Yuan Feng, Runyao Duan, Mingsheng Ying
We determine all $2\times 2$ quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a sufficient and necessary condition is derived under which a certain probabilistic transformation has useful catalysts.
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In this paper we summarize the necessary condition for incomparable states which can be catalyzed under entanglement-assisted LQCC (ELQCC). When we apply an extended condition for entanglement transformation to entanglement-assisted local manipulation we obtain a fundamental limit for entanglement catalysts. Some relative questions are also discussed.
I consider the use of entanglement between two parties to enable one to authenticate her identity to another over a quantum communication channel. Exploiting the phenomenon of entanglement-catalyzed transformations between pure states gives a potentially reusable entangled identification token. In analyzing this, I consider the independently interesting problem of the best possible approximation to a given pure entangled state realizable using local actions and classical communication by parties sharing a different entangled state.
We demonstrate that multiple copies of a bipartite entangled pure state may serve as a catalyst for certain entanglement transformations while a single copy cannot. Such a state is termed a "multiple-copy catalyst" for the transformations. A trade-off between the number of copies of source state and that of the catalyst is also observed. These results can be generalized to probabilistic entanglement transformations directly.
I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantu…
Advantage of flexible catalysis for entanglement and quantum thermodynamics
研究灵活催化在纠缠和量子热力学中的能力，发现其比标准催化更强大，能实现确定性转换和提高成功概率。
Machine learning techniques have been successfully applied to classifying an extensive range of phenomena in quantum theory. From detecting quantum phase transitions to identifying Bell non-locality, it has been established that classical machines can learn genuine quantum features via classical data. Quantum entanglement is one of the uniquely quantum phenomena in that range, as it has been shown that neural networks can be used to classify different types of entanglement. Our work builds on this topic. We investigate whether distinct models of neural networks can learn how to detect catalysi…
No-go theorem for entanglement distillation using catalysis
本文证明催化辅助无法从正偏置转置束缚纠缠态中蒸馏纠缠，从而排除催化使纠缠理论渐近可逆的可能，并给出关联催化剂辅助下的新渐近界。
We prove that any multiple-copy entanglement transformation [S. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A \textbf{65}, 052315 (2002)] can be implemented by a suitable entanglement-assisted local transformation [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. \textbf{83}, 3566 (1999)]. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assisted one is still equivalent to the pure entanglement-assisted one. The mathematical structure of multiple-copy entanglement transformations then is carefully investigated. Many interestin…
We consider entanglement-assisted remote quantum state manipulation of bi-partite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficie…
Entanglement Catalysis Beyond the Asymptotic Rate
该研究探讨用纠缠催化剂缓解有限尺寸对纠缠浓缩产率的惩罚，发现其虽不提升渐近产率，但可改变有限尺寸标度，完全克服非均匀施密特系数双纯态的有限尺寸惩罚。
Entanglement catalysis for quantum states and noisy channels
本工作研究了纠缠催化在量子通信中的作用，证明了双方纯态变换中通用催化剂的存在，并开发了有噪量子信道辅助下估计单重态数量的方法，导出了单次使用信道建立最大单重态的最优协议。
The tensor rank (also known as generalized Schmidt rank) of multipartite pure states plays an important role in the study of entanglement classifications and transformations. We employ powerful tools from the theory of homogeneous polynomials to investigate the tensor rank of symmetric states such as the tripartite state $\ket{W_3}=\tfrac{1}{\sqrt{3}}(\ket{100}+\ket{010}+\ket{001})$ and its $N$-partite generalization $\ket{W_N}$. Previous tensor rank estimates are dramatically improved and we show that (i) three copies of $\ket{W_3}$ has rank either 15 or 16, (ii) two copies of $\ket{W_N}$ has…
PPT Entanglement with Correlated Catalysis: Monotones and Irreversibility
该研究在PPT资源理论中，利用正则化PPT相对熵构造单调量，证明其完全可加且强超加性，发现关联催化无法消除混态纠缠操纵的基本限制，最优蒸馏率仍小于纠缠成本。
The non-Gaussian operation can be used not only to enhance and distill the entanglement between Gaussian entangled states, but also to improve quantum communications. In this paper, we propose an non-Gaussian continuous-variable quantum key distribution (CVQKD) by using quantum catalysis (QC), which is an intriguing non-Gaussian operation in essence that can be implemented with current technologies. We perform quantum catalysis on both ends of the Einstein-Podolsky-Rosen (EPR) pair prepared by a sender, Alice, and find that for the single-photon QC-CVQKD, the bilateral symmetrical quantum cata…
Starting from Barnum's recent proposal to use entanglement and catalysis for quantum secure identification [quant-ph/9910072], we describe a protocol for quantum authentication and authenticated quantum key distribution. We argue that our scheme is secure even in the presence of an eavesdropper who has complete control over both classical and quantum channels.
