Impossibility via W states and feasibility via W-like states for perfect quantum teleportation

TL;DR

This paper investigates perfect two-party quantum teleportation of an unknown qubit using different 3-qubit shared states. It proves that the standard W state cannot realize perfect teleportation for an arbitrary input, while the GHZ state and a modified W-like state can, by ensuring Bob’s subsystem is maximally entangled with Alice’s. A concrete W-like state is constructed with a matching measurement basis and Bob’s unitary set (Pauli-type), establishing a feasible route to perfect teleportation beyond GHZ. An alternative approach using a global unitary on the sender’s side shows success for GHZ, but generally fails for W and most W-like instances, except in special parameter regimes. The results are reinforced by an entanglement-entropy analysis, which ties the feasibility to whether Bob’s reduced state is maximally mixed, offering a clear resource-theory perspective on multipartite teleportation.

Abstract

We examine the two-party perfect quantum teleportation of an unknown 1-qubit state in the case of sharing various 3-qubit entangled states between a sender and a receiver: GHZ state, W state and W-like state. We give an impossibility proof that the W state cannot be used as the sharing state to realize the perfect quantum teleportation for transmitting an arbitrary 1-qubit state, in sharp contrast with the GHZ state which is well known to realize the perfect quantum transportation. Moreover, we give a procedure of obtaining a modified entangled state which we call the W-like state to achieve the perfect quantum transportation under a prescribed measurement basis.

Figures (2)

• Figure 1: The initial state of Alice and Bob before the operation $\hat{U}_{23}$
• Figure 2: The initial state of Alice and Bob after the operation $\hat{U}_{23}$