Deterministic Joint Remote Preparation of a Four-Qubit Cluster-Type State via GHZ States

A scheme for the deterministic joint remote preparation of a four-qubit cluster-type state using only two Greenberger-Horne-Zeilinger (GHZ) states as quantum channels is presented. In this scheme, the first sender performs a two-qubit projective measurement according to the real coefficient of the desired state. Then, the other sender utilizes the measurement result and the complex coefficient to perform another projective measurement. To obtain the desired state, the receiver applies appropriate unitary operations to his/her own two qubits and two CNOT operations to the two ancillary ones. Most interestingly, our scheme can achieve unit success probability, i.e., P _{s u c} =1. Furthermore, comparison reveals that the efficiency is higher than that of most other analogous schemes.     

Multiparty Joint Remote Preparation of an Arbitrary GHZ-Class State via Positive Operator-Valued Measurement

We present a scheme for multiparty joint remote preparation of an arbitrary GHZ-class state with a pure entangled quantum channel via positive operator-valued measurement (POVM). The M senders share the information of the original GHZ-class state. All the senders perform single particle measurements according to their knowledge of the original state, the receiver can reconstruct the original state if he cooperates with the all the senders. This scheme has the advantage of transmitting less particles for remote preparation of an arbitrary GHZ-class state. Moreover, the success probability for remote preparing an arbitrary GHZ-class state is higher than others.     

Controlled Remote Preparing of an Arbitrary 2-Qudit State with Two-Particle Entanglements and Positive Operator-Valued Measure

We present a scheme for symmetric controlled remote preparation of an arbitrary 2-qudit state form a sender to either of the two receivers via positive operator-valued measurement and pure entangled two-particle states. The first sender transforms the quantum channel shared by all the agents via POVM according to her knowledge of prepared state. All the senders perform singIe- or two-particle projective measurements on their entangled particles and the receiver can probabilisticaly reconstruct the original state on her entangled particles via unitary transformation and auxiliary qubit. The scheme is optimal as the probability which the receiver prepares the original state equals to the entanglement of the quantum channel. Moreover, it is more convenience in application than others as it requires only two-particle entanglements for preparing an arbitrary two-qudit state.     

Deterministic Joint Remote Preparation of Arbitrary Four-Qubit Cluster-Type State Using EPR Pairs

Using four Einstein-Podolsky-Rosen (EPR) pairs as the pre-shared quantum channel, an economic and feasible scheme for deterministic joint remote preparation of the four-particle cluster-type state is presented. In the scheme, one of the senders performs a four-qubit projective measurement based on a set of ingeniously constructed vectors with real coefficients, while the other performs the bipartite projective measurements in terms of the imaginary coefficients. Followed with some appropriate unitary operations and controlled-NOT operations, the receiver can reconstruct the desired state. Compared with other analogous JRSP schemes, our scheme can not only reconstruct the original state (to be prepared remotely) with unit successful probability, but also ensure greater efficiency.     

Efficient Remote Preparation of Four-Qubit Cluster-Type Entangled States with Multi-Party Over Partially Entangled Channels

We present a strategy for realizing multiparty-controlled remote state preparation (MCRSP) for a family of four-qubit cluster-type states by taking a pair of partial entanglements as the quantum channels. In this scenario, the encoded information is transmitted from the sender to a spatially separated receiver with control of the transmission by multiple parties. Predicated on the collaboration of all participants, the desired state can be faithfully restored at the receiver’s location with high success probability by application of additional appropriate local operations and necessary classical communication. Moreover, this proposal for MCRSP can be faithfully achieved with unit total success probability when the quantum channels are distilled to maximally entangled ones.     

Optimal Remote Preparation of a Four-Qubit Entangled Cluster-Type State Via Two Non-Maximally Entangled GHZ-Type States

We devise an highly efficient protocol for remotely preparing a four-qubit entangled cluster-type state. In this protocol, two non-maximally entangled GHZ-type states are employed to link the sender Alice and the receiver Bob, and the to-be-prepared state can be reconstructed successfully with the probability of (b₁b₂)² in general case. Then to achieve our concerns of constructing efficient remote preparation with higher success probability, some special ensembles of four-qubit states are minutely investigated. As a result, it is shown that the total probability of the RSP protocol, in these particular cases, can be improved to twice or even fourfold as that in general case.     

