W-class States Research Articles

Quantum Information Splitting of an Arbitrary Two-Atom State by Using W-Class States in Cavity QED

We demonstrate that three sets of W-class states can be used to realize the deterministic quantum information splitting of an arbitrary two-atom state in cavity QED. The scheme does not involve Bell-state measurement and is not sensitive to both the cavity decay and the thermal field.

Quantum state sharing of an arbitrary three-qubit state by using three sets of W-class states

A new application of the W-class state for quantum state sharing (QSTS) of an arbitrary three-qubit state with a certain probability is presented explicitly. We show that three sets of W-class states can be used to realize the QSTS of an arbitrary three-qubit state involving Bell-state measurement, single-qubit measurement and one high dimensional unitary operation. The performance demonstrates that our scheme can considerably reduce the difficulty of physical implementation.

CRYPTANALYSIS OF THE QUANTUM STATE SHARING PROTOCOL USING FOUR SETS OF W-CLASS STATES

Recently, a protocol is proposed for the quantum state sharing (QSTS) of an arbitrary three-photon state using four sets of W-class states. Unfortunately, its security analysis is inadequate. In this paper, we find the security loophole of this QSTS protocol. It is mainly caused by the fake quantum channel, whose security is not guaranteed by the legal participants. We present a simple but feasible strategy, by which an eavesdropper can successfully steal the exact secret. Furthermore, a secure QSTS protocol is put forward. The security of our improved protocol is analyzed in details.

Single-qubit-assisted entanglement concentration of partially entangled multi-electron spin W states

We propose an entanglement concentration protocol (ECP) for nonlocal N-electron systems in a partially entangled W state, resorting to ancillary single electrons and charge detection. Compared with other ECPs for W states, our ECP has some advantages. Firstly, only an entangled N-electron system is required in each round of entanglement concentration, not two copies. Secondly, only one of the users, say Charlie, needs to perform the protocol, while all parties should perform the same operations as Charlie in other ECPs for W-class states. Thirdly, only Charlie asks other parties to retain or discard their electrons, and they do not need to check their measurement results, which greatly simplifies the complication of classical communication. Fourthly, our ECP has a higher success probability than other ECPs for W-class states as the parties can recycle their concentration when they obtain a system in another W-class state with less entanglement. These advantages make our ECP more feasible for practical applications.

Monogamy of measurement-induced nonlocality

Measurement-induced nonlocality was introduced by Luo and Fu (2011 Phys. Rev. Lett. 106 120401) as a measure of nonlocality in a bipartite state. In this paper, we will discuss the monogamy property of measurement-induced nonlocality for some three- and four-qubit classes of states. Unlike discord, we find quite surprising results in this situation. Both the GHZ- and W-states satisfy monogamy relations in the three-qubit case; however, in general there are violations of monogamy relations in both the GHZ-class and W-class states. In the case of the four-qubit system, monogamy holds for most of the states in the generic class. The four-qubit GHZ-state does not satisfy the monogamy relation, but the W-state does. We provide several numerical results including counterexamples regarding the monogamy nature of measurement-induced nonlocality. We will also extend our results of the generalized W-class to n-qubit systems.

Quantum discord of a three-qubit W-class state in noisy environments

We study the dynamics of the pairwise quantum discord (QD), classical correlation (CC), and entanglement of formation (EOF) for the three-qubit W-class state |W>_{123}=\frac 12(|100>_{123}+|010>_{123}+\sqrt{2}|001>_{123}) under the influence of various Markovian noises by analytically solving the master equation in the Lindblad form. Through numerical analysis, we find that EOF decreases asymptotically to zero with time for the dephasing noise, but it undergoes sudden death for the bit-flip noise, the isotropic noise, as well as the dissipative and noisy environments. Moreover, QD decays to zero in an asymptotical way for all the noises we investigated. Thus, when the W-class state |W>_{123} is subject to the above Markovian noises, QD is more robust than EOF against decoherence excluding the phase-flip noise, implying that QD is more useful than entanglement to characterize the quantum correlation. We also find a remarkable character for the CC in the presence of the phase-flip noise, i.e., CC displays the behavior of sudden transition and then keeps constant permanently, but the corresponding QD just exhibits a very small sudden change. Furthermore, we verify the monogamic relation between the pairwise QD and EOF of the W-class state.

Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics

We propose a single-photon-assisted entanglement concentration protocol (ECP) for nonlocal N-photon systems in a partially entangled pure W-class state with linear optical elements. Only one of the N parties in quantum communication prepares an ancillary photon and operates the entanglement concentration process for picking up the standard N-photon W state from each partially entangled pure W-class state by choosing the two-mode instances from a polarization beam splitter. Compared with other ECPs for W-class states, our protocol has some advantages. First, it requires only linear optical elements. Second, it requires an N-photon system and an ancillary photon for each round of concentration, not two systems. Third, only one party asks other parties to retain or discard their photons. All these advantages make our ECP more feasible and more convenient than others.

Increasing Entanglement Monotones by Separable Operations

Quantum entanglement is fundamentally related to the operational setting of local quantum operations and classical communication (LOCC). A more general class of operations known as separable operations (SEP) is often employed to approximate LOCC, but the exact difference between LOCC and SEP is unknown. In this letter, we compare the two classes in performing particular tripartite to bipartite entanglement conversions and report a gap as large as 12.5% between SEP and LOCC, which is the first known appreciable gap between the classes. Our results rely on constructing a computable entanglement monotone with a clear operational meaning that, unlike all other such monotones previously studied, is not monotonic under SEP. Finally, we prove the curious fact that convergent sequences of LOCC protocols need not be LOCC feasible in the limit.

Quantum Information Splitting of an Arbitrary Three-Atom State by Using W-class States in Cavity QED

We demonstrate that four sets of W-class states can be used to realize the deterministic quantum information splitting of an arbitrary three-atom state in cavity QED. The scheme does not involve Bell-state measurement and is insensitive to both the cavity decay and the thermal field.

Multi-photon Entanglement Concentration Protocol for Partially Entangled W States with Projection Measurement

We propose a novel entanglement concentration protocol (ECP) for nonlocal N-photon systems in a partially entangled pure W-class state, following some ideas in the work by Deng (Phys. Rev. A 85:022311, 2012). Our ECP resorts to an ancillary single photon and the projection measurement on it. Compared with other ECPs for W-class states, our ECP requires only one copy of the multipartite entangled system in a partially entangled W-class pure state, not two copies, which reduces the difficulty of its implementation largely. Moreover, it requires only one of the N parties in quantum communication to perform the local unitary operation for reconstructing the standard W state from the W-class state and it only resorts to linear optical elements for its implementation. All these advantages make our ECP more feasible than others in practical applications in quantum communication.

Manipulation of entanglement and preparation of quantum states for moving two-atom and the light field via intensity-dependent coupling

In this paper, the Tavis-Cummings model is generalized to simultaneously consider the atomic motion and the field via intensity dependent coupling. Under the conditions of vacuum field, weakly and strongly coherent field, the entanglement evolution properties of two-atom-field and two-atom-two-atom are investigated using atomic reduced entropy and concurrence, respectively. According to evolution characteristics above, we prepare the W-class states of two-atom-field, two-atom Bell state, fidelity state of Bell-state atoms, single-photon state, two-photon state and stable number-states of field by selecting the interaction time of the two-atom-field, selecting the entanglement factor of the two-atom, regulating the field-mode structure parameter, controlling the probability amplitude of pure state of the system and selective measurement. The manipulation of two-atom Bell state sudden generation and its maintenance in a limited time, the formation of periodic quantum echo of Bell-state atoms and the continuous fidelity of Bell-state atomic information are achieved. The results show that the system has a powerful function of quantum information, and provide the physical carrier and theoretical parameters for experimental implementation of quantum information processing.

Randomly distillingW-class states into general configurations of two-party entanglement

In this article we obtain new results for the task of converting a \textit{single} $N$-qubit W-class state (of the form $\sqrt{x_0}\ket{00...0}+\sqrt{x_1}\ket{10...0}+...+\sqrt{x_N}\ket{00...1}$) into maximum entanglement shared between two random parties. Previous studies in random distillation have not considered how the particular choice of target pairs affects the transformation, and here we develop a strategy for distilling into \textit{general} configurations of target pairs. We completely solve the problem of determining the optimal distillation probability for all three qubit configurations and most four qubit configurations when $x_0=0$. Our proof involves deriving new entanglement monotones defined on the set of four qubit W-class states. As an additional application of our results, we present new upper bounds for converting a generic W-class state into the standard W state $\ket{W_N}=\sqrt{\frac{1}{N}}(\ket{10...0}+...+\ket{00...1})$.

Perfect Teleportation of an Arbitrary Three-Qubit State by Using W-Class States

A new application of the W-class state is investigated for teleportation of an arbitrary three-qubit state. We demonstrate that three sets of W-class states can be used to realize the perfect teleportation of an arbitrary three-qubit state by performing only the three-qubit von Neumann measurements and local unitary operations.

