We determine the degree of entanglement for two indistinguishable particles based on the two-qubit tensor product structure, which is a framework for emphasizing entanglement founded on observational quantities. Our theory connects canonical entanglement and entanglement based on occupation number for two fermions and for two bosons and shows that the degree of entanglement, based on linear entropy, is closely related to the correlation measure for both the bosonic and fermionic cases.
We study the problem of witnessing entanglement among indistinguishable particles. For this purpose, we derive a set of equations which results in necessary and sufficient conditions for probing multipartite entanglement between arbitrary systems of Bosons or Fermions. The solution of these equations yields the construction of optimal entanglement witnesses for partial and full entanglement in discrete and continuous variable systems. Our approach unifies the verification of entanglement for distinguishable and indistinguishable particles. We provide general solutions for certain observables t…
Hyper-hybrid entanglement for two indistinguishable bosons has been recently proposed by Li \textit{et al.} [Y. Li, M. Gessner, W. Li, and A. Smerzi, \href{https://doi.org/10.1103/PhysRevLett.120.050404}{Phys. Rev. Lett. 120, 050404 (2018)}]. In the current paper, we show that this entanglement exists for two indistinguishable fermions also. Next, we establish two {\em no-go} results: no hyper-hybrid entanglement for two {\em distinguishable} particles, and no unit fidelity quantum teleportation using {\em indistinguishable} particles. If either of these is possible, then the {\em no-signaling…
Two important results of quantum physics are the \textit{no-cloning} theorem and the \textit{monogamy of entanglement}. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results imply the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually), a maximum violation of the monogamy of entanglement is possible by the …
We provide a general framework which allows one to obtain the dynamics of $N$ noninteracting spatially indistinguishable particles locally coupled to separated environments. The approach is universal, being valid for both bosons and fermions and for any type of system-environment interaction. It is then applied to study the dynamics of two identical qubits under paradigmatic Markovian noises, such as phase damping, depolarizing and amplitude damping. We find that spatial indistinguishability of identical qubits is a controllable intrinsic property of the system which protects quantum entanglem…
There is a debate in course about the quantification of entanglement of indistinguishable particles and recently a new method due to Lo Franco and Compagno (LFC) [Sci. Rep. \textbf{6}, 20603 (2016)] appeared with the aim of settling the controversies of this debate. In this work we show that the LFC approach can be recovered using the second quantization formalism and a local single-particle basis to perform the trace over one particle state. The use of the second quantization formalism has the advantage of being well known in many-body physics. We also compare the LFC and second quantization …
We investigate the quantum phase transitions of the extended Hubbard model at half-filling with periodic boundary conditions employing the entanglement of particles, as opposed to the more traditional entanglement of modes. Our results show that the entanglement has either discontinuities or local minima at the critical points. We associate the discontinuities to first order transitions, and the minima to second order ones. Thus we show that the entanglement of particles can be used to derive the phase diagram, except for the subtle transitions between the phases SDW-BOW, and the superconducto…
Quantumness of correlations in indistinguishable particles
我们讨论了在费米子或玻色子不可区分的粒子的量子关联的一般概念。我们的方法主要是基于单粒子观测量的代数的识别，这使我们能够设计一个激活协议，其中系统中的\textit{quantumness of correlations}导致不可避免的创建与测量设备的纠缠。利用纠缠的可解性，即纠缠的相对熵作为纠缠度量，我们证明了我们的方法等价于单粒子冯诺依曼测量中的最小扰动概念，并给出了量子化的几何方法.
