Arbitrary Three-particle State Research Articles

The effect of quantum noise on two different deterministic remote state preparation of an arbitrary three-particle state protocols

Multi-particle quantum state deterministic remote preparation is a fundamental and important technical branch in quantum communication. Since quantum noise is unavoidable in realistic quantum communication, it is important to analyze the effect of noise on multi-particle quantum communication protocols. In this paper, we study the effects of noise, such as amplitude damping, phase damping, bit-flip and depolarizing noises, on two deterministic remote preparation of an arbitrary three-particle state protocols, which are based on two different entangled channels, namely $$\chi $$ state and Brown state. The detailed mathematical analysis shows that the output states of two deterministic remote state preparation (DRSP) protocols are the same in the same noisy environment. That is to say, in the same noisy environment, the effects of noise on two DRSP protocols are the same. This conclusion proves that these two DRSP protocols will produce the same arbitrary three-particle states in the same noise channel environment, and so that these protocols are inherently convergent and can be substituted for each other in certain circumstances. In addition, this paper also takes three-particle states $$a\left| {000} \right\rangle + b{\mathrm{e}^{ic}}\left| {111} \right\rangle $$ as an example and studies the relationship between the fidelity, the target state and the size of the noise factor. The results show that if the target state can be selected, an appropriate target state can effectively resist on the bit-flip noise. If the target state cannot be selected, as the increase in the size of noise factor, the fidelities of the two DRSP schemes in the amplitude damping noise and phase damping noise are always larger than those in the bit-flip noise and depolarizing noise. This conclusion indicates that two protocols have better resistance on amplitude damping and phase damping noise than the bit-flip and depolarizing noises. These findings and analyses will provide valid help in deterministic remote preparation of an arbitrary three-particle state in a noisy environment.

Novel Criteria for Deterministic Remote State Preparation via the Entangled Six-Qubit State

In this paper, our concern is to design some criteria for deterministic remote state preparation for preparing an arbitrary three-particle state via a genuinely entangled six-qubit state. First, we put forward two schemes in both the real and complex Hilbert space, respectively. Using an appropriate set of eight-qubit measurement basis, the remote three-qubit preparation is completed with unit success probability. Departing from previous research, our protocol has a salient feature in that the serviceable measurement basis only contains the initial coefficients and their conjugate values. By utilizing the permutation group, it is convenient to provide the permutation relationship between coefficients. Second, our ideas and methods can also be generalized to the situation of preparing an arbitrary N-particle state in complex case by taking advantage of Bell states as quantum resources. More importantly, criteria satisfied conditions for preparation with 100% success probability in complex Hilbert space is summarized. Third, the classical communication costs of our scheme are calculated to determine the classical recourses required. It is also worth mentioning that our protocol has higher efficiency and lower resource costs compared with the other papers.

Remote preparation of a three-particle state via positive operator-valued measurement

We present a scheme to remotely prepare an arbitrary three-particle pure state in real Hilbert space by using three bipartite partially entangled pairs as a quantum channel, and then generalize it to the tripartite equatorial-like case. Our results show that remote preparation of the three-particle state both in real space and in imaginary space can be probabilistically achieved with unity fidelity by performing an appropriate three-particle projective measurement at the sender's side and an optimal positive operator-valued measurement at the receiver's side. Moreover, the probability of success of our scheme is determined by the smaller parameters of the three initial entangled pairs.

Conclusive Teleportation of an Arbitrary Three-Particle State via Positive Operator-Valued Measurement

We present a scheme for conclusive teleportation of an arbitrary and unknown three-particle state by performing three Bell-state measurements at the sender's side and a positive operator-valued measurement at the receiver's side. Moreover, we obtain the successful probability of teleportation and make a brief discussion on the average fidelity for the conclusive teleportation scheme.

Teleportation of arbitrary three-particle GHZ state using single three-particle maximal GHZ state or two EPR states

Two schemes, using respectively the single three-particle maximal Greenberger-Horne-Zeilinger (GHZ) state and the two Einstein-Podolsky-Rosen (EPR) states as quantum channels, for deterministic teleportation of arbitrary three-particle GHZ state are proposed. These schemes are also generalized into the case of teleportation of arbitrary n-particle GHZ state (n≥4). The fidelity of teleportation when the quantum channels are affected by noise is discussed. It is found that when using single three-particle GHZ state which is affected by noise as quantum channel, the fidelity of teleportation is only related to the entanglement of the channel. However, when using two EPR states which is affected by noise as quantum channels, the fidelity of teleportation is related to the entanglement of both the channels and the unknown state to be delivered. Compared with previous proposals, our schemes require a reduced number of entangled states as quantum channels to achieve the same task.

The expansion of orthogonal complete set and transformation operator in teleportation

In accordance with the principle of superposition，for the teleportation of an arbitrary three-particle state via three pair nonmaximally entangled particles, the system state of particles can be expanded by Bell bases and transformation operator, and the teleportation can be realized only by performing a inverse transformation. The relation of transformation operators with unitary operation is discussed. The necessary condition to realize the teleportation is that the transformation operators have inverse operators.

Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.

Probabilistic and controlled teleportation of tripartite state in a general form and its quantum networks

We discuss a scheme for probabilistic and controlled teleportation of an unknown arbitrary three-particle state by constructing a peculiar non-maximally entangled state as a controlled quantum channel, which is teleported between two sides with the help of the auxiliary particle and the cooperation of the third side (Charlie) as a supervisor. In comparison with some existing schemes, on the receiver's side it is easy to have the sender's state through operating two uniform unitary transformations in turn. In addition, we also give an efficient quantum network for implementing the new scheme by means of some primitive operations.

Teleportation of an Arbitrary Three-Particle State via Three EPR Pairs

A scheme of teleportation of an arbitrary three-particle state is presented when three pairs of entangled particles are used as quantum channels. After the Bell state measurements are operated by the sender, the original state with deterministic probability can be reconstructed by the receiver when a corresponding unitary transformation is followed.

Probabilistic teleportation of an arbitrary three-particle state via a partial entangled four-particle state and a partial entangled pair

We present a scheme to probabilistically teleport an arbitrary and unknown three-particle state via a two-particle non-maximally entangled state and a four-particle non-maximally entangled state as the quantum channel. With the help of Bell-state measurements, an arbitrary three-particle state can be perfectly teleported if a receiver introduces a collective unitary transformation. All kinds of unitary transformations are given in greater detail. This scheme can be generalized to the teleportation of an arbitrary and unknown multiparticle state.

Probabilistic teleportation of a three-particle state via three pairs of entangled particles

A scheme for teleporting an arbitrary three-particle state is proposed when three pairs of entangled particles are used as quantum channels. Quantum teleportation can be successfully realized with a certain probability if the receiver adopts an appropriate unitary-reduction strategy. The probability of successful teleportation is determined by the smallest coefficients of the three entangled pairs.

Teleportation of an arbitrary three-particle state

We propose two schemes for teleporting an arbitrary three-particle state. In the first scheme, a two-particle state and a three-particle entangled state (both non-maximally entangled states) are used as quantum channels, while in the second scheme, three non-maximally entangled particle pairs are employed as quantum channels. We show that teleportation can be successfully realized with certain probability if a receiver adopts some appropriate unitary transformations. Their success probabilities and the classical communication costs are different.