Unitary Transformation in Quantum Teleportation

In the well-known treatment of quantum teleportation, the receiver should convert the state of his EPR particle into the replica of the unknown quantum state by one of four possible unitary transformations. However, the importance of these unitary transformations must be emphasized. We will show in this paper that the receiver cannot transform the state of his particle into an exact replica of the unknown state which the sender wants to transfer if he has not a proper implementation of these unitary transformations. In the procedure of converting state, the inevitable coupling between EPR particle and environment which is needed by the implementation of unitary transformations will reduce the accuracy of the replica.     

Unitary Application of the Quantum Error Correction Codes

For applying the perfect code to transmit quantum information over a noise channel,the standard protocol contains four steps:the encoding,the noise channel,the error-correction operation,and the decoding.In present work,we show that this protocol can be simplified.The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation.We also offer a quantum circuit,which can correct the arbitrary single-qubit errors.     

Unitary Application of the Quantum Error Correction Codes

For applying the perfect code to transmit quantum information over a noise channel, the standard protocol contains four steps: the encoding, the noise channel, the error-correction operation, and the decoding. In present work, we show that this protocol can be simplified. The error-correction operation is not necessary if the decoding is realized by the so-called complete unitary transformation. We also offer a quantum circuit, which can correct the arbitrary single-qubit errors.     

Quantum Teleportation of One-to-Many Using （n ＋ 1）-Particle Entanglement

In this paper, quantum teleportatlon of one-to-many using （n ＋1）-particle entanglement is presented. If the sender （Alice） wants to transmit an unknown quantum state to a distant receiver （Bob）, similar to the previous schemes, Alice performs Bell-state measurement on particles belonging to herself and informs the receiver the results through the classical channel. After that, it needs to perform the Hadamard operation on the other （n - 1） particles and measure them as well. With the aid of the measurement results, Bob can operate a corresponding unitary transformation on his particle to reconstruct the original state. Of course, the reconstruction may realize at either location of n, but it cannot realize at all locations at the same time.     

二粒子纠缠态受控传递的最佳量子通道

本文研究了如何在二粒子纠缠态的量子受控传递中选择最佳量子通道的问题。分别利用四粒子GHZ态和四粒子特殊"反关联GHZ态"作为量子通道,本文提出了二粒子反关联纠缠态的量子受控传递的两个方案。通过对比两个方案下接受者最后采取的幺正操作的具体矩阵形式,分析了待传量子纠缠态与量子通道的关系,指出了四粒子GHZ态和四粒子特殊"反关联GHZ态"分别是二粒子正关联和反关联纠缠态各自隐形传递应该选择的最佳的量子通道。     

Unitary Transformation in kq Representation

In this paper, we discuss the unitary transformation induced by Z6 rotations of noncommutative space on the states （k, q,s）, which plays a key role in construction for noncommutative solitons T^2/Z6 by GHS method. As a result, we prove a well-known ＂Gauss Sum＂ formula in the number theory through a concise way.     

Controlled Quantum Teleportation of a One-Particle Unknown State via a Three-Particle Entangled State

A kind of three-particle entangled state is applied as quantum channel of the controlled quantum teleporration of a one-particle unknown state. The one-particle unknown state is transmitted from the sender to the recipient under the control of the supervisor. After the sender makes Bell-state measurement and the supervisor performs von Neumann measurement, the recipient carries out unitary transformation on his own particle depending on classical information from the sender and the supervisor. The teleportation cannot be completed successfully by the recipient if the supervisor does not agree to cooperate. The roles of the recipient and the supervisor may be exchanged in this scheme. The scheme is flexible and feasible because the sequence of manipulation of the sender and the supervisor may be exchanged and only simple unitary transformation is included.     

Unitary Transformation in kq Representation

In this paper, we discuss the unitary transformation induced by Z₆ rotations of noncommutative space on the states |k,q,s>, which plays a key role in construction for noncommutative solitons T²/Z₆ by GHS method. As a result, we prove a well-known ``Gauss Sum' formula in the number theory through a concise way.     

Controlled Quantum Teleportation of a One-Particle Unknown State via a Three-Particle Entangled State

A kind of three-particle entangled state is applied as quantum channel of the controlled quantum teleportation of a one-particle unknown state. The one-particle unknown state is transmitted from the sender to the recipient under the control of the supervisor. After the sender makes Bell-state measurement and the supervisor performs von Neumann measurement, the recipient carries out unitary transformation on his own particle depending on classical information from the sender and the supervisor. The teleportation cannot be completed successfully by the recipient if the supervisor does not agree to cooperate. The roles of the recipient and the supervisor may be exchanged in this scheme. The scheme is flexible and feasible because the sequence of manipulation of the sender and the supervisor may be exchanged and only simple unitary transformation is included.     

