Unit Success Probability Research Articles

Controlled Cyclic and Bidirectional Hybrid Quantum Communication of Arbitrary Two‐Qubit States

AbstractHybrid quantum communication with the combination of quantum teleportation and remote preparation is hopeful for promoting the development of quantum networks and enriching the diversity of quantum network communication. To improve the communication efficiency and enhance the scalability of the quantum networks, a meaningful protocol for controlled cyclic and bidirectional hybrid quantum communication of arbitrary two‐qubit states is proposed, which allows quantum information to be transmitted simultaneously in both directions among multiple participants. With the permission of one controller, each observer can simultaneously transmit arbitrary known two‐qubit states and unknown ones to their adjacent observers, by implementing remote preparation and quantum teleportation in the clockwise and counterclockwise directions. Furthermore, the participants just carry out some quantum measurements and recovery operations to achieve the communication target, and the desired states can be attained with a unit success probability, thus the protocol is deterministic. Finally, some comparisons are also made with other similar protocols, which shows that the protocol is better in qubit efficiency and communication capacity.

Double-direction cyclic controlled quantum communication of single-particle states

The purpose of this paper is to investigate the double-direction cyclic (DDC) controlled quantum communication of single-particle states. We construct 13-particle, 19-particle and 16-particle entangled channels via Hadamard gates and controlled-NOT gates, separately. Based on these quantum channels that we construct, three novel theoretical schemes are proposed for achieving four-party DDC controlled quantum teleportation (QT), remote state preparation (RSP) and hybrid quantum communication, respectively. For any of these three schemes, each correspondent can simultaneously teleport two different single-particle states to two other correspondents under the control of the supervisor, which ensures that cyclic controlled quantum communication is implemented simultaneously in both clockwise and anticlockwise directions. Furthermore, the three presented four-party schemes for DDC controlled quantum communication can be extended to scenarios with n (n>3) correspondents. In each of our schemes, the general analysis formulas for both the sender’s manipulations and the receiver’s transformations are respectively given, and the unit success probability of each scheme is achieved. This article requires specific two-particle projective measurement, single-particle von Neumann measurement, Hadamard gate, controlled-NOT gates and Pauli gates, so our schemes can be physically implemented in terms of current technologies. We also analyzed the inherent efficiency, safety, and control power of the proposed schemes, and the results showed that our schemes are good.

Cyclic quantum state sharing with a nine-qubit entangled state

In this paper, we present a novel scheme for cyclic quantum state sharing (QSTS) by using a nine-qubit entangled state as quantum channel. In this scheme, each of the three dealers has a different unknown quantum state, and every dealer wants two agents to share his/her quantum state. At the same time, three dealers perform Bell basis measurements on his/her own qubits, and the controllers make a single-qubit measurement on his/her own qubits, after that, the receivers can recover the original states by applying suitable unitary operations, respectively. It is shown that, only if all agents collaborate with each other, the cyclic QSTS can be completed with unit success probability.

Deterministic remote state preparation of arbitrary three-qubit state through noisy cluster-GHZ channel

We propose a novel scheme for remote state preparation of an arbitrary three-qubit state with unit success probability, utilizing a nine-qubit cluster-GHZ state without introducing auxiliary qubits. Furthermore, we proceed to investigate the effects of different quantum noises (e.g., amplitude-damping, phase-damping, bit-flip and phase-flip noises) on the systems. The fidelity results of three-qubit target state are presented, which are usually used to illustrate how close the output state is to the target state. To compare the different effects between the four common types of quantum noises, the fidelities under one specific identical target state are also calculated and discussed. It is found that the fidelity of the phase-flip noisy channel drops the fastest through the four types of noisy channels, while the fidelity is found to always maintain at 1 in bit-flip noisy channel.

Quantum two-state sharing

In this paper, we propose a novel scheme for quantum two-state sharing (QTSS) by using a five-qubit entangled state as the quantum channel. In this scheme, a dealer Alice has two unknown quantum states and wants her three agents to share the quantum states. After the dealer performs a four-qubit measurement on her qubits, and the controller employs a single-qubit measurement on his own qubit, the state receivers can reconstruct the original states by using the appropriate unitary operations. It is shown that, only if all agents collaborate with each other, the QTSS can be completed with unit success probability.

