G. Vidal, J. I. Cirac
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.
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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…
Motivated by the desire to better understand the class of quantum operations on bipartite systems that preserve positivity of partial transpose (PPT operations) and its relation to the class LOCC (local operations and classical communication), we present some results on deterministic bipartite pure state transformations by PPT operations. Restricting our attention to the case where we start with a rank K maximally entangled state, we give a necessary condition for transforming it into a given pure state, which we show is also sufficient when K is two and the final state has Schmidt rank three.…
Flexible Catalysis
提出灵活催化框架，允许催化剂在保持催化能力的前提下变换状态，统一了标准催化和多副本变换，并在局域酉和置换矩阵操作下实现标准催化无法达到的状态提取。
Catalysis in Action via Elementary Thermal Operations
本文在基本热操作框架下研究催化动力学，提出新工具刻画 qutrit 系统状态转换，发现小型催化剂可显著扩大可达状态集并缩小与通用热操作的差距，同时通过时间分辨演化揭示自由能交换机制。
Re-examination of the role of displacement and photon catalysis operation in continuous variable measurement device-independent quantum key distribution
本文重新检验了位移与光子催化在CV-MDI-QKD中的作用，发现催化操作仅带来边际收益，位移无益。
Thermal activation of photon catalysis in difference-intensity Mach-Zehnder interferometry with squeezed thermal light
本文研究单模压缩热光作为初始资源的差强度马赫-曾德尔干涉仪，发现热激活的单光子催化可提升相位估计性能，差强度探测接近精度极限且鲁棒性良好。
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…
A hierarchy of thermal processes collapses under catalysis
本研究通过引入环境温度Gibbs态催化剂，克服了简化热操作固有的Markovian性限制，证明在任意催化作用下不同热过程层级会收敛，且结果适用于能量本征基含相干性的初始态。
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。
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…
Quantum multiparameter estimation with multi-mode photon catalysis entangled squeezed state
本研究提出基于Fredkin门生成多模纠缠催化压缩真空态的方法，将其用于多相位同时估计，证实可提升QCRB性能且对光子损耗鲁棒性更强，可应用于量子计量多参数估计场景。
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。
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.
Non-Gaussian operations in continous variable (CV) quantum key distribution (QKD) have been limited to photon subtraction on squeezed vacuum states only. This is mainly due to the ease of calculating the covariance matrix representation of such states. In this paper we study the effects of general non-Gaussian operations corresponding to photon addition, catalysis and subtraction on squeezed coherent states on CV measurement device independent (MDI) QKD. We find that non-Gaussianity coupled with coherence can yield significantly longer transmission distances than without. Particularly we obser…
The discrete modulation can make up for the shortage of transmission distance in measurement-device-independent continuous-variable quantum key distribution (MDI-CVQKD) that has an unique advantage against all side-channel attacks but also challenging for the further performance improvement. Here we suggest a quantum catalysis (QC) approach for enhancing the performance of the discrete-modulated (DM) MDI-CVQKD in terms of the achievable secret key rate and lengthening the maximal transmission distance. The numerical simulation results show that the QC-based MDI-CVQKD with discrete modulation t…
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。
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.
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。
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…
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…
Non-Gaussian two mode squeezed thermal states in continuous variable quantum teleportation
本文研究了在双模压缩热态上实施光子扣除、添加和催化等非高斯操作以提升连续变量量子隐形传态保真度，发现在低和中等压缩水平下单光子催化与扣除为最优方案。
Heralded Non-Gaussian Squeezed-State Inputs for Parity-Detection SU(1,1) Interferometry
研究预告式非高斯操作对SU(1,1)干涉仪计量性能的影响，发现单光子 subtraction 等操作在部分透射率区域提升相位信息，但优化相干-压缩分配后其性能仍低于高斯基准，明确了资源约束下非高斯增强与实际精度的边界。
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。
Realistic non-Gaussian operations scheme in parity detection based Mach-Zehnder quantum interferometry
本文理论分析了基于宇称检测的MZI在光子扣除、添加和催化等现实非高斯操作下的相位灵敏度，推导了统一Wigner函数，发现考虑成功概率后光子添加最具优势。
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…
Covariant catalysis requires correlations and good quantum reference frames degrade little
该研究针对对称与守恒律限制下的量子协变催化问题，证明有效精确催化剂需建立关联、纯态催化剂无效，并发现高精度模拟幺正动力学的量子参考系退化程度极低。
Husimi phase distribution in non-Gaussian operations
本文研究非高斯操作（光子减除、增加和催化）对单模和双模压缩真空态Husimi相位分布的影响，揭示其在噪声下增强相位鲁棒性与灵敏度的不同作用，并强调设计量子态工程协议需综合考虑压缩、分束器透射率和环境相互作用。
Advantage of probabilistic non-Gaussian operations in the distillation of single mode squeezed vacuum state
本文研究了使用光子减除、光子增加和光子催化三种概率非高斯操作对单模压缩真空态进行压缩蒸馏，推导了Wigner特征函数，发现PS和PC操作可有效蒸馏压缩而PA不能，并确定了最佳参数。
Optimal Quantum Illumination with Nonlocal Non-Gaussian Operations
本文提出一种非局域非高斯操作协议，通过工程化探针态在考虑光子损失等现实条件时，优于基于光子催化、加法和减法的局部非高斯方案，并通过50:50光束分裂器实现目标检测的信噪比显著提升。
Enhanced phase estimation in parity detection based Mach-Zehnder interferometer using non-Gaussian two-mode squeezed thermal input state
本文探讨了在基于宇称检测的马赫-曾德尔干涉仪中，对双模压缩热（TMST）态执行光子扣除、添加和催化等非高斯操作以增强相位估计的方法，推导了统一Wigner函数，并发现考虑成功概率时光子催化为最优操作。
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.
