A note on the entangling properties of the C-SIGN and related quantum gates

TL;DR

This paper proves that applying an essential n-qubit C-SIGN or similar quantum gate to a state that is not initially entangled across all qubits results in a state that is entangled across every bipartition, highlighting the entangling power of these gates.

Contribution

It establishes that essential C-SIGN and related gates inevitably produce global entanglement in non-entangled states, emphasizing their fundamental role in quantum information processing.

Findings

Essential C-SIGN gates create everywhere entangled states from non-entangled inputs.

The entangling property applies to gates not equivalent to smaller arity or identity.

The result clarifies the fundamental entangling power of these quantum gates.

Abstract

We show that any essential application of an $n$-qubit C-SIGN or related quantum gate $G$ leaves its qubits everywhere entangled, provided they were not everywhere entangled to begin with. By ``essential'' we mean roughly that $G$ is not equivalent to a similar gate of smaller arity (or to the identity) when applied to the same input state. By ``everywhere entangled'' we mean that the state is not separable with respect to any bipartition of the qubits.