The study of entanglement in systems composed of identical particles raises interesting challenges with far-reaching implications in both, our fundamental understanding of the physics of composite quantum systems, and our capability of exploiting quantum indistinguishability as a resource in quantum information theory. Impressive theoretical and experimental advances have been made in the last decades that bring us closer to a deeper comprehension and to a better control of entanglement. Yet, when it involves composites of indistinguishable quantum systems, the very meaning of entanglement, an…
Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated to the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude whose structure in terms of single-particle amplitudes we here derive by first principles. To characterise entanglement among the identical particles, this new method utilises the sam…
Entanglement is one of the strongest quantum correlation, and is a key ingredient in fundamental aspects of quantum mechanics and a resource for quantum technologies. While entanglement theory is well settled for distinguishable particles, there are five inequivalent approaches to entanglement of indistinguishable particles. We analyse the different definitions of indistinguishable particle entanglement in the light of the locality notion. This notion is specified by two steps: i) the identification of subsystems by means of their local operators; ii) the requirement that entanglement represen…
We introduce geometric measures of entanglement for indistinguishable particles, which apply to mixed states, multipartite systems, and arbitrary dimensions. They are based on generalized (i.e., not necessarily finite) norms on the set of quantum states and lead to the first necessary and sufficient computational separability criterion in this general setting. The coherent approach developed in the paper allows us to compare, in particular, entanglement for fermionic and distinguishable particles: The entanglement measure for fermionic particles coincides with the corresponding entanglement me…
Unlike in the case of distinguishable particles, the concept of entanglement-- not to mention, nonlocality-- remains debated in case of indistinguishable particles. Here, we show that certain existing all-versus-nothing type of proofs of contextuality or nonlocality for distinguishable particles, based on a logical contradiction, may be carried over to indistinguishable particles.
The development of scalable sources of non-classical light is fundamental to unlock the technological potential of quantum photonics\cite{Kimble:Nat2008}. Among the systems under investigation, semiconductor quantum dots are currently emerging as near-optimal sources of indistinguishable single photons. However, their performances as sources of entangled-photon pairs are in comparison still modest. Experiments on conventional Stranski-Krastanow InGaAs quantum dots have reported non-optimal levels of entanglement and indistinguishability of the emitted photons. For applications such as entangle…
In this paper, we construct $2n-1$ locally indistinguishable orthogonal product states in $\mathbb{C}^n\otimes\mathbb{C}^{4}~(n>4)$ and $\mathbb{C}^n\otimes\mathbb{C}^{5}~(n\geq 5)$ respectively. Moreover, a set of locally indistinguishable orthogonal product states with $2(n+2l)-8$ elements in $\mathbb{C}^n\otimes\mathbb{C}^{2l}~(n\geq 2l>4)$ and a class of locally indistinguishable orthogonal product states with $2(n+2k+1)-7$ elements in $\mathbb{C}^n\otimes\mathbb{C}^{2k+1}~(n\geq 2k+1>5)$ are also constructed respectively. These classes of quantum states are then shown to be distinguishabl…
Entanglement and Extreme Spin Squeezing for a Fluctuating Number of Indistinguishable Particles
我们从[A. S. Sørensen和K. Mølmer，Phys. Rev. Lett. { \bf 86}，4431（2001）]中描述的方法。我们还讨论了其他自旋压缩不等式如何推广到这种情况。此外，我们给出了一个操作意义的情况下，个别粒子不能解决的界限。作为一个副产品，这使我们能够表明，在自旋压缩实验与冷气体的粒子是典型的区分在实践中。我们的结果证明了Sørensen-Mølmer边界在最近的玻色-爱因斯坦凝聚体自旋压缩实验中的应用。
The cascade-emitted biphotons generated from the alkali metal atomic ensembles are an excellent entanglement resource which enables long-distance quantum communication. The communication of quantum information between distant locations can be realized by utilizing the low-loss telecom bandwidth in the upper transition of the cascaded photons in a fiber-based quantum network. Meanwhile, the infrared photon from the lower transition of this highly directional and frequency-correlated biphoton can be created under the four-wave mixing process and can be stored locally as a collective spin wave. H…
We extend a procedure exploiting spatial indistinguishability of identical particles to recover the spoiled entanglement between two qubits interacting with Markovian noisy environments. Here, the spatially localized operations and classical communication (sLOCC) operational framework is used to activate the entanglement restoration from the indistinguishable constituents. We consider the realistic scenario where noise acts for the whole duration of the process. Three standard types of noises are considered: a phase damping, a depolarizing, and an amplitude damping channel. Within this general…
