Distinguishing arbitrary multipartite basis unambiguously using local operations and classical communication

We show that an arbitrary basis of a multipartite quantum state space consisting of K distant parties such that the kth party has local dimension dk always contains at least N= Sigma(k=1)(K) (dk-1)+1 members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show that this lower bound is optimal by analytically constructing a special product basis having only N members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon "nonlocality without entanglement," but also implies the existence of a locally distinguishable entangled basis.     

Distinguishability and indistinguishability by local operations and classical communication

It is well known that orthogonal quantum states can be distinguished perfectly. However, if we assume that these orthogonal quantum states are shared by spatially separated parties, the distinguishability of these shared quantum states may be completely different. We show that a set of linearly independent quantum states [formula: see text] where U(m,n) are generalized Pauli matrices, cannot be discriminated deterministically or probabilistically by local operations and classical communication. On the other hand, any l maximally entangled states from this set are locally distinguishable if l(l-1)< or =2d. The explicit projecting measurements are obtained to locally discriminate these states. As an example, we show that four Werner states are locally indistinguishable.     

Teleportation of the three-level three-particle entangled state and classical communication cost

We propose a scheme to probabilistically teleport an unknown three-level three-particle entangled state. The quantum channel is composed of a partial entangled three-level two-particle state and a partial entangled three-level three-particle state. We calculate the successful total probability and the classical communication cost required in the ideal probabilistic teleportation process, respectively. It is shown that an unknown three-level three-particle entangled state can be teleported using fewer entangled particles and lesser classical communication cost than Bennett et al.’s original protocol.     

Stability of flip and exchange symmetric entangled state classes under invertible local operations

Flip and exchange symmetric (FES) many-qubit states, which can be obtained from a state with the same symmetries by means of invertible local operations (ILO), constitute a set of curves in the Hilbert space. Eigenstates of FES ILOs correspond to vectors that cannot be transformed to other FES states. This means equivalence classes of states under ILO can be determined in a systematic way for an arbitrary number of qubits. More important, for entangled states, at the boundaries of neighboring equivalence classes, one can show that when the fidelity between the final state after an ILO and a state of the neighboring class approaches unity, the probability of success decreases to zero. Therefore, the classes are stable under ILOs.     

Bipartite subspaces having no bases distinguishable by local operations and classical communication

It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of local operations and classical communication. A corollary of this fact is that there exist quantum channels having suboptimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment.     

Optimal local discrimination of two multipartite pure states

In a recent paper, Walgate et al. (Phys. Rev. Lett. 85 (2000) 4972) demonstrated that any two orthogonal multipartite pure states can be optimally distinguished using only local operations. We utilise their result to show that this is true for any two multipartite pure states, in the sense of inconclusive discrimination. There are also certain regimes of conclusive discrimination for which the same also applies, although we can only conjecture that the result is true for all conclusive regimes. We also discuss a class of states that can be distinguished locally according to any discrimination measure, as they can be locally recreated in the possession of one party. A consequence of this is that any two maximally entangled states can always be optimally discriminated locally, according to any figure of merit.     

Global state preparation using local pure operations

Several families of the pure states of a bipartite system were prepared using local pure operations. For these families, the difference in the maximal probabilities of successful preparations by Alice and Bob are shown to be related to the difference in the local fidelities of the reduced states.     

Twist-teleportation-based local discrimination of maximally entangled states

In this work, we study the local distinguishability of maximally entangled states(MESs). In particular, we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions. Fan and Tian et al. have already obtained two satisfactory results for the generalized Bell states(GBSs) and the qudit lattice states when applied to prime or prime power dimensions. We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in [Phys. Rev. A 70, 022304(2004)]. Using this teleportation scheme, we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs, which include the GBSs and the qudit lattice states as special cases.Moreover, we present a generalized version of the results in [Phys. Rev. A 92, 042320(2015)] for the arbitrary dimensional case.     

Probability of state preparation using local pure operations

In this study, a nonlocal phenomenon of pure states of a bipartite system is demonstrated. A pure state can be prepared from a pure state with maximal Schmidt number by using local pure operations on a subsystem. Nevertheless, the maximal probability of successful preparation depends on the reduced states in the other subsystem.     

Deterministic secure quantum communication using four-particle genuine entangled state and entanglement swapping

A deterministic secure quantum communication scheme using entanglement swapping is proposed. The sender prepares four-particle genuine entangled states and sends two particles in each state to the receiver and remains the rest particles. If the quantum channel is secure, they begin to communicate. After their four-particle projective measurements, the receiver can obtain the secret information according to his measurement outcomes and classical information from the sender. Using entanglement swapping, there are no particles carrying secret information to be transmitted.     