Multiple-shot and unambiguous discrimination of von Neumann measurements

We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case of minimum error discrimination, we focus on discrimination of measurements with the assistance of entanglement. We provide an alternative proof of the fact that all pairs of distinct von Neumann measurements can be distinguished perfectly (i.e. with the unit success probability) using only a finite number of queries. Moreover, we analytically find the minimal number of queries needed for perfect discrimination. We also show that in this scenario querying the measurements in parallel gives the optimal strategy, and hence any possible adaptive methods do not offer any advantage over the parallel scheme. In the unambiguous discrimination scenario, we give the general expressions for the optimal discrimination probabilities with and without the assistance of entanglement. Finally, we show that typical pairs of Haar-random von Neumann measurements can be perfectly distinguished with only two queries.

Deterministic Controlled Remote Preparation of Two-qutrit Equatorial States

We present a novel scheme for deterministically realizing remote preparation of three-dimensional quantum states in a controlled manner. In this scheme, to link the three legitimate parties, generalized Einstein-Podolsky-Rosen (EPR) states, generalized Greenberger-Horne-Zeilinger (GHZ) states or their combinations are employed to product the shared quantum resources. Then to complete the deterministic controlled remote state preparation (DCRSP) in a three-dimensional system, some suitable sets of mutually orthogonal quantum states are hired as the measuring bases. It is shown that, after performing projective measurements under the proper measuring bases, the remote preparation of two-qutrit equatorial states can be successfully realized under control of a third party with unit successful probability.

Deterministic bidirectional controlled remote preparation without information splitting

By using a five-qubit entangled state as the quantum channel, we propose an efficient protocol for implementing bidirectional controlled remote preparation of arbitrary single-qubit states with unit success probability. The senders do not need to perform information splitting and additional unitary operations due to the elaborately constructed measurement basis. Furthermore, three-bit classical communication can be saved at the controller’s broadcast channel with the aid of network coding. Then, we consider the effect of five-type noises on the proposed protocol. It is found that the fidelities of the output states are dependent on the coefficients of the prepared state and the noise parameter. Interestingly, the fidelity is irrelevant to the participators’ measurement results except in the amplitude-damping and phase-damping noises.

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.

Optimal quantum channel for perfect controlled super-dense coding protocol

Perfect super-dense coding protocol allows transmission of two classical bits (cbits) by sending just one quantum bit (qubit) with unit success probability. Perfect controlled super-dense coding protocol should be such that perfect super-dense coding is achieved with the controller’s cooperation. There are different possible types of quantum channels to be shared among the authorized parties to perform perfect controlled super-dense coding. Of our interest is the quantum channel which is optimal in the sense that no cbits can be transmitted with certainty without the controller’s cooperation. We attack this problem by means of the so-called control power. By calculating and analyzing the control power for specific quantum channels we figure out the one that is optimal. We also address the issue of how to prepare such optimal quantum channel.

Deterministic hierarchical joint remote state preparation with six-particle partially entangled state**Project supported by the National Natural Science Foundation of China (Grant Nos. 61701285 and 61701284), the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents, China (Grant No. 2017RCJJ070), and China Postdoctoral Science Foundation Funded Project (Grant No. 2017M622233).

In this paper, we present a novel scheme for hierarchical joint remote state preparation (HJRSP) in a deterministic manner, where two senders can jointly and remotely prepare an arbitrary single-qubit at three receivers’ port. A six-particle partially entangled state is pre-shared as the quantum channel. There is a hierarchy among the receivers concerning their powers to reconstruct the target state. Due to various unitary operations and projective measurements, the unit success probability can always be achieved irrespective of the parameters of the pre-shared partially entangled state.

