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Chinese Physics Letters

Quantum Remote Control of Unitary Operations on a Qubit of Pure Entangled States

Chunmei Yao

Published Feb 24, 2006• 10 citations
Publisher

Abstract

We consider the remote implementation of an arbitrary unitary operation on one qubit of a pure two-qubit entangled state with 100% efficiency via entanglement swapping in detail, then directly generalize this protocol from two-qubit to N -qubit entangled states. The overall classical information and distributed entanglement cost required for this quantum remote control protocol is less than the bi-directional quantum state teleportation method.

DOI
10.1088/0256-307x/23/3/006

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We consider the remote implementation of an arbitrary unitary operation on one qubit of a pure two-qubit entangled state with 100% efficiency via entanglement swapping in detail, then directly generalize this protocol from two-qubit to N -qubit entangled states. The overall classical information and distributed entanglement cost required for this quantum remote control protocol is less than the bi-directional quantum state teleportation method.
We consider the implementation of an arbitrary unitary operation U upon a distant quantum system. This teleportation of U can be viewed as quantum remote control. We investigate protocols that achieve this using local operations, classical communication, and shared entanglement. Lower bounds on the necessary entanglement and classical communication are determined using causality and the linearity of quantum mechanics. We examine in particular detail the resources required if the remote control is to be implemented as a classical black box. Under these circumstances, we prove that the required resources are, necessarily, those needed for implementation by bidirectional state teleportation.
We study the remote implementation of a unitary transformation on the state of a qubit. We show the existence of nontrivial protocols (i.e., using less resources than bidirectional state teleportation) that allow the perfect remote implementation of certain continuous sets of quantum operations. We prove that, up to a local change of basis, only two subsets exist that can be implemented remotely with a nontrivial protocol: Arbitrary rotations around a fixed direction $\stackrel{\ensuremath{\rightarrow}}{n}$ and a $\ensuremath{\pi}$ rotation about an arbitrary direction lying in a plane orthogonal to $\stackrel{\ensuremath{\rightarrow}}{n}.$ The former operations effectively constitute the teleportation of arbitrary angles. The overall classical information and distributed entanglement cost required for the remote implementation depends on whether it is known, a priori, in which of the two teleportable subsets the transformation belongs. If it is known, the optimal protocol consumes one e-bit of entanglement and one c-bit in each direction. If it is not known in which subset the transformation belongs, two e-bits of entanglement need to be consumed and the classical channel becomes asymmetric with two c-bits being conveyed from Alice to Bob but only one from Bob to Alice.
We present the generalized version of Wang's protocol[A.M.Wang, Phys.Rev.A 74,032317 (2006)] for the remote implementation(sometimes referred to as quantum remote control) of partially unknown quantum operations. The protocol only requires no more than half of the entanglements used in Bidirectional Quantum State Teleportation. We also propose a protocol for another form of quantum remote control. It can remotely implement a unitary operation which is a combination of the projective representations of a group. Moreover, we prove that the Schmidt rank of the entanglements cannot not be less than the number of controlled parameters of the operations, which for the first time gives a lower bound on entanglement costs in remote implementation of quantum operations.
We put forward an efficient quantum controlled teleportation scheme, in which arbitrary two-qubit state is transmitted from the sender to the remote receiver via two entangled states under the control of the supervisor. In this paper, we use the combination of one two-qubit entangled state and one three-qubit entangled state as quantum channel for achieving the transmission of unknown quantum states. We present the concrete implementation processes of this scheme. Furthermore, we calculate the successful probability and the amount of classical information of our protocol.
We propose a protocol for the remote implementation of an arbitrary two-qubit unitary operation using pre-shared entanglement. In our protocol, Bob possesses an unknown two-qubit state, while Alice implements the required operations using calibrated black-box devices. Alice does not need to know the parameters of these operations, and Bob's unknown state never leaves his laboratory. The protocol is based on the Euler decomposition of single-qubit unitary operations and the Cartan decomposition of two-qubit unitary operations. First, we construct protocols for the remote implementation of the single-qubit operation U=Rz(γ)Rx(β)Rz(α)U = R_z(γ)R_x(β)R_z(α)U=Rz​(γ)Rx​(β)Rz​(α) using pre-shared Bell states. We then construct a protocol for the two-qubit operation Rzz(θ)R_{zz}(θ)Rzz​(θ) using a single pre-shared Bell state and extend it to Rxx(θ)R_{xx}(θ)Rxx​(θ) and Ryy(θ)R_{yy}(θ)Ryy​(θ) through local unitary transformations. These elementary protocols are finally combined to implement an arbitrary two-qubit unitary operation. A third party, Charlie, determines the required decomposition and provides Alice with the corresponding black-box devices before the protocol begins. Thus, neither Alice nor Bob requires the classical description of the unitary operation.
We put forward two novel and perfect protocols for preparing an arbitrary single–particle state and simultaneously implementing a rotation operator or an arbitrary unitary operator on that particle. There are schemes for either only teleporting particles or only remotely controlling quantun particles. If one has to remotely control a prepared quantum, then he/ she has to first do remote state preparation and then executes the remote control on the prepared quantum. Both operations ware done separately on two sets of entanglements. However, this intuitive solution is inefficient because many resources are wasted. Thus, we attempt to complete both operations by sharing one three–particle Greenberger–Horne– Zeilinger (GHZ) state. Comparing our two protocols with the corresponding intuitive solutions, respectively, the results show that our protocols are more efficient than the corresponding intuitive solutions. Only Pauli operators, controlled–NOT gate, Bell–state measurement, single–qubit measurement, Einstein–Podolsky–Rosen (EPR) state and GHZ state are used in our schemes, so these schemes are easily realized in physical experiment.