E. Isasi, D. Mundarain
In this work we review the entire classification of 2x2 distillable states for protocols with a finite numbers of copies. We show a distillation protocol that allows to distill Bell states with non zero probability at any time for an initial singlet in vacuum. It is shown that the same protocol used in non zero thermal baths yields a considerable recovering of entanglement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
It is impossible to discriminate four Bell states through local operations and classical communication (LOCC), if only one copy is provided. To complete this task, two copies will suffice and be necessary. When $n$ copies are provided, we show that the distillable entanglement is exactly $n-2$.
We consider controllability of two conjugate observables Z and X by two parties with classical communication. The ability is specified by two alternative tasks, (i) agreement on Z and (ii) preparation of an eigenstate of X with use of an extra communication channel. We prove that their feasibility is equivalent to that of key distillation if the extra channel is quantum, and to that of entanglement distillation if it is classical. This clarifies the distinction between two entanglement measures, distillable key and distillable entanglement.
The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result, we provide here some additional examples of reversible, as well as irreversible states.
Magic can be distributed non-locally in many-body entangled states, such as the low energy states of condensed matter systems. Using the Bravyi-Kitaev magic state distillation protocol, we find that non-local magic is distillable and can improve the distillation outcome. We analyze a few explicit examples and show that spin squeezing can be used to convert non-distillable states into distillable ones. Our analysis also suggests that the conventional product input states assumed by magic distillation protocols are extremely atypical among general states with distillable magic. It further justif…
We show that the maximum fidelity obtained by a p.p.t. distillation protocol is given by the solution to a certain semidefinite program. This gives a number of new lower and upper bounds on p.p.t. distillable entanglement (and thus new upper bounds on 2-locally distillable entanglement). In the presence of symmetry, the semidefinite program simplifies considerably, becoming a linear program in the case of isotropic and Werner states. Using these techniques, we determine the p.p.t. distillable entanglement of asymmetric Werner states and ``maximally correlated'' states. We conclude with a discu…
Noise-robust 1-copy distillation protocol for all distillable Bell-diagonal qutrits
本文提出了一种抗噪声的1拷贝提纯协议，解决贝尔-对角三能级态的可提纯问题，证明违反PPT标准是1可提纯的必要充分条件，并展示了其对量子态白噪声的鲁棒性。
Entanglement distillation on symmetric two-qutrit entangled states of rank five
本文研究五秩对称双qutrit NPT纠缠态的蒸馏，构造五族态并给出特征值条件，证明部分态可1-蒸馏，部分区间不可蒸馏。
A mixed quantum state shared between two parties is said to be distillable if, by means of a protocol involving only local quantum operations and classical communication, the two parties can transform some number of copies of that state into a single shared pair of qubits having high fidelity with a maximally entangled state state. In this paper it is proved that there exist states that are distillable, but for which an arbitrarily large number of copies is required before any distillation procedure can produce a shared pair of qubits with even a small amount of entanglement. Specifically, for…
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.
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 …
We study the relation between violation of Bell inequalities and distillability properties of quantum states. Recently, Dür has shown that there are some multiparticle bound entangled states, non-separable and non-distillable, that violate a Bell inequality. We prove that for all the states violating this inequality there exist at least one splitting of the parties into two groups such that some pure-state entanglement can be distilled, obtaining a connection between Bell inequalities and bipartite distillable entanglement.
Magic state distillation is a crucial component in the leading approaches to implementing universal fault tolerant quantum computation, with existing protocols for both qubit and higher dimensional systems. Early work focused on determining the region of distillable states for qubit protocols, yet comparatively little is known about which states can be distilled and with what distillable region for d>2. Here we focus on d=3 and present new four-qutrit distillation schemes that improve upon the known distillable region, and achieve distillation tight to the boundary of undistillable states for …
Universal distillation of quantum entanglement
本文提出一种不依赖输入态描述的普适LOCC协议，证明即使未知输入态，也能达到最优的可蒸馏纠缠速率，从而将可蒸馏纠缠确立为稳健的操作量。
A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations that introduce noise. The most common method to eliminate the noise is magic state distillation (MSD) by stabilizer operations. Here we propose a hybrid MSD protocol by connecting a four-qubit H-type MSD with a five-qubit T-type MSD, in order to overcome some disadvantages of the previous MSD protocols. The hybrid MSD protocol further integrates distillable…
We introduce a formalism that connections entanglement witnesses and the distillation and activation properties of a state. We apply this formalism to two cases: First, we rederive the results presented in quant-ph/0104095 by Eggeling et al., namely that on copy of any bipartite state with non--positive partial transpose (NPPT) is either distillable, or activable. Second, we show that there exist three--partite NPPT states, with the property that two copies can neither be distilled, nor activated.