Deterministic joint remote preparation of an equatorial hybrid state via high-dimensional Einstein–Podolsky–Rosen pairs: active versus passive receiver

Entanglement plays a vital and in many cases non-replaceable role in the quantum network communication. Here, we propose two new protocols to jointly and remotely prepare a special so-called bipartite equatorial state which is hybrid in the sense that it entangles two Hilbert spaces with arbitrary different dimensions D and N (i.e., a type of entanglement between a quDit and a quNit). The quantum channels required to do that are however not necessarily hybrid. In fact, we utilize four high-dimensional Einstein–Podolsky–Rosen pairs, two of which are quDit–quDit entanglements, while the other two are quNit–quNit ones. In the first protocol the receiver has to be involved actively in the process of remote state preparation, while in the second protocol the receiver is passive as he/she needs to participate only in the final step for reconstructing the target hybrid state. Each protocol meets a specific circumstance that may be encountered in practice and both can be performed with unit success probability. Moreover, the concerned equatorial hybrid entangled state can also be jointly prepared for two receivers at two separated locations by slightly modifying the initial particles’ distribution, thereby establishing between them an entangled channel ready for a later use.

Deterministic Multi-hop Controlled Teleportation of Arbitrary Single-Qubit State

Multi-hop teleportation is of great significance due to long-distance delivery of quantum information and wireless quantum communication networks. In existing protocols of multi-hop teleportation, the more nodes, the smaller the success probability. In this paper, fusing the ideas of multi-hop teleportation and controlled teleportation, we put forward a scheme for implementing multi-hop controlled teleportation of single-qubit state. A set of ingenious three-qubit non-maximally entangled states are constructed to serve as the quantum channels. The information is perfectly transmitted hop by hop through teleportation under the control of the supervisors. Unit success probability can be achieved independent of channel’s entanglement degree and the number of intermediate nodes. Only Pauli operations, single-qubit rotation, Hadamard gate, controlled-NOT gate, Bell-state measurement and single-qubit measurement are used in our scheme, so this scheme is easily realized in physical experiment.

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.

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.

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 per- forms 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., Psuc=1. Furthermore, comparison reveals that the efficiency is higher than that of most other analogous schemes.

Deterministic joint remote state preparation via partially entangled quantum channel

In this paper, we propose a scheme for deterministic joint remote state preparation (JRSP). Two spatially separated senders intend to help a receiver remotely prepare an arbitrary single-qubit state. Four-particle partially entangled state is constructed to serve as the quantum channel. By determining right unitary operations for the senders and appropriate recovery operations for the receiver, the target state can be reestablished with unit success probability, irrespective of the channel parameter.

Controlled Remote Preparation Via the Brown State with no Restriction

Two controlled remote state preparation protocols via the Brown state as the entangled channel are proposed. One prepares an arbitrary two-qubit state, and the other prepares an arbitrary three-qubit state. It is worth mentioning that Hurwitz matrix equation plays a key role in the construction of measurement basis. Comparing with the previous protocols, the novel schemes have no restriction on the coefficients of the prepared state while keeping the same success probability 50 %. It means that the application of the proposed schemes are more extensive in practice. Moreover, we discuss the special complex coefficient ensembles with unit success probability.

Deterministic joint remote state preparation of arbitrary single- and two-qubit states**Project supported by the National Natural Science Foundation of China (Grant Nos. 61372076 and 61301171), the 111 Project (Grant No. B08038), and the Fundamental Research Funds for the Central Universities, China (Grant No. K5051201021).

In this paper, two novel schemes for deterministic joint remote state preparation (JRSP) of arbitrary single- and two-qubit states are proposed. A set of ingenious four-particle partially entangled states are constructed to serve as the quantum channels. In our schemes, two senders and one receiver are involved. Participants collaborate with each other and perform projective measurements on their own particles under an elaborate measurement basis. Based on their measurement results, the receiver can reestablish the target state by means of appropriate local unitary operations deterministically. Unit success probability can be achieved independent of the channel’s entanglement degree.

Controlled Secure Direct Communication with Six-Qubit Entangled States

We propose an experimentally feasible scheme for implementing controlled quantum secure direct communication by using six-qubit entangled states. According to the results measured by the sender and the controller, the receiver can obtain different secret messages in a deterministic way with unit successful probability. In our scheme, the information-carrying qubits do not need to be transmitted over the public channel. Therefore, the scheme is determinate and secure.