Unconditionally superposition-robust entangled state in all multiparty quantum systems

TL;DR

This paper identifies specific multipartite entangled states that remain inseparable after superposition with any product state, revealing a fundamental robustness property in quantum entanglement.

Contribution

It introduces the concept of unconditional superposition-robust entangled states in multipartite systems, extending previous bipartite results and characterizing their properties.

Findings

Certain multipartite entangled states are always inseparable after superposition with any product state.

In bipartite systems with at least one qubit, superposition can produce product states, contrasting multipartite behavior.

Unconditional inseparability of superposition can aid in local state discrimination tasks.

Abstract

We investigate the inseparability of states generated by superposition of a multipartite pure entangled state with a product state. In particular, we identify specific multipartite entangled states that will always produce inseparability after superposition with an arbitrary completely product state. Thus, these entangled states are unconditionally superposition-robust, and we refer to this phenomenon as ``unconditional inseparability of superposition" in multipartite quantum systems. In this way, we complete the picture of unconditional inseparability of superposition which was introduced earlier for bipartite systems. We also characterize the superposition of a multipartite pure entangled state with a pure bi-separable state. However, the present analysis allows us to obtain a more general result, viz., there exists at least one pure entangled state in any multipartite Hilbert space such that its superposition with an arbitrary completely product state always yields an entangled state. On the other hand, for any bipartite pure entangled state, if at least one of the subsystems is a qubit, then it is always possible to find a suitable product state such that the superposition of the entangled state and the product state produces a product state. In this way, we find a feature of multipartite quantum systems which is in sharp contrast with that of bipartite ones. We then show how unconditional inseparability of superposition can be useful in exhibiting an indistinguishability property within the local unambiguous state discrimination problem.