We provide analytic insight into the generation of stationary itinerant photon entanglement in a 3-mode optomechanical system. We identify the parameter regime of maximal entanglement, and show that strong entanglement is possible even for weak many-photon optomechanical couplings. We also show that strong tripartite entanglement is generated between the photonic and phononic output fields; unlike the bipartite photon-photon entanglement, this tripartite entanglement diverges as one approaches the boundary of system stability.
Phase-controlled bipartite and tripartite entanglement and Bell nonlocality in a closed-loop optomechanical system
Beijing Institute of Radio Metrology and Measurement（北京无线电计量测试研究所）；Science and Technology on Metrology and Calibration Laboratory, Beijing Institute of Radio Metrology and Measurement（北京无线电计量测试研究所计量与校准重点实验室）
We study a multimode optomechanical system where two mechanical oscillators are coupled to an electromagnetic cavity. Previously it has been shown that if the mechanical resonances have nearly equal frequencies, one can make the oscillators to interact via the cavity by strong pumping with a coherent pump tone. One can view the interaction also as emergence of an electromagnetically dark mode which gets asymptotically decoupled from the cavity and has a linewidth much smaller than that of the bare cavity. The narrow linewidth and long lifetime of the dark mode could be advantageous for example…
We examine one asymmetric adnd two fully symmetric Gaussian continuous-variable systems in terms of their tripartite and bipartite entanglement properties. We treat pure states and are able to find analytic solutions using the undepleted pump approximation for the Hamiltonian models, and standard beamsplitter relations for a model that mixes the outputs of optical parametric oscillators. Our two symmetric systems exhibit perfect tripartite correlations, but only in the unphysical limit of infinite squeezing. For more realistic squeezing parameters, all three systems exhibit both tripartite and…
It is an interesting problem to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. We consider the case that the states are two-qubit Werner states, we construct the interval of parameter of Werner states such that the tripartite state is genuine entangled. Further, we present the way of detecting the tripartite genuine entanglement using current techniques in experiments. We also investigate the lower bound of genuine multipartite entanglement concurrence.
Many three-party correlations, including some that are commonly described as genuinely tripartite nonlocal, can be simulated by a network of underlying subsystems that display only bipartite nonsignaling nonlocal behavior. Quantum mechanics predicts three-party correlations that admit no such simulation, suggesting there are versions of nonlocality in nature transcending the phenomenon of bipartite nonsignaling nonlocality. This paper introduces a rigorous framework for analyzing tripartite correlations that can be simulated by bipartite-only networks. We confirm that expected properties of so…
In this paper, we study theoretically the bipartite and tripartite continuous variable entanglement as well as the normal-mode splitting in a single-atom cavity optomechanical system with intensity-dependent coupling. The system under consideration is formed by a Fabry-Perot cavity with a thin vibrating end mirror and a two-level atom in the Gaussian standing-wave of the cavity mode. We first derive the general form of Hamiltonian describing the tripartite intensity-dependent atom-field-mirror coupling due to the presence of cavity mode structure. We then restrict our treatment to the first vi…
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.
We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations.
We study quantum effects in hybrid atomic optomechanics in a system comprising a cloud of atoms and a mobile mirror mediated by a single-mode cavity. Tripartite nonlocality is observed in the atom-light-mirror system, as demonstrated by the violation of the Mermin-Klyshko (MK) inequality. It has been shown [C. Genes, et al., PRA 77, 050307 (R) (2008)] that tripartite entanglement is optimized when the cavity is resonant with the anti-Stokes sideband of the driving laser and the atomic frequency matches the Stokes one. However, we show that this is not the case for the nonlocality. The MK funct…
We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of biqutrit states and twelve equivalent classes of triqutrit states respectively.
We study the problem of transforming a tripartite pure state to a bipartite one using stochastic local operations and classical communication (SLOCC). It is known that the tripartite-to-bipartite SLOCC convertibility is characterized by the maximal Schmidt rank of the given tripartite state, i.e. the largest Schmidt rank over those bipartite states lying in the support of the reduced density operator. In this paper, we further study this problem and exhibit novel results in both multi-copy and asymptotic settings. In the multi-copy regime, we observe that the maximal Schmidt rank is strictly s…
We propose a robust and efficient approach for tripartite-to-bipartite entanglement localization. By using weak measurements and quantum measurement reversal, an almost maximal entangled state shared by two parties can be generated with the assistance of the third party by local quantum operations and classical communication from a W-like state. We show that this approach works well in the presence of losses and phase diffusion. Our method provides an active way to fight against decoherence, and might help for quantum communication and distributed quantum computation.
