Entangled GHZ State Research Articles

Controlled teleportation of an arbitrary n-qudit state using nonmaximally entangled GHZ states

In this paper, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller.

Classical Communication Cost and Remote Preparation of Multi-qubit with Three-Party

We present a scheme for probabilistic remote preparation of multi-qubit with three-party from a sender to either of two receivers. The quantum channel is composed of a partial entangled tripartite GHZ state. We obtain the successful total probability of the scheme in the general case and special case, respectively. We also calculate total classical communication cost required in the RSP process with three-party in the general case and special case, respectively.

CONTROLLED QUANTUM SECURE DIRECT COMMUNICATION WITH QUANTUM ENCRYPTION

Utilizing a partially entangled GHZ state, we propose a novel controlled quantum secure direct communication (QSDC) with quantum encryption. Under the supervision and help of the third side, the sender and the receiver can securely share the private quantum entanglement keys used to encrypt and decrypt the secret message. According to the results of checking the eavesdropping on decoy photons, communicators can decide whether the quantum keys are reused in the next round. Not only will eavesdropping inevitably disturb the states of the decoy photons and be detected, but arbitrary transmission errors can also be corrected.

Classical Communication Cost and Remote Preparation of the Two-Atom Maximally Entangled State

We present a protocol for probabilistic remote preparation of the two-atom maximally entangled state using a four-atom GHZ entangled state as the quantum channel. The two-atom maximally entangled state can be successfully prepared between two distant parties with a success probability of 100%. The successful total probability and classical communication cost are calculated.

Controlled Entanglement Swapping for Continuous Variables

We propose a scheme for controlled entanglement swapping of continuous variable, where an EPR pair shared by two parties (Alice and Debbie) and a GHZ entangled state shared by three parties (Alice, Bob and Claire) are required. One optical beams of the EPR state will be entangled with the output mode displaced by Bob with the help of Claire. It is shown that the entanglement swapping can occur controlled by the third party (Claire).

Re-examining generalized teleportation protocol

We present an explicit generalized protocol for probabilistic teleportation of an arbitrary N-qubit GHZ entangled state via only one non-maximally two-qubit entangled state. Without entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that by properly choosing the measurement basis it is possible to achieve unity fidelity transfer of the state. Compared with Gordon et al’s protocol [G. Gordon, G. Rigolin, Phys. Rev. A 73 (2006) 042309], this protocol has the advantage of transmitting much less qubits and classical information for teleporting an arbitrary N-qubit GHZ state.

Controlled Teleportation of an Unknown N-qubitEntangled GHZ State

A scheme for controlled teleportation of an unknownN-qubit entangled GHZ state from the sender Alice to the distantreceiver Bob is proposed. And m-qubit GHZ state is sufficientfor the task of control by m spatially-separated supervisors.Conditioned on the local operations executed by all participants,Bob can faithfully restore the original state by performing relevantunitary transformations with the aid of some classical messageabout measurement results. Anyone's absence will absolutely leadto the failure of teleportation.

PROBABILISTIC AND CONTROLLED TELEPORTATION OF UNKNOWN IONIC STATES VIA LINEAR OPTICAL ELEMENTS

We propose a simple scheme for teleporting an unknown state in a probabilistic and controlled manner via linear optical elements using a tripartite entangled GHZ state. By using a Mach–Zehnder interferometer, we realize all teleportation processes by only single-qubit measurements; thus our scheme is readily realizable within current technology.

Scheme for Concentration of UnknownGreeberger–Horne–Zeilinger Entangled States via Cavity Decay

We present a scheme for entanglement concentration of an unknown atomicnon-maximally entangled GHZ state via cavity decay. In the scheme, theatom trapped in a cavity is manipulated by laser field, so the maximallyentangled GHZ state can be obtained by performing certain operation,which can be realized by illuminating the atom in a cavity. Our methodis robust against spontaneous atomic decay.

Quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled GHZ states

We explicitly present a scheme for quantum state sharing of an arbitrary multiqubit state using nonmaximally entangled GHZ states as the quantum channel and generalized Bell states as the measurement basis. The scheme succeeds only probabilistically with its total success probability depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. Security of the scheme is guaranteed by the fact that attacks of an outside eavesdropper or/and an inside dishonest party will inevitably introduce detectable errors.

Quantum dense coding using a peculiar tripartite entangled state

Following a recent proposal (Phys. Lett. A 346 (2005) 330) about quantum dense coding using a tripartite entangled GHZ state and W state, this paper proposes an experimentally feasible scheme for dense coding in cavity QED by using another peculiar tripartite entangled state. In the scheme the atoms interact simultaneously with a highly detuned cavity mode with the assistance of a classical field, the successful probability of dense coding scheme with this peculiar tripartite entangled state equals 1.

Teleportation of N-Particle Entangled GHZ Statevia Entanglement Swapping

In this scheme, N non-maximally entangled particlepairs are used as quantum channel to teleport an unknown N-particleentangled GHZ state via entanglement swapping. In order to realizethis teleportation, the sender Alice operates Bell-state measurementon particles belonging to herself. Then she informs the resultsto the receiver Bob through classical communication. Accordingto the results, Bob operates corresponding transformation toreconstruct the initial state. The advantage of this scheme isthat it needs only one common unitary matrix for Alice'sdifferent results, which has a more general meaning. As a specialcase, teleporting an unknown three-particle entangled GHZ state is proposed.