A ROBUST SCHEME FOR GENERATING A PECULIAR W-CLASS STATE WITH ATOMS TRAPPED IN SEPARATE CAVITIES

Utilizing coincidence measurement of photons leaking out of distinct cavities, we present a scheme for generating a peculiar W-class state which has recently been shown to be better than canonical W states for several quantum information processing tasks. In the traditional coincidence measurement, the probability of success can only be as high as 50% for each measurement. While under the condition of "weakly driven approach", the successful probability of coincidence measurement could achieve 100% in an ideal situation. Moreover, the scheme presented is robust and has high fidelity. The realization of teleportation with the peculiar W-class state has also been discussed briefly.

Implementing ancilla-free phase covariant quantum cloning with atoms trapped in cavities

We propose a scheme to implement ancilla-free 1 to 2 optimal phase covariant quantum cloning with atoms trapped in cavities. In the scheme the W-class state of three atoms, which are individually trapped in three spatially separated cavities, is deterministically generated. Then by the use of this W-class state and detection of the atomic state, an optimal ancilla-free 1 to 2 phase-covariant quantum cloning between two spatially separated trapped atoms can be realized. The scheme is robust for atomic spontaneous decay, cavity decay and photon leakage out of the fiber. In principle, an M+1-atom W-class state can be generated by using such an approach. Thus this scheme also can be generalized to implement 1 to M ancilla-free phase-covariant quantum cloning.

Quantum state sharing of an arbitrary three-qubit state by using four sets of W-class states

A new application of the W-class state is investigated for quantum state sharing (QSTS) of an arbitrary three-qubit state. We demonstrate that four sets of W-class states can be used to realize the deterministic QSTS of an arbitrary three-qubit state based on the three-qubit von Neumann measurements and the local unitary operations. Our scheme considered here is secure against certain eavesdropping attacks.

Svetlichny’s inequality and genuine tripartite nonlocality in three-qubit pure states

The violation of the Svetlichny's inequality (SI) [Phys. Rev. D, 35, 3066 (1987)] is sufficient but not necessary for genuine tripartite nonlocal correlations. Here we quantify the relationship between tripartite entanglement and the maximum expectation value of the Svetlichny operator (which is bounded from above by the inequality) for the two inequivalent subclasses of pure three-qubit states: the GHZ-class and the W-class. We show that the maximum for the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838 (1990)] modulo a constant factor, and although it is a function of the three tangle and the residual concurrence, large number of states don't violate the inequality. We further show that by design SI is more suitable as a measure of genuine tripartite nonlocality between the three qubits in the the W-class states, and the maximum is a certain function of the bipartite entanglement (the concurrence) of the three reduced states, and only when their certain sum attains a certain threshold value, they violate the inequality.

Deterministic remote preparation of an arbitrary W-class state with multiparty

Our concern is to design some deterministic schemes for remotely preparing an arbitrary W-class state from one sender to one of a number of receivers. Compared with previous remote preparation schemes, the real receiver in our schemes is unknown to the sender. Firstly, by introducing a novel entanglement transformation the sender can deterministically prepare an arbitrary W-class state with complex spectra to one of two remote receivers via two four-particle GHZ states as the quantum channel. As for preparing a W-class state with real spectra, by constructing a general and useful measurement basis for the sender, another economical protocol can be designed with unit success probability. These schemes are extended to multiparties via two multi-particle GHZ states as the quantum channel. The classical communication costs of all the schemes are calculated to determine the classical resources required.

Deterministic quantum teleportation and information splitting via a peculiar W-class state

In the paper (Phys. Rev. 2006 A 74 062320) Agrawal et al. have introduced a kind of W-class state which can be used for the quantum teleportation of single-particle state via a three-particle von Neumann measurement, and they thought that the state could not be used to teleport an unknown state by making two-particle and one-particle measurements. Here we reconsider the features of the W-class state and the quantum teleportation process via the W-class state. We show that, by introducing a unitary operation, the quantum teleportation can be achieved deterministically by making two-particle and one-particle measurements. In addition, our protocol is extended to the process of teleporting two-particle state and splitting information.

W-State Generation and Manipulation for Ion-Trap-Based Quantum-Information Processing

We propose an ion-trap scheme for one-step generation of a special configuration of W-class state which has recently been shown to be better than canonical W states for several quantum-information processing tasks. We also present a method for one-step realization of a nontrivial collective operation which can transform a canonical W state into a fully separable state. Such a transformation plays a key role in recently proposed quantum protocols. The operation speed in our schemes increases with the number of qubits. This is contrary to usual entanglement generation and quantum manipulation schemes which take more and more time with the increase of the number of qubits.