Optimal non-Gaussian operations in difference-intensity detection and parity detection-based Mach-Zehnder interferometer
本研究探讨了在差分强度和奇偶探测MZI中，通过光子减法、加法和催化等非高斯操作提升相位估计精度，并确定了各自最优操作及参数，同时推导了矩生成函数以支持其他探测方案。
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.
Energy-Invariant Catalysis of Stable Ergotropy in Strongly Coupled Spin-Chain Quantum Batteries
本文研究了通过能量不变催化剂稳定强耦合自旋链量子电池中的稳态能量，通过非马尔可夫效应的系统表征，抑制非马尔可夫振荡，促进可提取工作准稳态。
Continuous variable quantum teleportation in a dissipative environment: Comparison of non-Gaussian operations before and after noisy channel
本文研究了连续变量量子隐形传态中，在噪声信道前后执行非高斯操作（光子减除、添加、催化）的相对优势，发现最优策略取决于操作类型、初始压缩和信道参数，可用于提升耗散环境中的量子信息处理效率。
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…
Non-Gaussian operations have been studied intensively in recent years due to their ability to enhance the entanglement of quantum states. However, most previous studies on such operations are carried out in a single-mode setting, even though in reality any quantum state contains multi-mode components in frequency space. Whilst there have been general frameworks developed for multi-mode photon subtraction (PS) and photon addition (PA), an important gap exists in that no framework has thus far been developed for multi-mode photon catalysis (PC). In this work we close that gap. We then apply our …
Conversion of entangled states under (Stochastic) Local Operations and Classical Communication admits the phenomenon of catalysis. Here we explore the possibility of a copy of the initial state itself to perform as a catalyst, which we call a self-catalytic process. We show explicit examples of self-catalysis. Necessary and sufficient conditions for the phenomenon to take place are discussed. We numerically estimate how frequent it is and we show that increasing the number of copies used as catalyst can increases the probability of conversion, but do not make the process deterministic. By the …
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…
Parity-detection-based Mach-Zehnder interferometry with coherent and non-Gaussian squeezed vacuum states as inputs
本文理论上研究了基于宇称探测的Mach-Zehnder干涉仪在相位估计中引入非高斯操作的优势，发现光子扣除、添加和催化均能提升相位灵敏度，其中单光子添加为最佳操作。
Reversible state transformations under entanglement non-increasing operations give rise to entanglement measures. It is well known that asymptotic local operations and classical communication (LOCC) are required to get a simple operational measure of bipartite pure state entanglement. For bipartite mixed states and multipartite pure states it is likely that a more powerful class of operations will be needed. To this end \cite{BPRST01} have defined more powerful versions of state transformations (or reducibilities), namely LOCCq (asymptotic LOCC with a sublinear amount of quantum communication)…
Quantum computing enhanced computational catalysis
本文提出改进的量子算法以显著降低计算成本，并对钌催化剂转化二氧化碳为甲醇的催化循环进行了准确的量子计算资源估计，探讨了未来量子硬件的要求。
The power of quantum catalytic local operations
该研究探讨了量子催化在局域操作中的作用，通过引入催化局域操作（CLO）并与LOCC及有界量子通信增强的随机LOCC比较，证明这些类别不可比较，揭示了量子态变换的不同方面。
Long-distance high-fidelity continuous-variable quantum key distribution with non-Gaussian operations: An exact closed form solution
本研究推导了含零光子催化和量子剪刀的连续变量量子密钥分发协议输出态的闭式解，通过参数优化显著提升协议的传输距离与保真度，纯损耗信道下最大距离仅比无中继极限低6.5%，且二者存在权衡关系。
Catalytic Enhancement of Coherence in Noisy Quantum Channels and Characterization of Strictly Incoherent Operations
本文研究了在噪声量子通道中通过预处理输入态来增强输出态相干分数的可能性，并提出了严格不可约操作的必要且充分条件，为相干性操控提供了新的结构理解。
Optomechanical non-Gaussian quantum steering and remote preparation of large-size motional Schördinger cat states
本文提出利用腔光机械系统中的多光子操作产生非高斯量子导引，并基于Fisher信息判据揭示其增强特性，进而通过零差探测远程制备大尺寸机械振子薛定谔猫态，为量子基础检验与应用提供新途径。
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 …
Understanding the interplay of entanglement and nonlocality: motivating and developing a new branch of entanglement theory
本文提出以局域操作与共享随机性（LOSR）替代LOCC作为自由操作，解决非定域性异常、建立无病态特征的多体纠缠与非定域性概念，并推广自检验的资源论解释，从而开创纠缠理论新分支。
We investigate the local implementation of nonlocal operations with the block matrix form, and propose a protocol for any diagonal or offdiagonal block operation. This method can be directly generalized to the two-party multiqubit case and the multiparty case. Especially, in the multiparty cases, any diagonal block operation can be locally implemented using the same resources as the multiparty control-U operation discussed in Ref. [Eisert et al., Phys. Rev. A 62, 052317(2000)]. Although in the bipartite case, this kind of operations can be transformed to control-U operation using local operati…