We show how entanglement can be used, without being consumed, to accomplish unitary operations that could not be performed with out it. When applied to infinitesimal transformations our method makes equivalent, in the sense of Hamiltonian simulation, a whole class of otherwise inequivalent two-qubit interactions. The new catalysis effect also implies the asymptotic equivalence of all such interactions.
We show that entanglement-assisted transformations of bipartite entangled states can be more efficient than catalysis [D. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 (1999)}, i.e., given two incomparable bipartite states not only can the transformation be enabled by performing collective operations with an auxiliary entangled state, but the entanglement of the auxiliary state itself can be enhanced. We refer to this phenomenon as supercatalysis. We provide results on the properties of supercatalysis and its relationship with catalysis. In particular, we obtain a useful necessary and s…
Catalysis of entanglement and other quantum resources
本文综述量子催化领域的最新进展与发展历史，聚焦纠缠与相干催化，探讨其在量子热力学等领域的应用及通用催化、催化挪用等现象。
Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation. However, an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively. In this paper we are mainly concerned with the feasibility of partial entanglement recovery. The bas…
Enhancing quantum entanglement is important for many quantum information processing applications. In this paper, we consider a protocol for entanglement enhancing in a two-mode squeezed vacuum state (TMSVS), attained based on photon subtraction, photon catalysis, and photon addition. Central to such an operation is the task of mixing and detecting number states with each mode of TMSVS. We analyze various settings and find an optimal setup for improving the entanglement of the state.
We show that bipartite and tripartite entangled states cannot be used as catalysis states to enable local transformations inbetween inequivalent classes of three-particle entangled states which are non-interchangeable under local transformations. We find the optimal protocol for conversion of a certain family of the W-states and an EPR-pair into the GHZ-state.
Photon catalysis for general multimode multi-photon quantum state preparation
本文提出了一种基于光子催化机制，利用多端口干涉仪等设备实现任意多模式多光子态的精确制备，并验证了其在不同态类上的100%保真度。
Quantum-enhanced distributed network sensing using multiple quantum resources
本文提出了一种理论方案，通过整合三种量子资源（量子催化、纠缠和压缩）来实现量子增强的分布式网络传感，展示了在多相估计中利用这些资源所带来的性能优势。
We analyze approximate transformations of pure entangled quantum states by local operations and classical communication, finding explicit conversion strategies which optimize the fidelity of transformation. These results allow us to determine the most faithful teleportation strategy via an initially shared partially entangled pure state. They also show that procedures for entanglement manipulation such as entanglement catalysis [Jonathan and Plenio, Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states involved, and motivate the notion of non-local fidelity, which qua…
We are concerned with catalyst-assisted probabilistic entanglement transformations. A necessary and sufficient condition is presented under which there exist partial catalysts that can increase the maximal transforming probability of a given entanglement transformation. We also design an algorithm which leads to an efficient method for finding the most economical partial catalysts with minimal dimension. The mathematical structure of catalyst-assisted probabilistic transformation is carefully investigated.
A utility theory of entanglement is formulated, based on the von Neumann--Morgenstern theorem. As a specific example, a protocol for measurement--induced entanglement is studied, in which the amount of entanglement obtained depends on the random result of a measurement on an ancilla. It is shown that the maximization of the utility requires a non--trivial strategy. The results are especially useful when the interaction between the ancilla and the systems to be entangled is weak.
Nonlocal gate operation is based on sharing an ancillary pair of qubits in perfect entanglement. When the ancillary pair are partially entangled, the efficiency of the gate operation drops. Using general transformations, we devise probabilistic nonlocal gates, which perform the nonlocal operation conclusively when the ancillary pair are only partially entangled. We show that a controlled purification protocol can be implemented by the probabilistic nonlocal operation.
