We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monogamy inequality, is an entanglement monotone under Gaussian local operations and classical communication and defines a measure of genuine tripartite entanglement. We analytically determine the residual contangle for arbitrary pure three-mode Gaussian states and study the distribution of quantum correlations for such states. This will lead us to show that pure, symmetric states allow for a promiscuous entanglement sharing, having both maximum tripartite residual entanglement and maximum couplewise entanglement between any pair of modes. We thus name these states GHZ/$W$ states of continuous variable systems because they are simultaneous continuous-variable counterparts of both the GHZ and the $W$ states of three qubits. We finally consider the action of decoherence on tripartite entangled Gaussian states, studying the decay of the residual contangle. The GHZ/$W$ states are shown to be maximally robust under both losses and thermal noise.
Operational Classification and Quantification of Multipartite Entangled States
本文形式化和推广了T. R.奥利维拉湾Rigolin和M. C. de Oliveira，Phys.Rev.A73，010305（R）（2006），通过全球纠缠（GE）的推广[D. A. Meyer和N. R. Wallach，J.Math.Phys.43，4273（2002）]。与通用电气的主要特点，这一措施在于，我们研究的平均线性熵的所有可能的分区的多部系统。这使得一个可操作的多体纠缠措施，这是能够区分不同的多体纠缠态，GE未能区分的建设。此外，它也是最大的伊辛链在横向磁场的临界点，从而能够检测到量子相变。
In this paper, we investigate the dynamics behaviors of genuine multipartite Einstein-Podolsky-Rosen steering (GMS) and genuine multipartite nonlocality (GMN), and explore how to recover the lost GMS and GMN under a mixed decoherence system. Explicitly, the decoherence system can be modeled by that a tripartite Werner-type state suffers from the non-Markovian regimes and one subsystem of the tripartite is under a non-inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner-type state established initially. GMS and GMN are very fragi…
Decoherence-free subspaces and Markovian revival of genuine multipartite entanglement in a dissipative system
Poornaprajna Institute of Scientific Research (PPISR)（普尔纳普拉吉纳科学研究学院）；Manipal Academy of Higher Education（马帕尔高等教育学院）；Amrita Vishwa Vidyapeetham（阿弥塔大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）；Chennai Institute of Technology（金奈理工学院）
Quantum entanglement is of central importance to quantum computing, quantum metrology, quantum information as well as the nature of quantum physics. Quantum theory does not prevent entanglement from being created and observed in macroscopic physical systems, in reality however, the accessible scale of entanglement is still very limited due to decoherence effects. Recently, entanglement has been observed among atoms from thousands to millions level in extremely low-temperature and well-isolated systems. Here, we create multipartite entanglement of billions of motional atoms in a quantum memory …
Decoherence Mitigation with Local NOT Gates in Multipartite Systems
Qdit Labs Pvt. Ltd.（Qdit Labs有限公司）；Indian Institute of Technology Hyderabad（印度理工学院海德拉巴分校）；Poornaprajna Institute of Scientific Research（普尔纳普拉贾科学研究学院）；University of Calgary（卡尔加里大学）
Certain quantum states are well-known to be particularly fragile in the presence of decoherence, as illustrated by Schrodinger's famous gedanken cat experiment. It has been better appreciated more recently that quantum states can be characterized in a hierarchy of quantum quantities such entanglement, quantum correlations, and quantum coherence. It has been conjectured that each of these quantities have various degrees of fragility in the presence of decoherence. Here we experimentally confirm this conjecture by preparing tripartite photonic states and subjecting them to controlled amounts of …
This paper is concerned with multimode open quantum harmonic oscillators (OQHOs), described by linear quantum stochastic differential equations with multichannel external bosonic fields. We consider the exponentially fast decay in the two-point commutator matrix of the system variables as a manifestation of quantum decoherence. Such dissipative effects are caused by the interaction of the system with its environment and lead to a loss of specific features of the unitary evolution which the system would have in the case of isolated dynamics. These features are exploited as nonclassical resource…
One of the key manifestations of quantum mechanics is the phenomenon of quantum entanglement. While the entanglement of bipartite systems is already well understood, our knowledge of entanglement in multipartite systems is still limited. This dissertation covers various aspects of the quantification of entanglement in multipartite states and the role of symmetry in such systems. Firstly, we establish a connection between the classification of multipartite entanglement and knot theory and investigate the family of states that are resistant to particle loss. Furthermore, we construct several exa…
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…
Quantum entanglement is usually considered a fragile quantity and decoherence through coupling to an external environment, such as a thermal reservoir, can quickly destroy the entanglement resource. This doesn't have to be the case and the environment can be engineered to assist in the formation of entanglement. We investigate a system of qubits and higher dimensional spins interacting only through their mutual coupling to a reservoir. We explore the entanglement of multipartite and multidimensional system as mediated by the bath and show that at low temperatures and intermediate coupling stre…
We study robustness of genuine multipartite entanglement for a system of three qubits under collective dephasing. Using a computable entanglement monotone for multipartite systems, we found that almost every state is quite robust under this type of decoherence. We analyze random states and weighted graph states at infinity and found all of them to be genuinely entangled.
We investigate the dynamical evolution of multipartite entanglement in tripartite systems with three qubits present in independent thermal reservoirs, modelled as infinite set of quantum harmonic oscillators. We show that the presence of temperature gradient between reservoirs play a significant role in robustness of multipartite correlation against environmental decoherence. Considering a bilinear form of interaction Hamiltonian, an exact expression for time evolved density matrix is presented. Interestingly, it is observed that the preservation duration of genuine multipartite concurrence fo…
We study the quantification of genuine multipartite entanglement (GME) for general multipartite states. A set of inequalities satisfied by the entanglement of $N$-partite pure states is derived by exploiting the restrictions on entanglement distributions, showing that the bipartite entanglement between each part and its remaining ones cannot exceed the sum of the other partners with their remaining ones. Then a series of triangles, named concurrence triangles, are established corresponding to these inequalities. Proper genuine multipartite entanglement measures are thus constructed by using th…
We study a quantum switch that distributes maximally entangled multipartite states to sets of users. The entanglement switching process requires two steps: first, each user attempts to generate bipartite entanglement between itself and the switch; and second, the switch performs local operations and a measurement to create multipartite entanglement for a set of users. In this work, we study a simple variant of this system, wherein the switch has infinite memory and the links that connect the users to the switch are identical. Further, we assume that all quantum states, if generated successfull…