We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small amount of entanglement; (ii) that a known, noisy, non-local unitary operation as well as an unknown, noisy, local unitary operation can be purified; (iii) how to perform the tomography of arbitrary, unknown, non-local operations; (iv) that a set of local unitary operations as well as a set of non-local unitary operations can be stored and compressed; (v) how t…
We propose a protocol for local implementation of two consecutive nonlocal operations by three parters. It consumes one shared GHZ state in this protocol. We also demonstrate that these resources are sufficient and necessary to locally implement two consecutive CNOT operations.
The problem behind this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of $k=1$, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfe…
Einstein introduced the locality principle which states that all physical effect in some finite space-time region does not influence its space-like separated finite region. Recently, in algebraic quantum field theory, Rédei captured the idea of the locality principle by the notion of operational separability. The operation in operational separability is performed in some finite space-time region, and leaves unchanged the state in its space-like separated finite space-time region. This operation is defined with a completely positive map. In the present paper, we justify using a completely posit…
We deal with families of probability distributions satisfying non-signalling condition, called non-signalling boxes and consider class of operations that transform local boxes into local ones (the one that admit LHV model). We prove that any operation from this class can not broadcast a nonlocal box in 2x2 case. We consider a function called anti-Robustness which can not decrease under these operations. The proof reduces to showing that anti-Robustness would decrease after broadcasting.
We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguishable by local operations and classical communication when a finite number of runs is allowed. We then directly extend this result into the case when the number of unitary operations to be discriminated is more than two. Intuitively, our result means that the lost identity of a nonlocal (entangled) unitary operation can be recovered locally, without any use of entanglement or joint quantum operations.
We study when a multipartite non--local unitary operation can deterministically or probabilistically simulate another one when local operations of a certain kind -in some cases including also classical communication- are allowed. In the case of probabilistic simulation and allowing for arbitrary local operations, we provide necessary and sufficient conditions for the simulation to be possible. Deterministic and probabilistic interconversion under certain kinds of local operations are used to define equivalence relations between gates. In the probabilistic, bipartite case this induces a finite …
Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established: (i) There is a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. (ii) The existence of the ball of local operations with shared randomness is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. (iii) Local operations with shared entanglement are characterized in terms of linear…
Graph states are quantum states that can be described by a stabilizer formalism and play an important role in quantum information processing. We consider the action of local unitary operations on graph states and hypergraph states. We focus on non-Clifford operations and find for certain transformations a graphical description in terms of weighted hypergraphs. This leads to the indentification of hypergraph states that are locally equivalent to graph states. Moreover, we present a systematic way to construct pairs of graph states which are equivalent under local unitary operations, but not equ…
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyse classical communication from a quantum action.
We study the discrimination of multipartite quantum states by local operations and classical communication. We derive that any optimal discrimination of quantum states spanning a two-dimensional Hilbert space in which each party's space is finite dimensional is possible by local operations and one-way classical communication, regardless of the optimality criterion used and how entangled the states are.
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