The basic \emph{entanglement swapping protocol} allows to project two qubits, which have never interacted, onto a maximally entangled state. For deterministic swapping, the key ingredient is the maximal entanglement that was initially contained in two pairs of qubits and the capacity of projecting onto a Bell basis. Thus the basic and deterministic entanglement swapping scheme involves three maximal level of entanglement. In this work we propose probabilistic entanglement swapping processes performed with different amounts of initial entanglement. Besides that we suggest a non Bell measuring-b…
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。
Recently it has been demonstrated that it is possible to harvest quantum resources other than entanglement from a coherent scalar field. Employing time-dependent perturbation theory, we present a complete analysis of the conditions under which a spatially extended Unruh-DeWitt detector coupled to the proper time derivative of the field can harvest coherence for any initial state of the field, as well as the energy cost that is required for each harvest. By studying harvesting under repeatable extractions it is proven that when the detector interacts with the field through a delta coupling cohe…
Catalytic channels are the only noise-robust catalytic processes
研究证明鲁棒催化在特定量子资源理论中不可行，但热力学场景中可实现最大催化优势。
Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We …
Teleportation may be taken as sending and extracting quantum information through quantum channels. In this report, it is shown that to get the maximal probability of exact teleportation through partially entangled quantum channels, the sender (Alice) need only to operate a measurement which satisfy an ``entanglement matching'' to this channel. An optimal strategy is also provided for the receiver (Bob) to extract the quantum information by adopting general evolutions.
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
We propose to produce entanglement by measuring the transmission of an optical cavity. Conditioned on the detection of a reflected photon, pairs of atoms in the cavity are prepared in maximally entangled states. The success probability depends on the cavity parameters, but high quality entangled states may be produced with a high probability even for cavities of moderate quality.
We address fundamental limitations of quantum teleportation -- the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e. without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faith…
We propose a method to speed up the quantum adiabatic algorithm using catalysis by many-body delocalization. This is applied to random-field antiferromagnetic Ising spin models. The algorithm is catalyzed in such a way that the evolution approximates a Heisenberg model in the middle of its course, and the model is in a delocalized phase. We show numerically that we can speed up the standard algorithm for finding the ground state of the random-field Ising model using this idea. We also demonstrate that the speedup is due to gap amplification, even though the underlying model is not frustration-…
Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical co…
Optimal stellar rank approximation of squeezed cat states with photon catalysis
本文利用恒星秩形式化方法，分析光子催化协议在生成压缩猫态中的最优性，并量化非高斯资源复杂度、保真度与损耗之间的权衡。
A scheme is proposed to entangle two systems that have not interacted by using an ancillary particle in a Mach-Zehnder interferometer, by making a suitable post--selection of the particle followed by a conditional feedback on one of the subsystems to be entangled. For a strong interaction, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state.
We show that the resource theory of contextuality does not admit catalysts, i.e., there are no correlations that can enable an otherwise impossible resource conversion and still be recovered afterward. As a corollary, we observe that the same holds for nonlocality. As entanglement allows for catalysts, this adds a further example to the list of "anomalies of entanglement," showing that nonlocality and entanglement behave differently as resources. We also show that catalysis remains impossible even if, instead of classical randomness, we allow some more powerful behaviors to be used freely in t…
Entanglement gain in supercatalytic state transformations
本研究引入了超催化纠缠增益作为衡量标准，探讨了在不同催化剂选择下超催化变换的性能及最大增益实现方法。
In this paper we analyze the existence of joint probabilities for the Bell-type and GHZ entangled states. We then propose the usage of nonmonotonic upper probabilities as a tool to derive consistent joint upper probabilities for the contextual hidden variables. Finally, we show that for the extreme example of no error, the GHZ state allows for the definition of a joint upper probability that is consistent with the strong correlations.
