Sequential Implementation of Global Quantum Operations

TL;DR

This paper investigates whether complex quantum operations can be implemented sequentially with limited interactions, finding that genuine entangling operations generally cannot, but some quantum information tasks can be performed sequentially.

Contribution

It proves the impossibility of sequential decompositions for genuine entangling operations and identifies specific quantum tasks that can be executed sequentially.

Findings

Sequential decompositions are impossible for genuine entangling operations.

Certain quantum information tasks like error correction and cloning can be performed sequentially.

Abstract

We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.