Ancilla-assisted sequential approximation of nonlocal unitary operations

TL;DR

This paper revisits the impossibility of sequentially implementing nonlocal unitaries with an ancilla, providing alternative proofs and developing a flexible MPO-based protocol with a new variational technique for high-fidelity implementation.

Contribution

It offers an alternative proof of the no-go theorem using operator-Schmidt decomposition and introduces the VMPO method for efficient sequential implementation of nonlocal unitaries.

Findings

Operator-Schmidt decomposition provides an alternative proof of the no-go theorem.

MPO formalism enables flexible protocols for sequential implementation.

VMPO technique efficiently characterizes nonlocal unitaries' entangling capabilities.

Abstract

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the "no-go" theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary entanglers. Despite the negative response from the "no-go" theorem, we demonstrate explicitly how the matrix-product operator(MPO) formalism provides a flexible structure to develop protocols for sequential implementation of such entanglers with an optimal fidelity. The proposed numerical technique, that we call variational matrix-product operator (VMPO), offers a computationally efficient tool for characterizing the "globalness" and entangling capabilities of nonlocal unitary operations.