We study the entanglement structure, i.e., the structure of quantum composite system from operational aspects. The structure is not uniquely determined in General Probabilistic Theories (GPTs) even if we impose reasonable postulate about local systems. In this paper, we investigate the possibility that the standard entanglement structure can be determined uniquely by repeatability of measurement processing and its saturated situation called self-duality. Surprisingly, self-duality cannot determine the standard entanglement structure even if we additionally impose local unitary symmetry assumpt…
An inversion method is formulated for extracting entanglement-related information on two-particle interactions in a one-dimensional system from measurable one-particle position- and momentum-distribution functions. The method is based on a shell-like expansion of these norm-1 measured quantities in terms of product states taken from a parametric orthonormal complete set. The mathematical constraints deduced from these point-wise expansions are restricted by the underlying physics of our harmonically confined and interacting Heisenberg model. Based on these exact results, we introduce an approx…
It is well-known that pure quantum states are typically almost maximally entangled, and thus have close to maximally mixed subsystems. We consider whether this is true for probabilistic theories more generally, and not just for quantum theory. We derive a formula for the expected purity of a subsystem in any probabilistic theory for which this quantity is well-defined. It applies to typical entanglement in pure quantum states, coin tossing in classical probability theory, and randomization in post-quantum theories; a simple generalization yields the typical entanglement in (anti)symmetric quan…
Utilizing probabilistic entanglement between sensors in quantum networks
针对星形量子传感网络中纠缠概率生成且保真度有限的问题，本文利用量子 Fisher 信息比较协议，给出纠缠使用、存储与提纯的条件及经典传感更优的保真度阈值。
An ideal controlled-NOT gate followed by projective measurements can be used to identify specific Bell states of its two input qubits. When the input qubits are each members of independent Bell states, these projective measurements can be used to swap the post-selected entanglement onto the remaining two qubits. Here we apply this strategy to produce heralded two-photon polarization entanglement using Bell states that originate from independent parametric down-conversion sources, and a particular probabilistic controlled-NOT gate that is constructed from linear optical elements. The resulting …
Finite-size catalysis in quantum resource theories
本文研究了有限尺寸催化剂在量子资源理论中的应用，提出有限尺寸催化条件及与多份转换的联系，揭示了催化共振现象，通过纠缠和热力学资源理论示例验证了结果。
A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres--Horodecki positive partial transpose (ppt)-criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevic…
We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for ``pure contraction'' transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.
We demonstrate a complete, probabilistic quantum dynamical simulation of the standard nonlinear Hamiltonian of optomechanics, including decoherence at finite temperatures. Robust entanglement of an optical pulse with the oscillator is predicted, as well as strong quantum steering between the optical and mechanical systems. Importantly, our probabilistic quantum simulation method uses the positive-P technique, which is scalable to large Hilbert spaces.
We study the entanglement of entangled coherent states in vacuum environment by employing the entanglement of formation and propose a scheme to probabilistically teleport a coherent superposition state via entangled coherent states, in which the amount of classical information sent by Alice is restricted to one bit. The influence of decoherence due to photon absorpation is considered. It is shown that decoherence can improve the mean fidelity of probabilistic teleportation in some situations.
We study a quantum theory based on two assumptions: In the intrinsic frame of reference of an isolated, macroscopic system, (i) the system has no global motion and is not entangled with any other system, (ii) time evolution of statevectors of systems outside the system satisfy Schrödinger equation. A process of collision-type interaction between a microscopic system and a macroscopic system is studied in an auxiliary frame of reference. In transforming the statevector of the two systems obtained in the auxiliary frame of reference to the intrinsic frame of reference of the macroscopic system, …
Entanglement-swapping in generalised probabilistic theories, and iterated CHSH games
本文研究广义概率理论中的纠缠交换，引入迭代CHSH博弈衡量非经典关联保持能力，并构造出在任意轮数后仍达到CHSH值4的GPT，回应了量子理论最优性问题。
In this article, a procedure called Probabilistic Swapped-Bell-States Analysis (PSBA) is proposed. Using this procedure two communication partners can transmit (binary-encoded) information over large spatial distances. This procedure is unusual insofar as no classical communication channels are used either during or after information encoding. To make this possible, entanglement swapping is used as a transport channel. The encoding of bits is realized by the execution (or non-execution, as the case may be) of entanglement swapping on multiple photon pairs, while decoding is realized by a stati…
We proposed a general transformation in probabilistic teleportation, which is based on different entanglement matching coefficients $K$ corresponding to different unitary evolution which provides one with more flexible evolution method experimentally. Through analysis based on the Bell basis and generalized Bell basis measurement for two probabilistic teleportation, we suggested a general probability of successful teleportation, which is not only determined by the entanglement degree of transmission channels and measurement methods, but also related to the unitary transformation in the telepor…
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability, hence probabilistic teleportation. We also give a generalized protocol for entanglement swapping using non-maximally e…
We formulate the problem of finding the optimal entanglement swapping scheme in a quantum repeater chain as a Markov decision process and present its solution for different repeater's sizes. Based on this, we are able to demonstrate that the commonly used "doubling" scheme for performing probabilistic entanglement swapping of probabilistically distributed entangled qubit pairs in quantum repeaters does not always produce the best possible raw rate. Focussing on this figure of merit, without considering additional probabilistic elements for error suppression such as entanglement distillation on…
Fundamental trade-off relation in probabilistic entanglement generation
该研究通过量子过程叠加推导出纠缠生成的普遍权衡关系，并展示了如何利用量子开关实现该原则，提出了一种新的纠缠生成控制方法。
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