic noiseless linear amplification based on the quantum scissors is a candidate for entanglement distillation from noisy continuous-variable (CV) entangled states. Being a non-Gaussian operation, quantum scissors is challenging to analyze. We present a derivation of the non-Gaussian state heralded by multiple quantum scissors in a pure loss channel with two-mode squeezed vacuum input. We choose the reverse coherent information (RCI)---a proven lower bound on the distillab…
We study the one-shot distillation of general quantum resources, providing a unified quantitative description of the maximal fidelity achievable in this task, and revealing similarities shared by broad classes of resources. We establish fundamental quantitative and qualitative limitations on resource distillation applicable to all convex resource theories. We show that every convex quantum resource theory admits a meaningful notion of a pure maximally resourceful state which maximizes several monotones of operational relevance and finds use in distillation. We endow the generalized robustness …
We characterize the operational task of environment-assisted distillation of quantum coherence under different sets of free operations when only a finite supply of copies of a given state is available. We first evaluate the one-shot assisted distillable coherence exactly, and introduce a semidefinite programming bound on it in terms of a smooth entropic quantity. We prove the bound to be tight for all systems in dimensions 2 and 3, which allows us to obtain computable expressions for the one-shot rate of distillation, establish an analytical expression for the best achievable fidelity of assis…
Logic-qubit entanglement has attracted much attention in both quantum communication and quantum computation. Here, we present an efficient protocol to distill the logic-qubit entanglement with the help of cross-Kerr nonlinearity. This protocol not only can purify the logic bit-flip error and logic phase-flip error, but also can correct the physical bit-flip error completely. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors. Our distillation protocol for logic-qubit entanglement may be useful for the practical applications in quantum information, especially in long-di…
High-threshold magic state distillation with quantum quadratic residue codes
本文探讨了量子二次剩余码在魔态提纯中的应用，展示了现有提纯魔态的编码与量子二次剩余码等价，并提出新的高阈值提纯编码。
Weak distillation of quantum resources
本文提出一种框架，将基于准概率的协议从期望值估计提升到弱模拟器，通过有限量子资源采样实现目标分布，减少样本数量，应用于错误缓解、纠缠蒸馏和魔法态蒸馏等场景。
Quantum algorithms for quantum chemistry map the dynamics of electrons in a molecule to the dynamics of a coupled spin system. To reach chemical accuracy for interesting molecules, a large number of quantum gates must be applied which implies the need for quantum error correction and fault-tolerant quantum computation. Arbitrary fault-tolerant operations can be constructed from a small, universal set of fault-tolerant operations by gate compilation. Quantum chemistry algorithms are compiled by decomposing the dynamics of the coupled spin-system using a Trotter formula, synthesizing the decompo…
The ability to distill quantum coherence is pivotal for optimizing the performance of quantum technologies; however, such a task cannot always be accomplished with certainty. Here we develop a general framework of probabilistic distillation of quantum coherence in a one-shot setting, establishing fundamental limitations for different classes of free operations. We first provide a geometric interpretation for the maximal success probability, showing that under maximally incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO) the problem can be simplified into efficiently…
Virtual quantum resource distillation
本文提出虚拟量子资源蒸馏方法，通过仅近似目标纯态的测量统计并允许经典后处理，显著优于传统蒸馏，能从无法常规蒸馏的噪声态中纯化资源，且成本与资源量成反比，可通过凸和半定规划高效估计。
Entropy Bounds via Hypothesis Testing and Its Applications to Two-Way Key Distillation in Quantum Cryptography
本文通过量子渐进假设检验与熵界建立联系，提升密钥率并改进QKD安全性分析。
Imaging with quantum states of light promises advantages over classical approaches in terms of resolution, signal-to-noise ratio and sensitivity. However, quantum detectors are particularly sensitive sources of classical noise that can reduce or cancel any quantum advantage in the final result. Without operating in the single-photon counting regime, we experimentally demonstrate distillation of a quantum image from measured data composed of a superposition of both quantum and classical light. We measure the image of an object formed under quantum illumination (correlated photons) that is mixed…
Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully-fledged quantum computer, in such a way that the server cannot learn anything about client's input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pa…
We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state …
Conditional Error Exponents of Probabilistic Quantum Resource Distillation
本文建立统一框架分析概率性量子资源蒸馏的条件误差指数，通过后选择复合假设检验获得纠缠、相干性和魔法蒸馏的解析刻画，证明后选择可严格提升误差指数衰减率。
Knowledge Distillation Inspired Variational Quantum Eigensolver with Virtual Annealing
本文提出KD-VQE方法，在VQE中引入基于玻尔兹曼分布和虚拟温度的虚拟退火机制，动态分配测量资源以过滤次优态，并在两格点费米-哈伯德模型上验证了其更广的搜索范围和更好的收敛可靠性。
Distillation of quantum non-Markovianity
本研究围绕开放量子系统动力学非马尔可夫性与量子信息回流的关联，构建操作框架，探究多份信道副本下量子比特动力学非马尔可夫性的蒸馏机制及对信息回流的增强效应。
Advantage Distillation for Quantum Key Distribution
本文提出了一种优势蒸馏框架，用于提升量子密钥分发的性能，通过经典线性码实现更高的密钥速率。
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