Scheme for sharing classical information via tripartite entangled states

We investigate schemes for quantum secret sharing and quantum dense coding via tripartite entangled states. We present a scheme for sharing classical information via entanglement swapping using two tripartite entangled GHZ states. In order to throw light upon the security affairs of the quantum dense coding protocol, we also suggest a secure quantum dense coding scheme via W state in analogy with the theory of sharing information among involved users.

Probabilistic Teleportation of an Arbitrary Two-ParticleState and Its Quantum Circuits

Two simple schemes for probabilistic teleportationof an arbitrary unknown two-particle state using a non-maximallyentangled EPR pair and a non-maximally entangled GHZ state asquantum channels are proposed. After receiving Alice's Bell statemeasurement results, Bob performs a collective unitary transformationon his inherent particles without introducing the auxiliary qubit.The original state can be probabilistically teleported. Meanwhile,quantum circuits for realization of successful teleportation are also presented.

Decoherence of tripartite states—a trapped ion coupled to an optical cavity

We investigate the decoherence process of a three-qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Interaction of the ion with a resonant laser and the cavity field tuned to red sideband of ionic vibrational motion generates tripartite entanglement of the internal state of the ion, vibrational state of ionic centre of mass motion and the cavity-field state. Non-dissipative decoherence occurs due to entanglement of the system with the environment, modelled as a set of non-interacting harmonic oscillators. Analytic expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state and the population inversion have been obtained. Coupling to environment results in exponential decay of off-diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different values of system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence sources has been analysed. The maximum tripartite entanglement is found to decrease with increase in the strength of system–environment coupling. The negativity as well as the linear entropy as entanglement measures gives qualitatively similar results, uniquely identifying maximally entangled and separable states of the system. For large values of system–environment coupling strength, the mixed states of the composite system lying at the boundary of an entangled–separable region are reached. For these states, whereas the negativity measures only quantum correlations, the linear entropy measures classical correlations as well.

Scheme for implementing quantum dense coding using tripartite entanglement in cavity QED

We propose an experimentally feasible scheme for dense coding in cavity QED by using a tripartite entangled GHZ state and W state, respectively. In the scheme the atoms interact simultaneously with a highly detuned cavity field and at the same time driven by a classical field.

Controlled Implementation of Non-local CNOT Operation UsingThree-Qubit Entanglement

We investigate the controlled implementation of a non-local CNOT operationusing a three-qubit entangled state. Firstly, we show how the non-local CNOToperation can be implemented with unit fidelity and unit probability byusing a maximally entangled GHZ state as controlled quantum channel. Then,we put forward two schemes for conclusively implementing the non-localoperation with unit fidelity by employing a partially entangled pure GHZstate as quantum channel. The feature of these schemes is that a thirdside is included, who may participate the process of quantum non-localimplementation as a supervisor. Furthermore, when the quantum channel ispartially entangled, the third one can rectify the state distorted byimperfect quantum channel. In addition to the GHZ class state, the W classstate can also be used to implement the same non-local operationprobabilistically. The probability of successful implementation using the Wclass state is always less than that using the GHZ class state.

Teleportation of an Arbitrary Two-Particle State by Two Partial Entangled Three-Particle GHZ States

We present a scheme for teleporting an unknown arbitrarytwo-particle state from a sender to either one of two receivers. The quantumchannel is composed of two partial entangled three-particle GHZ states. Anunknown arbitrary two-particle state can be perfectly teleportedprobabilistically if the sender performs two generalized Bell-statemeasurements and each receiver introduces an appropriate unitarytransformation with the help of the other receiver's Hadamard operations andsimple measurements.

IMPLEMENTATION OF NON-LOCAL CNOT WITH MULTIPLE TARGETS OPERATION BY GHZ STATE AND ENTANGLED PURIFICATION

We show how a non-local quantum CNOT with (N-1)-target operation can be implemented with unit fidelity and unit probability by using a N-qubit maximally entangled GHZ state as quantum channel. We also put forward two schemes for probabilistic implementing the operation with unit fidelity by employing a partially entangled pure GHZ state as quantum channel. The overall physical resources required for accomplishing these schemes are different, and the successful implementation probabilities are also different. We also point out the non-local CNOT with (N-1)-target operation can be used as a purification protocol to concentrate entanglement from an ensemble of partially entangled GHZ states into a subensemble of maximally entangled ones.

Hardy's nonlocality for generalized n-particle GHZ states

In this Letter we extend Hardy's nonlocality proof for two spin-1/2 particles [Phys. Rev. Lett. 71 (1993) 1665] to the case of n spin-1/2 particles configured in the generalized GHZ state. We show that, for all n⩾3, any entangled GHZ state violates the Bell inequality associated with the Hardy experiment. This feature is important since it has been shown [Phys. Rev. Lett. 88 (2002) 210402] that, for all n odd, there are entangled GHZ states that do not violate any standard n-particle correlation Bell inequality.