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Gate teleportation using Parallel and Series entanglement distributions on arbitrary remote states

Debashis Saha, Sanket Nandan, Prasanta Kumar Panigrahi

Published Jun 27, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
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.
Quantum gate teleportation provides an approach to introduce nonlinear interactions between long-distance qubits, facilitating distributed quantum computation. We present two alternative protocols for deterministically teleporting controlled-not (cnot) and controlled-phase-flip (cpf) gates, using minimal resources---one entangled qubit (ebit) and two classical bits (cbits). Our protocols eliminate the need for local cnot gates at each party, which are typically required in the standard quantum circuit model [Eisert et al. Phys. Rev. A 62, 052317 (2000)]. Instead, by using a superposition of single-qubit gate orders, our approach makes quantum gate teleportation more experimentally feasible and flexible. Remarkably, the teleportation of the cpf gate and other two-qubit controlled unitary gates can be achieved by adjusting inherent single-qubit operations, reducing the need for single-qubit gates in cnot-based constructions. Additionally, we develop two optical architectures for the teleportation of these gates. The polarization-based and transverse spatial-based setups show that this approach is more feasible and practical, and pave a way for a distributed quantum computing network.
Gate teleportation allows us to implement a nonlocal unitary using local operations, classical communication (LOCC), and a shared entangled state. Known deterministic teleportation protocols consume at least one full ebit and achieve optimal entanglement consumption only for Clifford gates. Here, we present a deterministic LOCC protocol for implementing the two-qubit controlled-phase gate Uφ=diag(1,1,1,eiφ)U_φ=\mathrm{diag}(1,1,1,e^{i φ})Uφ​=diag(1,1,1,eiφ) with φ∈[0,π]φ\in [0,π]φ∈[0,π] whose entanglement consumption is close to optimal for every φφφ. In particular, vanishing rotation angles require vanishing entanglement.
Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.
Abstract Quantum gate teleportation enables spatially separated parties to implement nonlocal quantum operations using preshared entanglement, local operations, measurement, and classical communication. Here, we present a two-branch entanglement-assisted coherent-control architecture for the deterministic remote implementation of nonlocal two-qubit gates. In this architecture, the two parties coherently select between two pairs of local unitary operations acting on their respective input qubits, a structure that can be naturally encoded through spatial-path superposition. The protocol is formulated at the operator level, allowing deterministic operation to be established independently of the input-state parametrization and making its scope explicit. For two-qubit unitary targets, we show that the deterministic branch conditions restrict the nonlocal domain of the balanced two-branch ansatz: apart from local product operations, any implementable nonlocal unitary must be locally unitarily equivalent to the CNOT/CZ class. We construct explicit CNOT and controlled- Z realizations as two representatives of this unique nonlocal equivalence class. We also introduce a photonic path-encoding and destructive branch-readout scheme in which spatial path encodes the coherent-control degree of freedom and polarization carries the computational qubits, illustrating how the proposed architecture can be physically encoded.