On PPT entanglement distillation
该研究针对PPT信道下的纠缠蒸馏，推导了PPT可蒸馏纠缠的正则化公式与两种单字母逆定理，证明其可严格小于正则化Rains界，还给出了基于纠缠负性的可靠下界，解决了相关开放问题。
Non-locality can be quantified by the violation of a Bell inequality. Since this violation may be amplified by local operations an alternative measure has been proposed - distillable non-locality. The alternative measure is difficult to calculate exactly due to the double exponential growth of the parameter space. In this article we give a way to bound the distillable non-locality of a resource by the solutions to a related optimization problem. Our upper bounds are exponentially easier to compute than the exact value and are shown to be meaningful in general and tight in some cases.
Positive and non-positive measurements in energy distillation from quantum batteries
该研究在广义量子测量框架下，分析了正测量（POVMs）与两类非正测量（NPOVMs）在环境噪声下从量子电池提取能量的性能，证明NPOVMs具能量提取优势，1型NPOVMs在多种噪声下性能优于或等于POVMs，2型在振幅阻尼噪声下更优。
Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether all mixed states outside this set may be distilled. In this Letter we show that, when resources are finitely limited, non-distillable states exist outside the stabilizer octahedron. In analogy with the …
We derive general upper bounds on the distillable entanglement of a mixed state under one-way and two-way LOCC. In both cases, the upper bound is based on a convex decomposition of the state into 'useful' and 'useless' quantum states. By 'useful', we mean a state whose distillable entanglement is non-negative and equal to its coherent information (and thus given by a single-letter, tractable formula). On the other hand, 'useless' states are undistillable, i.e., their distillable entanglement is zero. We prove that in both settings the distillable entanglement is convex on such decompositions. …
Auxiliary-assisted energy distillation from quantum batteries
该研究提出通过辅助系统和测量提取量子电池能量，发现可蒸馏能量高于ergotropy，且测量在功率方面具有优势。
Measures of entanglement can be employed for the analysis of numerous quantum information protocols. Due to computational convenience, logarithmic negativity is often the choice in the case of continuous variable systems. In this work, we analyse a continuous variable measurement-based entanglement distillation experiment using a collection of entanglement measures. This includes: logarithmic negativity, entanglement of formation, distillable entanglement, relative entropy of entanglement, and squashed entanglement. By considering the distilled entanglement as a function of the success probabi…
We study the relation between distillability of multipartite states and violation of Bell's inequality. We prove that there exist multipartite bound entangled states (i.e. non-separable, non-distillable states) that violate a multipartite Bell inequality. This implies that (i) violation of Bell's inequality is not a sufficient condition for distillability and (ii) some bound entangled states cannot be described by a local hidden variable model.
Distilling highly entangled quantum states from weaker ones is a process that is crucial for efficient and long-distance quantum communication, and has implications for several other quantum information protocols. We introduce the notion of distillation under limited resources, and specifically focus on the energy constraint. The corresponding protocol, which we call the canonical distillation of entanglement, naturally leads to the set of canonically distillable states. We show that for non-interacting Hamiltonians, almost no states are canonically distillable, while the situation can be dras…
No-go theorem for heralded exact one-way key distillation
基于双粒子态通过局部操作和单向经典通信提取完美秘密密钥的最大期望速率，定义超双扩展态集并证明其无法用于 heralded exact one-way 密钥蒸馏，揭示了精确与近似密钥蒸馏间的极大差距。
Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain distillable secrecy, if not they could be produced by quantum measurements performed on a separable state of larger dimension. We introduce a new QKD protocol and prove its security against any individual attack by an adversary only limited by the no-signaling condition.
