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IEEE Access

Asymmetric Controlled Bidirectional Remote Preparation of Single- and Three-Qubit Equatorial State in Noisy Environment

Yiru Sun, Gang Xu, Xiu‐Bo Chen, Yu Yang, Yixian Yang

Published Dec 7, 2018• 19 citations
Publisher

Abstract

We present an asymmetric controlled bidirectional remote preparation scheme under the control of Charlie, where Alice transmits an arbitrary single-qubit equatorial state to Bob and Bob transmits an arbitrary three-qubit equatorial state to Alice. First, the quantum channel is constructed by usingHadamard(${H}$) andCNOToperations. Second, we consider our scheme in the noiseless environment and construct the appropriate measurement bases. In addition, the participants can recover the prepared states through implementing the corresponding recovery operations determinately. Third, we discuss our scheme in five types of noisy environments (amplitude-damping, phase-damping, bit-flip, phase-flip, and depolarizing noisy environment). The fidelities of the output states are calculated, which depend on the coefficients of the prepared states and the decoherence rates. Finally, some discussions and conclusions are given. Compared with previous schemes, our scheme does not need additional operations or auxiliary qubits. So it is slightly more efficient.

DOI
10.1109/access.2018.2885340

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We present an asymmetric controlled bidirectional remote preparation scheme under the control of Charlie, where Alice transmits an arbitrary single-qubit equatorial state to Bob and Bob transmits an arbitrary three-qubit equatorial state to Alice. First, the quantum channel is constructed by usingHadamard(H{H}H) andCNOToperations. Second, we consider our scheme in the noiseless environment and construct the appropriate measurement bases. In addition, the participants can recover the prepared states through implementing the corresponding recovery operations determinately. Third, we discuss our scheme in five types of noisy environments (amplitude-damping, phase-damping, bit-flip, phase-flip, and depolarizing noisy environment). The fidelities of the output states are calculated, which depend on the coefficients of the prepared states and the decoherence rates. Finally, some discussions and conclusions are given. Compared with previous schemes, our scheme does not need additional operations or auxiliary qubits. So it is slightly more efficient.
In this paper, a novel asymmetric controlled bidirectional remote preparation scheme is proposed. In our scheme, Alice and Bob are not only the senders but also the receivers with the control of Charlie. By using the eleven-qubit entangled state as the quantum channel, Alice prepares an arbitrary two-qubit equatorial state for Bob and Bob prepares an arbitrary three-qubit equatorial state for Alice simultaneously. Firstly, we give the construction process of the quantum channel. Secondly, the whole recovery operations are given. Alice and Bob can recover the prepared state determinately. Thirdly, we consider the effect of the noisy environment (amplitude-damping and phase-damping) in our scheme and calculate the fidelities of the output states. Finally, since our scheme does not need additional operations and auxiliary qubits, the efficiency of our scheme is higher than that of the previous schemes.
In this paper, two novel schemes for bidirectional controlled remote state preparation (BCRSP) and asymmetric bidirectional controlled remote state preparation (ABCRSP) in four-dimensional systems are proposed. The first scheme uses a six-particle entangled state as the quantum channel. Under Charlie’s supervision, Alice and Bob can simultaneously create a single-particle four-dimensional equatorial state at each other’s location. Moreover, in the second scheme, using a seven-particle entangled state as the quantum channel, Alice remotely prepares a two-particle four-dimensional equatorial state for Bob, while Bob remotely prepares another single-particle four-dimensional equatorial state for Alice under the supervision of controller Charlie. Both schemes employ quantum operations such as control-not, projective measurement and unitary transformation in four-dimensional systems. It is worth noting that the proposed schemes have a total success probability of 100% in ideal environment. In addition, we also investigate the proposed two schemes in the noisy environment. The fidelities of output states are calculated and the effect factors are discussed. Finally, we give the advantages of these schemes compared to other schemes.
A scheme for asymmetric controlled bidirectional remote state preparation by utilizing 15-qubit entangled state as quantum channel is proposed. In this paper, we present a new protocol that Alice prepares a three-qubit equatorial state for Bob and Bob prepares a four-qubit equatorial state for Alice at the same time under Charlie’s control. The success of this scheme cannot be separated from the controller Charlie. In addition, we give some analysis and conclusions by comparing with other schemes. The auxiliary qubits and operations are not required in our scheme. In particular, the success probability of the receivers restoring the prepared states can reach 100%. Thus, our scheme has better performance.
In this paper, a novel protocol for asymmetric bidirectional controlled quantum teleportation (ABCQT) by using the nine-qubit entangled state as a quantum channel is proposed. Alice transmits an arbitrary three-qubit entangled state to Bob and at the same time, Bob transmits an arbitrary single-qubit entangled state to Alice under the permission of a third party as a controller. This protocol is based on the Hadamard (H) gates, controlled-not (CNOT) operations, appropriate unitary operations, and single-qubit Von Neumann measurements (SM) which are more efficient than multi-qubit joint measurements (JM). This scheme explicitly shows how the channel of nine-qubit entangled state prepares, and it is discussed in six types of noisy scenarios (amplitude-damping, phase-damping, bit-flip, phase-flip, bit-phase-flip, and depolarizing noisy scenarios). Then, we analytically derive the fidelities of the ABCQT process and show that they only depend on the amplitude parameter of the initial state and the decoherence noisy rate. Finally, compared with previous schemes, this scheme also shows remarkable advantages.
The scheme for controlled unidirectional cyclic remote state preparation of single-qutrit equatorial states is put forward. Alice, Bob, Charlie, and David share a seven-qutrit entangled state as the quantum channel. Under the control of David, Alice can remotely prepare a single-qutrit equatorial state at Bob’s site, Bob can remotely prepare a single-qutrit equatorial state at Charlie’s site, Charlie can remotely prepare a single-qutrit equatorial state at Alice’s site simultaneously. The direction of controlled unidirectional cyclic remote state preparation can be reversed by changing measured qutrits of the quantum channel. The scheme for controlled bidirectional cyclic remote state preparation of single-qutrit equatorial states is also proposed. The schemes can be generalized to controlled unidirectional and bidirectional multi-party cyclic remote state preparation of single-qudit equatorial states.
We investigate the influence of a noisy environment on the remote preparation of the multi-qubit equatorial state, and specifically deduce the final states and fidelities of the remote preparation of the three-qubit and four-qubit equatorial states under diverse types of noisy environments, namely, amplitude damping, bit flip, phase damping, phase flip, bit-phase flip, depolarization, and non-Markov environments. The results show that when the decoherence factors of the front six noises are equal, the influence degrees of phase damped noise, bit flip noise, phase flip noise, and bit-phase flip noise are similar, while the information loss caused by the amplitude damped noise and depolarizing noise is less. In particular, the bit flip noise and depolarizing noise may have more complex effects on the remote state preparation (RSP) schemes depending on the phase information of the target states, even for the ideal cases where the fidelity values are always 1 for specific phase relations. In the non-Markov environment, owing to the back and forth of information between the environment and systems, fidelities exhibit oscillating behavior and the minimum value may stay greater than zero for a long evolutionary time. These results are expected to have potential applications for understanding and avoiding the influence of noise on remote quantum communication and quantum networks.