We consider the distribution of entanglement from a multi-mode optical driving source to a network of remote and independent optomechanical systems. By focusing on the tripartite case, we analyse the effects that the features of the optical input states have on the degree and sharing-structure of the distributed, fully mechanical, entanglement. This study, which is conducted looking at the mechanical steady-state, highlights the structure of the entanglement distributed among the nodes and determines the relative efficiency between bipartite and tripartite entanglement transfer. We discuss a f…
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed lig…
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our …
We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the redu…
For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite $(2\otimes 2\otimes n)$ …
The fine-grained uncertainty relation can be used to discriminate among classical, quantum and super-quantum correlations based on their strength of nonlocality, as has been shown for bipartite and tripartite systems with unbiased measurement settings. Here we consider the situation when two and three parties, respectively, choose settings with bias for playing certain non-local games. We show analytically that while the fine-grained uncertainty principle is still able to distinguish classical, quantum and super-quantum correlations for biased settings corresponding to certain ranges of the bi…
Controllable multipartite entanglement is a crucial element in quantum information processing. Here we present a scheme that generates switchable bipartite and genuine tripartite entanglement between microwave and optical photons via an optoelectromechanical interface, where microwave and optical cavities are coupled to a mechanical mode with controllable coupling constants. We show that by tuning an effective gauge phase between the coupling constants to the "sweet spots", bipartite entanglement can be generated and switched between designated output photons. The bipartite entanglement is rob…
We demonstrate and characterize the extraction of genuine tripartite entanglement from the vacuum of a periodic cavity field. That is, three probe quantum systems (detectors) can become both bipartitely and tripartitely entangled without coming into causal contact, by means of interaction with a common quantum field. We do this by using an oscillator-detector model that forgoes the need for perturbation theory and which instead is solved exactly. We find that the extraction of tripartite entanglement is considerably easier than that of bipartite. As a secondary result, we also compare a period…
For a general tripartite system in some pure state, an observer possessing any two parts will see them in a mixed state. By the consequence of Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the third part will correspond to a particular decomposition of the bipartite mixed state into a weighted sum of pure states. It is possible to associate an average bipartite entanglement ($\bar{\mathcal{S}}$) with each of these decompositions. The maximum value of $\bar{\mathcal{S}}$ is called the entanglement of assistance ($E_A$) while the minimum value is called the entanglement…
The effect of quantum steering describes a possible action at a distance via local measurements. Whereas many attempts on characterizing steerability have been pursued, answering the question as to whether a given state is steerable or not remains a difficult task. Here, we investigate the applicability of a recently proposed method for building steering criteria from generalized entropic uncertainty relations. This method works for any entropy which satisfy the properties of (i) (pseudo-) additivity for independent distributions; (ii) state independent entropic uncertainty relation (EUR); and…
The flat band localization, as an important phenomenon in solid state physics, is fundamentally interesting in the exploration of exotic ground property of many-body system. Here we demonstrate the appearance of a flat band in a general bipartite optomechanical lattice, which could have one or two dimensional framework. Physically, it is induced by the hybrid interference between the photon and phonon modes in optomechanical lattice, which is quite different from the destructive interference resulted from the special geometry structure in the normal lattice (e.g., Lieb lattice). Moreover, this…
We investigate quantum entanglement in an analogue black hole realized in the flow of a Bose-Einstein condensate. The system is described by a three-mode Gaussian state and we construct the corresponding covariance matrix at zero and finite temperature. We study associated bipartite and tripartite entanglement measures and discuss their experimental observation. We identify a simple optical setup equivalent to the analogue Bose-Einstein black hole which suggests a new way of determining the Hawking temperature and grey-body factor of the system.
