利用部分纠缠的量子信道确定性地实现N→1和1→N的受控量子远程旋转

Deterministic and controlled many-to-one and one-to-many remote quantum rotations via partially entangled quantum channels

提出利用部分纠缠的量子信道确定性地实现多个发送者1个接受者和1个发送者多个接受者的受控量子远程旋转方案.首先考虑利用两个(N?M?1)粒子部分纠缠的Greenberger-Horne-Zeilinger(GHZ)态确定性地实现N个发送者在M个监控者的控制下确定性地将她们的旋转分别传给远处接受者的操作(N→1).然后考虑在一个(2K?M?1)粒子部分纠缠的Einstein-Podolsky-Rosen(EPR)-GHZ态或K个(M+2)粒子部分纠缠的GHZ态辅助下,发送者随意地将她的旋转分为N份(N<K)并在M个监控者的控制下确定性地将它们分别传给远处N个接受者的操作(1→N).方案中,量子旋转的发送者或接受者或监控者的正定算符值测量(POVM)起着关键作用,我们给出了它们的数学表式.值得注意的是,用非理想的量子信道可确定性地实现N→1或1→N的量子远程旋转.这些方案可用于量子秘密共享,量子选举等,它们具极强的保密性.

We show how a many-to-one and a one-to-many controlled remote quantum rotations（CRQRs） can be implemented deterministically and exactly by using partially entangled quantum channels. Firstly, we present a theoretical scheme for a N-to-1 CRQR, in which the quantum rotations initially distributed in N spatially separated qubits can be exactly and deterministically performed onto a remote single qubit via two partially entangled（N＋M＋1）-qubit Greenberger-Horne-Zeilinger（GHZ） states without performing any global operations. The feature of this scheme is that, apart from N senders and a receiver, M agents are included in the process as controllers. Should any one of the M agents not cooperate, the receiver could not gain the original rotations. Then, we design another scheme for implementing a 1-to-N CRIC with unit fidelity and unit probability by employing a partially entangled（2M＋N＋1）-qubit Einstein-Podolsky-Rosen（EPR）-GHZ state or K partially entangled（M＋2）-qubit GHZ states, in which a quantum rotation can be divided into N pieces（N〈K） and performed from a sender onto N distant receivers via the control of M agents in a quantum network. In these schemes, the sender’s（or the receiver’s, or the controller’s） local positive operator valued measurement（POVM） lies at the heart. We construct the required POVMs. The fact that deterministic and exact implementation of a many-to-one or a one-to-many CRQR could be realized using partially entangled quantum channel is notable. These schemes can be used to quantum secret sharing, quantum voting, and so on. They definitely have the strong security.