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi (arXiv:1510.07455), we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the LOCC distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure abelian gauge theories in the weak coupling limit, while it is in general nonzero for the nonabelian case. We …
The resource framework of quantum coherence was introduced by Baumgratz, Cramer and Plenio [PRL 113, 140401 (2014)] and further developed by Winter and Yang [PRL 116, 120404 (2016)]. We consider the one-shot problem of distilling pure coherence from a single instance of a given resource state. Specifically, we determine the distillable coherence with a given fidelity under incoherent operations (IO) through a generalisation of the Winter-Yang protocol. This is compared to the distillable coherence under maximal incoherent operations (MIO) and dephasing-covariant incoherent operations (DIO), wh…
Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. \textbf{116}, 070402 (2016)] studied the manipulation of quantum coherence in bipartite or multipartite systems under the protocol Local Incoherent Operation and Classical Communication (LQICC). Here we present the first experimental realization of obtaining maximal coherence in assisted distillation protocol based on linear optical system. The results of our work show that the optimal distillable coherence rate…
We provide generalizations of known two-qubit entanglement distillation protocols for arbitrary Hilbert space dimensions. The protocols, which are analogues of the hashing and breeding procedures, are adapted to bipartite quantum states which are diagonal in a basis of maximally entangled states. We show that the obtained rates are optimal, and thus equal to the distillable entanglement, for a (d-1) parameter family of rank deficient states. Methods to improve the rates for other states are discussed. In particular, for isotropic states it is shown that the rate can be improved such that it ap…
We complete the task of optimal probabilistic coherence distillation protocol, whose aim is to transform a general state into a set of n-level maximally coherent states via strictly incoherent operations (SIO). Specifically, we present the necessary and sufficient condition for the transformation from a mixed state into a pure-state ensemble via SIO. With the aid of this condition and the simplex algorithm, we can accomplish the probabilistic distillation protocol by presenting an analytical expression of the maximal average distillable coherence of a general state and constructing the corresp…
A solution to 2-copy distillability of Werner states
研究维纳态双拷贝可蒸馏性问题，通过证明任意维度维纳态双拷贝可蒸馏当且仅当单拷贝可蒸馏，回答了长期问题，是确定非正定部分转置态是否可蒸馏的重要一步。
We investigate non-locality distillation using measures of non-locality based on the Elitzur-Popescu-Rohrlich decomposition. For a certain number of copies of a given non-local correlation, we define two quantities of interest: (i) the non-local cost, and (ii) the distillable non-locality. We find that there exist correlations whose distillable non-locality is strictly smaller than their non-local cost. Thus non-locality displays a form of irreversibility which we term bound non-locality. Finally we show that non-local distillability can be activated.
Finite-Blocklength and Exponential Analyses for Universal Entanglement and Coherence Distillation under Various Free Operations
本文提出纠缠纯化中的指数分析，通过正则化量子Hoeffding分歧度刻画可靠性函数，并构建了在黑盒设置下的最优纯化协议。
We present new algorithms for mixed-state multi-copy entanglement distillation for pairs of qubits. Our algorithms perform significantly better than the best known algorithms. Better algorithms can be derived that are tuned for specific initial states. The new algorithms are based on a characterization of the group of all locally realizable permutations of the 4^n possible tensor products of n Bell states.
We analyze the security of quantum cryptography schemes for $d$-level systems using 2 or $d+1$ maximally conjugated bases, under individual eavesdropping attacks based on cloning machines and measurement after the basis reconciliation. We consider classical advantage distillation protocols, that allow to extract a key even in situations where the mutual information between the honest parties is smaller than the eavesdropper's information. In this scenario, advantage distillation protocols are shown to be as powerful as quantum distillation: key distillation is possible using classical techniqu…
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.
Constant-Overhead Fault-Tolerant Bell-Pair Distillation using High-Rate Codes
本文提出基于高速率qLDPC码的容错贝尔对蒸馏方案，实现恒定开销和恒定蒸馏率，在输入保真度低于约10%时保持容错，并可直接用于分布式量子计算。
Entanglement distillation, an essential quantum information processing task, refers to the conversion from multiple copies of noisy entangled states to a smaller number of highly entangled states. In this work, we study the non-asymptotic fundamental limits for entanglement distillation. We investigate the optimal tradeoff between the distillation rate, the number of prepared states, and the error tolerance. First, we derive the one-shot distillable entanglement under completely positive partial transpose preserving operations as a semidefinite program and demonstrate an exact characterization…
We describe a protocol for distilling maximally entangled bipartite states between random pairs of parties from those sharing a tripartite W state, and show that, rather surprisingly, the total distillation rate (the total number of EPR pairs distilled per W, irrespective of who shares them) may be done at a higher rate than distillation of bipartite entanglement between specified pairs of parties. Specifically, the optimal distillation rate for specified entanglement for the W has been previously shown to be the asymptotic entanglement of assistance of 0.92 EPR pairs per W, while our protocol…