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
Local distinguishability of five orthogonal product states on bipartite and tripartite quantum systems
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；Faculty of Information Technology, Beijing University of Technology（北京工业大学信息学部）；College of Mathematics and Systems Science, Shandong University of Science and Technology（山东科技大学数学与系统科学学院）
The entanglement of assistance quantifies the entanglement that can be generated between two parties, Alice and Bob, given assistance from a third party, Charlie, when the three share a tripartite state and where the assistance consists of Charlie initially performing a measurement on his share and communicating the result to Alice and Bob through a one-way classical channel. We argue that if this quantity is to be considered an operational measure of entanglement, then it must be understood to be a tripartite rather than a bipartite measure. We compare it with a distinct tripartite measure th…
The dynamics of tripartite entanglement of fermionic system in noninertial frames through linear contraction criterion when one or two observers are accelerated is investigated. In one observer accelerated case the entanglement measurement is not invariant with respect to the partial realignment of different subsystems and for two observers accelerated case it is invariant. It is shown that the acceleration of the frame does not generate entanglement in any bipartite subsystems. Unlike the bipartite states, the genuine tripartite entanglement does not completely vanish in both one observer acc…
We investigate the stationary bipartite entanglement is a useful hybrid optomechanical system, which is constituted of two coupled-cavity optomechanics through a photon hopping process and both are driven by squeezed light. The transfer of correlations from an entangled light source to optomechanical cavities is explored. It is found that the generation of bipartite entanglement and entanglement transfer depend strongly on photon hopping strength and the matching of the input squeezed modes to the cavity modes. It is revealed that the generated stationary bipartite entanglement due to squeezed…
Quantumness for a bipartite unsteerable quantum correlation is operationally characterized by the notion of super-unsteerability. Super-unsteerability refers to the requirement of a larger dimension of the random variable that the steering party has to preshare with the party to be steered in the classical simulation protocol to generate an unsteerable correlation than the local Hilbert space dimension of the quantum states (reproducing the given unsteerable correlation) at the steering party's side. In the present study, this concept of super-unsteerability is generalized by defining the noti…
We investigate bipartite and tripartite entanglement in an open quantum system, specifically three qubits, all of which are damped, and one of which is driven. We adapt a systematic approach in calculating the entanglement of various bipartite splits usinga generalized concurrence as an indicator of entanglement. Our calculations are based on a direct detection scheme that is a particular unravelling of the density matrix. This system has a collective dipole-dipole energy shift that couples the atoms and the dissipation is via partially collective spontaneous emission described by the Lehmberg…
A large number of inequalities have been proposed for the detection of bipartite continuous variable entanglement and Einstein-Podolsky-Rosen steering. Many of these are based on either measured or inferred variances and are relatively easily measured via homodyne detection of optical outputs. In this work we examine a number of bipartite inequalities in the process of cascaded downconversion and sum-frequency generation inside an optical cavity. This has previously been predicted to be a potential source of continuous-variable tripartite entanglement, therefore we know that there are no separ…
An array of ultracold polar molecules trapped in an external electric field is regarded as a promising carrier of quantum information. Under the action of this field, molecules are compelled to undergo pendular oscillations by the Stark effect. Particular attention has been paid to the influence of intrinsic decoherence on the model of linear polar molecular pendular states, thereby we evaluate the tripartite entanglement with negativity, as well as fidelity of bipartite quantum systems for input and output signals using electric dipole moments of polar molecules as qubits. According to this s…
It is challenging task to detect and measure genuine multipartite entanglement. We investigate the problem by considering the average based positive partial transposition(PPT) criterion and the realignment criterion. Sufficient conditions for detecting genuine tripartite entanglement are presented. We also derive lower bounds for the genuine tripartite entanglement concurrence with respect to the conditions. While the PPT criterion and the realignment criterion are powerful for detecting bipartite entanglement and for providing lower bounds of bipartite concurrences, our results give an effect…
Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions
College of Computer Science and Engineering, Shandong University of Science and Technology（山东科技大学计算机科学与工程学院）；College of Mathematics and Systems Science, Shandong University of Science and Technology（山东科技大学数学与系统科学学院）；College of Cyberspace Science and Technology, Beijing University of Technology（北京工业大学网络空间科学技术学院）
Self-testing refers to a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. Especially, the self-testing of entangled states is of great importance in quantum information process. A comprehensible example is that violating the CHSH inequality maximally necessarily implies the bipartite shares a singlet. One essential question in self-testing is that, when one observes a non-maximum violation, how close is the tested state to the target state (which maximally violates certain Bell inequality)? The answer to this question des…
The influence of thermal noise on bipartite and tripartite quantum steering induced by a short laser pulse in a hybrid three-mode optomechanical system is investigated. The calculation is carried out under the bad cavity limit, the adiabatic approximation of a slowly varying amplitude of the cavity mode, and with the assumption of driving the cavity mode with a blue detuned strong laser pulse. Under such conditions, explicit expressions of the bipartite and tripartite steering parameters are obtained, and the concept of collective tripartite quantum steering, recently introduced by He and Reid…
Entanglement degradation caused by the Unruh effect is discussed for the tripartite GHZ or W states constructed by modes of a non-interacting quantum field viewed by one inertial observer and two uniformly accelerated observers. For fermionic states, the Unruh effect even for infinite accelerations cannot completely remove the entanglement. However, for the bosonic states, the situation is different and the entanglement vanishes asymptotically. Also, the entanglement is studied for the bipartite subsystems. While for the GHZ states all the bipartite subsystems are identically disentangled, for…
We establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement. Our results pertain to the asymptotic limit of local manipulations on a large number of copies of the state. We show that additivity of the relative entropy would imply that there are at least two inequivalent types of asymptotic tripartite entanglement. The methods used include the application of some useful lemmas that enable us to analytically calculate the relative entropy for some classes of bipartite states.