Deterministic Remote Preparation of a Four-Qubit Cluster-Type Entangled State

We propose a scheme for remotely preparing a four-qubit cluster-type state with complex coefficients by using six EPR pairs as the quantum channel. To complete the remote state preparation scheme, a novel set of four-qubit mutually orthogonal basis vectors has been introduced. It is shown that, after the sender performs two different four-qubit projective measurements, the receiver can reconstruct the original state (to be prepared remotely) with unit successful probability. Moreover, the scheme is also generalized to the case that non-maximally two-qubit entangled states are taken as the quantum channel.     

Remote Preparation of Three-Particle GHZ Class States

We propose a remote state preparation （RSP） scheme of three-particle Greenberger Horne-Zeilinger （GHZ） class states, where quantum channels are composed of two maximally entangled states. With the aid of forward classical bits, the preparation of the original state can be successfully realized with the probability 1/2, the necessary classical communication cost is 0.5 bit on average. If the state to be prepared belongs to some special states, the success probability of preparation can achieve 1 after consuming one extra bit on average. We then generalize this scheme to the case that the quantum channels consist of two non-maximally entangled states.     

Hierarchical Controlled Remote State Preparation by Using a Four-Qubit Cluster State

We propose a scheme for hierarchical controlled remote preparation of an arbitrary single-qubit state via a four-qubit cluster state as the quantum channel. In this scheme, a sender wishes to help three agents to remotely prepare a quantum state, respectively. The three agents are divided into two grades, that is, an agent is in the upper grade and other two agents are in the lower grade. In this process of remote state preparation, the agent of the upper grade only needs the assistance of any one of the other two agents for recovering the sender’s original state, while an agent of the lower grade needs the collaboration of all the other two agents. In other words, the agents of two grades have different authorities to reconstruct sender’s original state.     

Joint Remote State Preparation of Arbitrary Two- and Three-Particle States

We propose a scheme to joint remotely prepare arbitrary two- and three-particle entangled states by using non-maximally three-particle GHZ state as the quantum channel. Our scheme consists of two senders and one receiver. It will be shown that two senders can help the receiver to remotely prepare the original state with certain probability. The projective measurement and corresponding unitary operation are needed in this article.     

Local Invariants for a Class of Tripartite Quantum Mixed States

We study the equivalence of tripartite mixed states under local unitary transformations. The nonlocal properties for a class of tripartite quantum states in ${\mathbb C}^K \otimes {\mathbb C}^M \otimes {\mathbb C}^N$ composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.     

Controlled Remote State Preparation of an Arbitrary Two-Qubit State by Using Two Sets of Four-Qubit GHZ States

Recently, Huang and Zhao (Int. J. Theor. Phys. 56, 678, 2017) proposed a new scheme for controlled remote state preparation of an arbitrary two-qubit state by using two sets of three-qubit GHZ states as the quantum channel. In the scheme, Alice and Bob choose four different kinds of two-qubit projective measurement bases to measure their local qubits, respectively. We demonstrate that two sets of four-qubit GHZ states can be used to realize the deterministic controlled remote state preparation of an arbitrary two-qubit state by performing only two-qubit projective measurements.     

Joint Remote Preparation of a General Three-Qubit State via Non-maximally GHZ States

In this paper, we use three non-maximally GHZ states as the quantum channel and then propose two schemes to realize joint remotely preparing the general three-qubit state. For the first scheme, we show that the joint remotely state preparation (JRSP) can be successfully realized with a certain probability by performing information splitting, introducing an ancilla and proper measurement. Moreover, for the second scheme, we establish a new method to split information which needn’t to introduce the ancilla on the receiver’s side and can achieve better security.     

