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Chinese Control Conference (CCC)

An efficient scheme for implementation of multi-qudit parallel control operations on distant audits in quantum network

Lipeng Xue, Min Jiang

Published Jul 1, 2015• 0 citations
Publisher

Abstract

In a quantum network, it often occurs that there are many remote nodes which should collaborate with each to perform unitary operations. Most of the time, it can be addressed by bi-direction quantum teleportation. However, it often consumes too much quantum resources. In this paper, we propose an efficient scheme for implementation of remote control of some restricted sets of multi-qudit unitary operation. Alice (controller) prepares one cat-like-state by CONT operation and sends them to the remote Bobs (BobbBob2) by sharing Bell channels respectively. Then Bobs perform a series of local operations with cat-like-state's control. By comparing with the previous work, our scheme generalizes it from one controller and one target to one controller and two targets. Our scheme does not only save the working time, but also reduces the quantum communication resources. Moreover, we also give its quantum circuit, which could lead us to a better and clearer understanding. Finally, we generalize our scheme to the case of rf-dimensional qudits.

DOI
10.1109/chicc.2015.7260685

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In a quantum network, it often occurs that there are many remote nodes which should collaborate with each to perform unitary operations. Most of the time, it can be addressed by bi-direction quantum teleportation. However, it often consumes too much quantum resources. In this paper, we propose an efficient scheme for implementation of remote control of some restricted sets of multi-qudit unitary operation. Alice (controller) prepares one cat-like-state by CONT operation and sends them to the remote Bobs (BobbBob2) by sharing Bell channels respectively. Then Bobs perform a series of local operations with cat-like-state's control. By comparing with the previous work, our scheme generalizes it from one controller and one target to one controller and two targets. Our scheme does not only save the working time, but also reduces the quantum communication resources. Moreover, we also give its quantum circuit, which could lead us to a better and clearer understanding. Finally, we generalize our scheme to the case of rf-dimensional qudits.
We present a controlled teleportation scheme for teleporting an arbitrary superposition state of an M -qudit quantum system. The scheme employs only one entangled state as quantum channel, which consists of the qudits from Alice, Bob and every agent. The quantum operations used in the teleportation process are a series of qudit Bell measurements, single-qudit projective measurements, qudit H -gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on the condition that all the agents collaborate. If any agent does not cooperate, the original state can not be fully recovered.
the purpose of this paper is to promote a butterfly quantum network coding scheme for remote state preparation of multi-qudit states. Firstly, we perform channel preparation and amplitude modulation; secondly, each sender simultaneously performs projection measurement; thirdly, both senders send measurement results as precoding information and auxiliary information to the intermediate node and the neighboring receivers respectively; fourthly, the first intermediate node performs encoding operation and sends the encoded information to both receivers via next intermediate node. Finally, by decoding the coded information with auxiliary information, two receivers perform corresponding unitary operations to recover the target multi-qudit quantum states. Compared with other schemes, our scheme can enhance the throughput and transmission efficiency of communication network for remote state preparation of multi-qudit states.
We consider two different entanglement distributions; Series and Parallel, between remote parties for imple-menting non-local controlled-Unitary gates. In parallel network, each of the control parties shares one entangled state with the target party and none of the control parties shares entanglement between them. In series network, the entanglement distribution forms a series, such that the control parties share entanglement with the adjacent control parties and only one of them shares entanglement with the target party, which is located at the end of the network. We demonstrate the protocol of simultaneous teleportation of controlled operation through both the distributions of Bell state entangled channels using local operations and classical communications (LOCC). For the parallel network, the communication cost of implementing controlled-Unitary gate on ‘n ’ qubit arbitrary state is (n − 1) ebits and 2(n − 1) cbits. Whereas, in general the series network allows controlled-Hermitian gate implementation on arbitrary state using (n−1) ebits and (n2+n−2)/2 cbits. We then explicate the protocol for complete teleportation of controlled-controlled-Unitary gate, a generalized form of Toffoli gate and subsequently generalize the protocol for ‘n’-qubit gate. Keywords: Bell state, controlled-Unitary gate, controlled-Hermitian gate, Toffoli gate, Gate 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.
In this paper, we develop an efficient and economic scheme in distributing quantum information scenario for remote partners via the control of many agents that are constrained by limited resources in a quantum communication network. Within such a network, quantum information is composed of multiple independent multi-qudit states, although each controlling agent is assigned only one controlling qudit, the agent can still control the distribution of all the quantum information. This scheme involves only generalized Bell-state measurement, single-qudit measurement and one-qudit gates, leading to a more flexible and achievable physical implementation.
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.