用两粒子纠缠对进行{\bf\large{N}}粒子纠缠态的隐形传送

本文提出了一个方案:将三粒子纠缠态从一个发送者传给两个接收者之一,并将其推广到N粒子纠缠态的传送。这里，我们仅用两粒子纠缠对作通道就实现了N粒子纠缠态的传送。此方案相比以往的方案节省了大量纠缠资源，且成功传送的几率达到了1。     

Entanglement evolution in multipartite cavity-reservoir systems under local unitary operations

We analyze the entanglement evolution of two cavity photons being affected by the dissipation of two individual reservoirs. Under an arbitrary local unitary operation on the initial state, it is shown that there is only one parameter which changes the entanglement dynamics. For the bipartite subsystems, we show that the entanglement of the cavity photons is correlated with that of the reservoirs, although the local operation can delay the time at which the photon entanglement disappears and advance the time at which the reservoir entanglement appears. Furthermore, via a new defined four-qubit entanglement measure and two three-qubit entanglement measures, we study the multipartite entanglement evolution in the composite system, which allows us to analyze quantitatively both bipartite and multipartite entanglement within a unified framework. In addition, we also discuss the entanglement evolution with an arbitrary initial state.     

Minimal set of local measurements and classical communication for two-mode Gaussian state entanglement quantification

We develop the minimal requirements for the complete entanglement quantification of an arbitrary two-mode bipartite Gaussian state via local measurements and a classical communication channel. The minimal set of measurements is presented as a reconstruction protocol of local covariance matrices and no previous knowledge of the state is required but its Gaussian character. The protocol becomes very simple mostly when dealing with Gaussian states transformed to its standard form, since photocounting or intensity measurements define the whole set of entangled states. In addition, conditional on some prior information, the protocol is also useful for a complete global state reconstruction.     

Method for generating a new class of multipartite entangled state in cavity quantum electrodynamics

Recently, Yeo and Chua introduced a genuine four-qubit entangled state |χ〉 which can implement perfect teleportation of an arbitrary two-qubit state [Y. Yeo, W.K. Chua, Phys. Rev. Lett. 96 (2006) 060502]. It has been shown that the state |χ〉 is inequivalent to the well-known Greenberger-Horne-Zeilinger state, W state, and linear cluster state, in terms of stochastic local operations and classical communication [C.F. Wu, Y. Yeo, L.C. Kwek, C.H. Oh, Phys. Rev. A 75 (2007) 032332]. This “new” class of state has many interesting entanglement properties and possible applications in quantum-information processing and fundamental tests of quantum mechanics. Here, we propose a simple scheme to generate the state |χ〉 in cavity quantum electrodynamics. Our idea may be helpful for in-depth study on such a class of state and its practical applications.     

Enhancement of Kerr nonlinearity and its application to entangled state discrimination

In this paper, the recent research on the enhanced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously generated coherence, are presented to enhance the Kerr nonlinearity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr nonlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Horne-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.      

用一个纠缠态实现多粒子纠缠态的量子隐形传送

提出分别在二维和高维系统中利用一个纠缠态作量子通道实现M粒子纠缠态的量子隐形传送方案. 该方案有多个接收者,通过控制引进辅助粒子数,可以任意调节传送后的纠缠态在各接收者之间的粒子数分布, 且成功传送的概率为1. 关键词： 量子隐形传态 纠缠态 量子通道     

Parametric down-conversion with local operation and two-way classical communication

The decoy-state quantum key distribution protocol suggested by Adachi et al. (Phys. Rev. Lett. 99 180503 (2007)) is proven to be secure and feasible with current techniques. It owns two attractive merits,i.e.,its longer secure transmission distance and more convenient operation design. In this paper,we first improve the protocol with the aid of local operation and two-way classical communication (2-LOCC). After our modifications,the secure transmission distance is increased by about 20 km,which will make the protocol more practicable.     

Genuine quantum and classical correlations in multipartite systems

Generalizing the quantifiers used to classify correlations in bipartite systems, we define genuine total, quantum, and classical correlations in multipartite systems. The measure we give is based on the use of relative entropy to quantify the distance between two density matrices. Moreover, we show that, for pure states of three qubits, both quantum and classical bipartite correlations obey a ladder ordering law fixed by two-body mutual informations, or, equivalently, by one-qubit entropies.     

Mixed state geometric phases, entangled systems, and local unitary transformations

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.     

Classification of general n-qubit states under stochastic local operations and classical communication in terms of the rank of coefficient matrix

We solve the entanglement classification under stochastic local operations and classical communication (SLOCC) for general n-qubit states. For two arbitrary pure n-qubit states connected via local operations, we establish an equation between the two coefficient matrices associated with the states. The rank of the coefficient matrix is preserved under SLOCC and gives rise to a simple way of partitioning all the pure states of n qubits into different families of entanglement classes, as exemplified here. When applied to the symmetric states, this approach reveals that all the Dicke states |?,n> with ?=1,…,[n/2] are inequivalent under SLOCC.