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arXiv:1206.6323 · Journal of Quantum Information Science

Local Implementations of Non-Local Quantum Gates in Linear Entangled Channel

Debashis Saha, Sanket Nandan, Prasanta K. Panigrahi

Published Jan 1, 2014• 9 citations
arXivHTMLPDF

Abstract

In this paper, we demonstrate n-party controlled unitary gate implementations locally on arbitrary remote state through linear entangled channel where control parties share entanglement with the adjacent control parties and only one of them shares entanglement with the target party. In such a network, we describe the protocol of simultaneous implementation of controlled-Hermitian gate starting from three party scenarios. We also explicate the implementation of three party controlled-Unitary gates, a generalized form of Toffoli gate and subsequently generalize the protocol for n-party using minimal cost.

DOI
10.4236/jqis.2014.42010

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In this paper, we demonstrate n-party controlled unitary gate implementations locally on arbitrary remote state through linear entangled channel where control parties share entanglement with the adjacent control parties and only one of them shares entanglement with the target party. In such a network, we describe the protocol of simultaneous implementation of controlled-Hermitian gate starting from three party scenarios. We also explicate the implementation of three party controlled-Unitary gates, a generalized form of Toffoli gate and subsequently generalize the protocol for n-party using minimal cost.
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.
Remote implementation of nonlocal quantum gates is one of the central tasks in quantum communication. Researchers devote much interest in remote implementation of nonlocal quantum gates via quantum entangled channel. Remote implementation protocols of two-qubit controlled-not gate, three-qubit Toffoli gate have been presented. We present two schemes for remote implementation of nonlocal Toffoli gate via partially entangled quantum channel against collective noise. The first is used to remote implementing of nonlocal Toffoli gate via partially entangled channel against collective-dephasing noise, and the second is used to remote implementing of nonlocal Toffoli gate against collective-rotation noise. The schemes are tolerant of collective-dephasing noise and collective-rotating noise. The agents can implement the Toffoli gate nonlocally with partially entangled quantum channel by introducing an auxiliary qubit and performing general evolution. The schemes are more convenient in application since they only requires partially entangled quantum states for nonlocal implementation of quantum operations.
We propose some protocols to implement various classes of bipartite unitary operations on two remote parties with the help of repeater nodes in-between. We also present a protocol to implement a single-qubit unitary with parameters determined by a remote party with the help of up to three repeater nodes. It is assumed that the neighboring nodes are connected by noisy photonic channels, and the local gates can be performed quite accurately, while the decoherence of memories is significant. A unitary is often a part of a larger computation or communication task in a quantum network, and to reduce the amount of decoherence in other systems of the network, we focus on the goal of saving the total time for implementing a unitary including the time for entanglement preparation. We review some previously studied protocols that implement bipartite unitaries using local operations and classical communication and prior shared entanglement, and apply them to the situation with repeater nodes without prior entanglement. We find that the protocols using piecewise entanglement between neighboring nodes often require less total time compared to preparing entanglement between the two end nodes first and then performing the previously known protocols. For a generic bipartite unitary, as the number of repeater nodes increases, the total time could approach the time cost for direct signal transfer from one end node to the other. We also prove some lower bounds of the total time when there are a small number of repeater nodes. The application to position-based cryptography is discussed.
Abstract In distributed quantum computation, quantum remote-controlled gates are used frequently and applied on separate nodes or subsystems of a network. One of the universal and well-known controlled gates is the n-qubit controlled-NOT gate, especially Toffoli gate for the case of three qubits, which are frequently used to synthesize quantum circuits. In this paper, we considered a more general case, an n-qubit controlled-U gate, and present a general protocol for implementing these gates remotely with minimum required resources. Then, the proposed method is applied to implement a Toffoli gate in bipartite and tripartite systems. In this method, we considered cases in which a group of qubits belongs to one subsystem of the network. Then, we improved its consumption resources.
Quantum gate teleportation enables the implementation of nonlocal quantum operations without direct interactions between distant nodes. We propose an efficient protocol for implementing arbitrary controlled-unitary (CU) gates acting on two spatially separated parties via indefinite causal order (ICO). By establishing a maximally entanglement between two remote nodes and coherently superposing orders of single-qubit gates, our protocol circumvents the drawback of complex local two-qubit operations. This ICO-based approach enables full programmability of CU gates by adjusting the inherent single-qubit operations, offering advantages over conventional fixed causal-order methods in terms of reduced circuit complexity and improved experimental flexibility. Furthermore, we develop an optical construction to implement the polarization CU gate using a stable and reciprocal Sagnac interferometer. Our work establishes a practical framework for scalable distributed quantum computation with flexible operations.
We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate (QCPG) operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.