Probabilistic Teleportation of an Arbitrary Two-Particle State and Its Quantum Circuits

Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on 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.     

二粒子纠缠态(EPR对)的量子隐形传送

采用三粒子最大纠缠态作辅助量子信道,定义出能被Alice作联合测量的四个特殊的"GHZ"态,Bob实施简单操作,两粒子纠缠态(EPR对)的量子隐形传递顺利达成.     

任意 n 粒子纠缠态的概率传送及其量子逻辑线路

采用n对两粒子非最大纠缠态作为量子通道,使用纠缠交换的方法实现了n粒子任意纠缠态的概率隐形传送。在传输过程中,发送者Alice对自己所拥有的粒子进行贝尔基测量,并将测量结果通过经典通道通知远方的接收者Bob,Bob根据所获取的信息对他的粒子实行相应的幺正变换以恢复原始的粒子信息态,从而成功实现隐形传送。该方案将所有参与传送的粒子划分为n个单元,将对n 1个粒子在2n 1维基下的复杂联合幺正操作分解为n次类似的重复操作,每次重复都是对两个粒子在四维基下的简单操作,大大降低了实验实现的难度。设计了n粒子量子态概率传送的量子逻辑线路,并对每组重复操作的单元线路做了提取。传送成功的总概率为2n∏ni=1ci2。     

Teleportation of Atomic States in a Vacuum-Induced Environment

We present a scheme for teleporting atomic state through a dissipative quantum channel induced by spontaneous emission and investigate the destructive effect of the atomic decay on the success probability and the fidelity of teleportation associated to different channels. It is found that there exists an optimal channel to realize faithful teleportation.     

Local Unitary Invariants for Multipartite Quantum Systems

We present an approach of constructing invariants under local unitary transformations for multipartite quantum systems. The invariants constructed in this way can be complement to that in [Science 340 (2013) 1205-1208]. Detailed examples are given to compute such invariant in detail. It is shown that these invariants can be used to detect the local unitary equivalence of degenerated quantum states.     

多控制者下的双向量子隐形传态

提出了一种多控制者的双向量子隐形传态方案。在该理论方案中有三个控制者协助通信,纠缠资源为最大七粒子纠缠态,其中通信者Alice和Bob以及三个控制者预先秘密共享最大七粒子纠缠态以构建量子信道。三个控制者的参与提高了通信的安全性,同时也避免了执行三粒子联合测量的复杂性。在通信过程中,首先Bob对自己密享的粒子执行酉操作,接着通信方各自对自己手中的粒子执行Bell基测量。假如控制者同意双方通信,便对自己手中的粒子执行单粒子测量并将测量结果通过经典信道传输给通信者。通信方分别结合控制者所公布的测量结果做相应的酉操作,这样便能完美地实现双向量子控制隐形传态。     

通过幺正操作传送未知两个三能级粒子纠缠态

我们提出一个把未知的两个三能级粒子纠缠态传送给两个接收者的方案,该方案使用一个未知的五个三能级粒子纠缠态作为量子通道。必须指出该方案能够推广到传送未知的N个三能级粒子纠缠态给M个接收者的情况,使用的是未知(N.M 1)个三能级粒子纠缠态作为量子通道。在传送过程中,需要执行适当的幺正操作和(N.M 1)次独立测量,而且该方案不涉及Bell态测量。     

Quantum Teleportation of Tripartite Arbitrary State via W State

A scheme of teleportation of a tripartite state via W state is suggested. The W state serves as quantum channels. Standard Bell-state measurements and Von Neumann measurements are performed. After the sender operates the measurements and informs the receiver her results＇ he can reconstruct the original state by the corresponding unitary transformation. The probability of the successful teleportation is also obtained.     

Quantum Teleportation of Tripartite Arbitrary State via W State

A scheme of teleportation of a tripartite state via W state is suggested. The W state serves as quantum channels. Standard Bell-state measurements and Von Neumann measurements are performed. After the sender operates the measurements and informs the receiver her results, he can reconstruct the original state by the corresponding unitary transformation. The probability of the successful teleportation is also obtained.