Multipartite device-independent quantum key distribution using W states

TL;DR

A long-distance multipartite DI-QKD protocol with single-photon interference is proposed that enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states and opens an alternative path toward long-distance multipartite DI-QKD.

Abstract

Multipartite device-independent quantum key distribution (DI-QKD), also known as device-independent conference key agreement, enables more than two remote parties to share a common key with information-theoretic security even without trusting the devices. So far, several multipartite DI-QKD protocols have been proposed where Greenberger-Horne-Zeilinger (GHZ) states are used as multipartite entanglement. A natural question is then whether one can construct multipartite DI-QKD with the other type of multipartite entanglement. W state is of particular interest since it is intrinsically different from GHZ state and in some cases, easier to optically implement. In this paper, we show that multipartite DI-QKD is possible with W states. To this end, we construct Bell inequalities largely violated by W states, which can be used for the multipartite DI-QKD. Furthermore, we consider several different implementation scenarios. First, we analyze the minimum required detection efficiencies to extract finite amount of keys. Then we propose a long-distance multipartite DI-QKD protocol with single-photon interference and make detailed analyses with several physical implementation scenarios. We show that the protocol enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states. This study provides new insight about the relationship between multipartite entanglement and device-independent quantum information processing as well as opens an alternative path toward long-distance multipartite DI-QKD.

Figures (8)

• Figure 1: Schematics of multipartite DI-QKD using W states. $N$ parties, Alice and $\text{Bob}_i$ ($i \in \{ 1, \ldots, N-1\}$) share a common secret key. A W state is first distributed among the parties and the parties perform some measurements on the distributed W state. The parties share a common secret key based on their measurement results. (a) Direct transmission. a W state is generated locally and distributed among the parties through pure-loss channels with transmissivity $\eta$. (b) RIHT protocol. Each party locally prepares an entangled state and sends one part to a central station through a pure-loss channel with transmissivity $\eta$. A W state is distributed among the parties when single-photon interference succeeds at the central station.
• Figure 2: Key rate versus detection efficiency $\eta_e$ for the scenarios (3, 2, 2) and (4, 2, 2) where the legitimate parties perform arbitrary Pauli measurements. Blue circles show key rates of the (3, 2, 2) scenario and red triangles show key rates of the (4, 2, 2) scenario. We numerically optimize the measurement parameters $\theta_x^A, \theta_{y_1}^{B_1}, \ldots, \theta_{y_{N-1}}^{B_{N-1}}$ and the probability $p_n$ to maximize key rates.
• Figure 3: Key rate versus detection efficiency $\eta_e$ for the scenarios (3, 2, 2) and (4, 2, 2) where the legitimate parties perform the displacement-based measurements. Blue circles show key rates of the (3, 2, 2) scenario and red triangles show key rates of the (4, 2, 2) scenario. We numerically optimize the displacements $\alpha$ of all the legitimate parties and the probability $p_n$ to maximize key rates.
• Figure 4: Schematic of the RIHT protocol. Every party prepares a two-mode entangled state $\sqrt{q} \ket{00} + \sqrt{1-q} \ket{11}$ and transmits one part to a central station through a pure-loss channel with transmissivity $\eta$. The central station is composed of an interferometer $U$ with 50:50 beamsplitters and $N$ single-photon detectors. The parties distil a secret key from events where only one of the single-photon detectors detects a single photon.
• Figure 5: Key rate with the RIHT protocol versus distance $L$ for the scenario (3, 2, 2) for different values of the parameter $q$ of the entangled state which each party prepares. We use the detection efficiency $\eta_e = 1$ and the dark count probability $p_d = 10^{-6}$. Black dashed line shows key rates of a multipartite DI-QKD protocol with locally generated GHZ states.