Generation and Enhancement of Bipartite and Tripartite Entanglement in an Electro-Optomechanical Ring Cavity
Polydisciplinary Faculty, Sultan Moulay Slimane University（苏丹穆莱·斯莱曼大学多学科学院）；Ecole Supérieure de l’Education et de la Formation, Sultan Moulay Slimane University（苏丹穆莱·斯莱曼大学教育与高等师范学院）
We show that some tripartite quantum correlations are inexplicable by any causal theory involving bipartite nonclassical common causes and unlimited shared randomness. This constitutes a device-independent proof that Nature's nonlocality is fundamentally at least tripartite in every conceivable physical theory - no matter how exotic. To formalize this claim we are compelled to substitute Svetlichny's historical definition of genuine tripartite nonlocality with a novel theory-agnostic definition tied to the framework of Local Operations and Shared Randomness (LOSR). A companion article [PRA. 10…
Effects of Quadratic Optomechanical Coupling on Bipartite Entanglements, Mechanical Ground-State Cooling and Squeezing in an Electro-Optomechanical System
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
Article presents general formulation of entanglement measures problem in terms of correlation function. Description of entanglement in probabilistic framework allow us to introduce new quantity which describes quantum and classical correlations. This formalism is applied to calculate bipartite and tripartite correlations in two special cases of entangled states of tripartite systems.
Recent experimental progress in prolonging the coherence time of a quantum system prompts us to explore the behavior of quantum entanglement at the beginning of the decoherence process. The response of the entanglement under an infinitesimal noise can serve as a signature of the robustness of entangled states. A crucial problem of this topic in multipartite systems is to compute the degree of entanglement in a mixed state. We find a family of global noise in three-qubit systems, which is composed of four W states. Under its influence, the linear response of the tripartite entanglement of a sym…
The present paper illustrates the realization of an atom-optomechanical system where an atomic ensemble is confined in a ring optomechanical cavity consisting of a fixed mirror and two movable ones. An analysis of the dynamics and the linearization of the equations allows to derive the multimode covariance matrix. Under realistic experimental conditions, we numerically simulate the steady-state bipartite and tripartite continuous variable entanglement using the logarithmic negativity, and analyze the shared entanglement in the multimode system. The introduction of the atomic medium allows to o…
We study a quantum entanglement distribution switch serving a set of users in a star topology with equal-length links. The quantum switch, much like a quantum repeater, can perform entanglement swapping to extend entanglement across longer distances. Additionally, the switch is equipped with entanglement switching logic, enabling it to implement switching policies to better serve the needs of the network. In this work, the function of the switch is to create bipartite or tripartite entangled states among users at the highest possible rates at a fixed ratio. Using Markov chains, we model a set …
We study the entanglement and memristive properties of three coupled quantum memristors. We consider quantum memristors based on superconducting asymmetric SQUID architectures which are coupled via inductors. The three quantum memristors are arranged in two different geometries: linear and triangular coupling configurations. We obtain a variety of correlation measures, including bipartite entanglement and tripartite negativity. We find that, for identical quantum memristors, entanglement and memristivity follow the same behavior for the triangular case and the opposite one in the linear case. …
Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevan…
The study of classical and quantum correlations in bipartite and multipartite systems is crucial for the development of quantum information theory. Among the quantifiers adopted in tripartite systems, the genuine tripartite quantum discord (GTQD), estimating the amount of quantum correlations shared among all the subsystems, plays a key role since it represents the natural extension of quantum discord used in bipartite systems. In this paper, we derive an analytical expression of GTQD for three-qubit systems characterized by a subclass of symmetrical X-states. Our approach has been tested on b…
We study theoretically a driven hybrid optomechanical system with a membrane-in-the-middle configuration containing two identical elongated cigar-shaped Bose-Einstein condensates (BECs) in each side of the membrane. In the weakly interacting regime, the BECs can be considered as single-mode oscillators in the Bogoliubov approximation which are coupled to the optical field through the radiation pressure interaction so that they behave as two quasi-membranes. We show that the degree of squeezing of each BEC and its entanglement with the moving membrane can be controlled by the \textit{s}-wave sc…
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intra-cavity squeezing, and optomechani…