Optimal Joint Remote State Preparation of Arbitrary Equatorial Multi-qudit States

As an important communication technology, quantum information transmission plays an important role in the future network communication. It involves two kinds of transmission ways: quantum teleportation and remote state preparation. In this paper, we put forward a new scheme for optimal joint remote state preparation (JRSP) of an arbitrary equatorial two-qudit state with hybrid dimensions. Moreover, the receiver can reconstruct the target state with 100 % success probability in a deterministic manner via two spatially separated senders. Based on it, we can extend it to joint remote preparation of arbitrary equatorial multi-qudit states with hybrid dimensions using the same strategy.     

Probabilistic Remote Preparation of a Tripartite High-Dimensional Equatorial Entangled State

We present a scheme for probabilistic remote preparation of a tripartite qutrit entangled state with a partial tripartite qutrit entangled state and a partial bipartite qutrit entangled state as the quantum channel. It is found that a bipartite qutrit orthogonal projective measurement, an auxiliary qutrit particle, and the corresponding unitary transformation are required. A scheme for probabilistic remote preparation of a tripartite qudit equatorial entangled state by using a partial tripartite qudit entangled state and a partial bipartite qudit entangled state as the quantum channel is also proposed. We calculate the successful total probability and the total classical communication cost required in the RSP process, respectively.     

Preparation and Analysis of Two-Dimensional Four-Qubit Entangled States with Photon Polarization and Spatial Path

Entanglement states serve as the central resource for a number of important applications in quantum information science, including quantum key distribution, quantum precision measurement, and quantum computing. In pursuit of more promising applications, efforts have been made to generate entangled states with more qubits. However, the efficient creation of a high-fidelity multiparticle entanglement remains an outstanding challenge due to the difficulty that increases exponentially with the number of particles. We design an interferometer that is capable of coupling the polarization and spatial paths of photons and prepare 2-D four-qubit GHZ entanglement states. Using quantum state tomography, entanglement witness, and the violation of Ardehali inequality against local realism, the properties of the prepared 2-D four-qubit entangled state are analyzed. The experimental results show that the prepared four-photon system is an entangled state with high fidelity.     

Controlled Joint Remote Preparation of a Six-Qubit Cluster-Type State by Using GHZ States

A scheme for the controlled joint remote preparation of an arbitrary six-qubit cluster-type state by using only two sets of five-qubit GHZ states as quantum channel is proposed. In our scheme, Alice firstly performs two sets of two-qubit projective measurement according to the real coefficients and the complex coefficients of the desired six-qubit cluster-type state. Then, the controller Charlie must apply another two-qubit projective measurement according to the Alice’s measurement result. Finally, Bob can obtain the desired six-qubit cluster-type state according to an appropriate unitary operation. Our scheme can achieve unit success probability.

     

Probabilistic Joint Remote Preparation of Four-Particle Cluster-Type States with Quaternate Partially Entangled Channels

We put forward a new and feasible scheme to realize joint remote preparation of four-particle cluster-type states based on two quaternate partially entangled states as quantum channels. During the preparation, each of the states’ senders is just required to perform a bipartite projective measurement in a 2×2-dimensional Hilbert space, and the receiver needs to implement some appropriate unitary operations including a local triplet collective transformation. It is proved that our scheme can be accomplished in a probabilistic manner, and the success probability of preparation (SPP) is dependent on the entangled states set up in prior. Moreover, it is explored that SPP can be greatly enhanced to be quadruple of that in general case, when the prepared states belong to some special ensembles. And the scheme feasibility is evaluated finally.     

Efficient Joint Remote Preparation of an Arbitrary m-qudit State with Partially Entangled States

We present an efficient scheme for multiparty joint remote preparation of an arbitrary m-qudit state by using partially entangled states as the quantum channel. One of the senders first performs a collective unitary transformation on his entangled particles and the auxiliary qubit, and then he performs a Z-basis measurement on the auxiliary qubit for transforming the partially entangled quantum channel into the two types of multi-particle entangled states. In the first case, the quantum channel shared by all the senders and the receiver is the target channel. In the second case, the quantum channel transforms into another partially entangled state which is the resource for the quantum channel transformation in the next round. Compared with other protocols, our scheme has advantage of having high success probability for joint remote preparation of an arbitrary m-qudit state via partially entangled states.