Remote state preparation by multiple observers using a single copy of a two-qubit entangled state

TL;DR

This paper investigates how multiple Bobs can sequentially perform remote state preparation on a single entangled qubit shared with Alice, establishing bounds on the number of Bobs who can surpass classical fidelity using unsharp measurements.

Contribution

It introduces a limit of six Bobs for successful sequential remote state preparation with shared entanglement and proposes a new protocol for non-equatorial states.

Findings

Maximum of six Bobs can surpass classical fidelity with shared entanglement.

The bound decreases when remote states are shifted from equatorial to polar regions.

A new RSP protocol is introduced for non-equatorial state ensembles.

Abstract

We consider a scenario of remote state preparation (RSP) of qubits in the context of sequential network scenario. A single copy of an entangled state is shared between Alice on one side, and several Bobs on the other, who sequentially perform unsharp single-particle measurements in order to prepare a specific state. In the given scenario without any shared randomness between the various Bobs, we first determine the classical bound of fidelity for the preparation of remote states by the Bobs. We then show that there can be at most 6 number of Bobs who can sequentially and independently prepare the remote qubit state in Alice's lab with fidelity exceeding the classical bound in the presence of shared quantum correlations. The upper bound is achieved when the singlet state is initially shared between Alice and the first Bob and every Bob prepares a state chosen from the equatorial circle of the Bloch sphere. Then we introduce a new RSP protocol for non-equatorial ensemble of states. The maximum number of Bobs starts to decrease from six when either the choice of remote states is shifted from the equatorial circle towards the poles of the Bloch sphere, or when the initial state shifts towards non-maximally entangled pure and mixed states.