Universal Entanglement Distillation
提出一种通用纠缠蒸馏协议，通过层析成像与自适应蒸馏结合，在未知双态系统中渐近达到最优可蒸馏纠缠速率，证明状态未知不导致速率损失。
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…
Universal, unambiguous concentration and distillation of Bell pairs
该研究提出了一种能无歧义地提纯贝尔对的方案，通过本地操作和测量实现高效提纯，适用于实际应用。
Forster, Winkler, and Wolf recently showed that weak nonlocality can be amplified by giving the first protocol that distills a class of nonlocal boxes (NLBs) [Phys. Rev. Lett. 102, 120401 (2009)]. We first show that their protocol is optimal among all non-adaptive protocols. We next consider adaptive protocols. We show that the depth 2 protocol of Allcock et al. [Phys. Rev. A 80, 062107, (2009)] performs better than previously known adaptive depth 2 protocols for all symmetric NLBs. We present a new depth 3 protocol that extends the known region of distillable NLBs. We give examples of NLBs fo…
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。
Basic entanglement distillation with realistic noise
本文结合多种噪声模型模拟与 IBM 固定频率器件实验，验证基础纠缠蒸馏可在真实噪声下提升 Bell 保真度并抑制相干误差。
Measurement-Based Entanglement Distillation and Constant-Rate Quantum Repeaters over Arbitrary Distances
提出可利用任意稳定子码的基于测量的纠缠纯化与量子中继协议，并以 QLDPC 码实现任意距离恒定产率 Bell 态分发及容错阈值。
We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2,1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer better than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer cod…
Cost of quantum secret key
本文研究了量子保密密钥的成本理论，证明了正则化形成密钥是量子态密钥成本的上界，并探讨了隐私稀释协议及单次 regime 中的收益-成本关系。
The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of any of these inequalities by a quantum state implies that pure-state entanglement can be distilled from it. The corresponding distillation protocol may require that some of the parties join into several groups. We show that there exists a link between the amount of the Bell inequality violation and the size of the groups they have to form for distillation. Thus, a strong violation is always sufficien…
We show the equivalence of two approaches to the design of entanglement distillation protocols. The first approach is based on local unitary operations that yield permutations of tensor products of Bell states. The second approach is based on stabilizer codes.
We construct new entanglement distillation protocols by interpolating between the recurrence and hashing protocols. This leads to asymptotic two-way distillation protocols, resulting in an improvement of the distillation rate for all mixed Bell diagonal entangled states, even for the ones with very high fidelity. We also present a method how entanglement-assisted distillation protocols can be converted into non-entanglement-assisted protocols with the same yield.
Blind quantum computation (BQC) provides an efficient method for the client who does not have enough sophisticated technology and knowledge to perform universal quantum computation. The single-server BQC protocol requires the client to have some minimum quantum ability, while the double-server BQC protocol makes the client's device completely classical, resorting to the pure and clean Bell-state shared by two servers. In this paper, we provide a deterministic entanglement distillation protocol in a practical noisy environment for the double-server BQC protocol. This protocol can obtain the pur…
A complementary behavior between local mutual information and average output entanglement is derived for arbitrary bipartite ensembles. This leads to bounds on the yield of entanglement in distillation protocols that involve disinguishing. This bound is saturated in the hashing protocol for distillation, for Bell-diagonal states.
Distillable entanglement under dually non-entangling operations
本文在保持可分态和可分测量的对偶非纠缠操作下给出了纠缠蒸馏速率的精确正则化公式，证明任意纠缠态均可蒸馏，并通过构造上界解决了Li和Winter提出的公开问题，同时表明DNE操作下纠缠理论具有强不可逆性。
Computational entanglement distillation beyond pure states: efficient protocols and fundamental limitations
本研究针对混合态纠缠蒸馏，确定Rényi相干信息为最坏情况下的最优速率，并设计了无需输入态知识的通用样本高效协议及高效协议，赋予其新的操作意义。
We present a new asymptotic bipartite entanglement distillation protocol that outperforms all existing asymptotic schemes. This protocol is based on the breeding protocol with the incorporation of two-way classical communication. Like breeding, the protocol starts with an infinite number of copies of a Bell-diagonal mixed state. Breeding can be carried out as successive stages of partial information extraction, yielding the same result: one bit of information is gained at the cost (measurement) of one pure Bell state pair (ebit). The basic principle of our protocol is at every stage to replace…
We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a family of attacks of two qubits, acting on half of a maximally entangled state of two qubits, the violation of a Bell inequality implies the possibility of an efficient secret-key extraction.
Hardware-Efficient Entanglement Distillation Using Bosonic Systems
本文提出利用单对玻色子系统的高维希尔伯特空间存储纠缠，并设计仅用局域玻色子操作的纠缠蒸馏协议，在损耗和退相干错误下显著提升保真度，实现比多贝尔对方法更硬件高效的纠缠蒸馏。
Quantum correlations: entanglement and quantumness of correlations are main resource for quantum information theory. In this chapter it is presented the scenarios which quantumness of correlations plays an interesting role in entanglement distillation protocol. By means of Koashi - Winter relation, it is discussed that quantumness of correlations are related to the irreversibility of the entanglement distillation protocol. The activation protocol is introduced, and it is proved that quantumness of correlations can create distillable entanglement between the system and the measurement apparatus…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。