Geometric quantifier of the incompatibility of single-particle property attribution in indistinguishable boson systems
Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba（科尔多瓦国立大学数学、天文学、物理与计算学院）；Instituto de Física Enrique Gaviola, CONICET - UNC（恩里克·加维亚拉物理研究所，阿根廷国家科学研究委员会-科尔多瓦国立大学）；Instituto de Física, Universidad Nacional Autónoma de México（墨西哥国立自治大学物理研究所）；Universidad Nacional de Hurlingham (UNAHUR)（乌尔辛汉姆国立大学）
For systems consisting of distinguishable particles, there exists an agreed upon notion of entanglement which is fundamentally based on the possibility of addressing individually each one of the constituent parties. Instead, the indistinguishability of identical particles hinders their individual addressability and has prompted diverse, sometimes discordant definitions of entanglement. In the present review, we provide a comparative analysis of the relevant existing approaches, which is based on the characterization of bipartite entanglement in terms of the behaviour of correlation functions. …
Studying quantum entanglement in systems of indistinguishable particles, in particular anyons, poses subtle challenges. Here, we investigate a model of one-dimensional anyons defined by a generalized algebra. This algebra has the special property that fermions in this model are composites of anyons. A Hubbad-like Hamiltonian is considered that allows hopping between nearest neighbour sites not just for the fundamental anyons, but for the fermionic anyon composites. Some interesting results regarding the quantum entanglement of these particles are obtained.
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum …
Issues related to quantum entanglement in systems of indistinguishable particles, as discussed in the information theoretic approach, are extended to anyonic statistics. Local and non-local measurements discussed in this framework are carefully analysed in the two-site anyonic Hubbard model which provides a concrete case-study. The von Neumann entropy, the single-particle density matrix, the pair correlation function, and the pseudo-momentum distribution function are worked out paying special attention to the dependence on the statistics parameter.
We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the indistinguishable ones, including the reduced density matrix and familiar entanglement measures. The rigorous quantitative relation between the amount of entanglement and the spatial coherence of particles is possible in this formalism. Our entanglement detection process is a generalization of the entanglement extraction protocol for identical particles with mode split…
It was shown recently that entanglement of identical particles has a feature called dualism [Phys. Rev. Lett. 110, 140404 (2013)], which is fundamentally connected with quantum indistinguishability. Here we report an experiment that observes the entanglement duality for the first time with two identical photons, which manifest polarization entanglement when labeled by different paths or path entanglement when labeled by polarization states. By adjusting the mismatch in frequency or arrival time of the entangled photons, we tune the photon indistinguishability from quantum to classical limit an…
A central challenge in developing quantum computers and long-range quantum networks lies in the distribution of entanglement across many individually controllable qubits. Colour centres in diamond have emerged as leading solid-state 'artificial atom' qubits, enabling on-demand remote entanglement, coherent control of over 10 ancillae qubits with minute-long coherence times, and memory-enhanced quantum communication. A critical next step is to integrate large numbers of artificial atoms with photonic architectures to enable large-scale quantum information processing systems. To date, these effo…
Hong-Ou-Mandel interference of more than 10 indistinguishable atoms
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)（德国航空航天中心）；Instituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (INO-CNR)（意大利国家光学研究所，国家研究委员会）；University of the Basque Country UPV/EHU（巴斯克大学）
Trapped atomic ions embedded in optical cavities are a promising platform to enable long-distance quantum networks and their most far-reaching applications. Here we achieve and analyze photon indistinguishability in a telecom-converted ion-cavity system. First, two-photon interference of cavity photons at their ion-resonant wavelength is observed and found to reach the limits set by spontaneous emission. Second, this limit is shown to be preserved after a two-step frequency conversion replicating a distributed scenario, in which the cavity photons are converted to the telecom C band and then b…
