Wojciech Roga

Device-independent conference key agreement (DI-CKA) realizes information-theoretically secure key distribution among more than two remote parties without any assumptions on the inner workings of the devices, relying instead on the violation of Bell inequalities. While several DI-CKA protocols based on Greenberger-Horne-Zeilinger states have been proposed, it remains an open question whether W states can also be used for DI-CKA. In this study, we affirmatively answer this open question by constructing Bell inequalities that are maximally violated by W states.

Device-Independent quantum key distribution (DI-QKD) enables the distribution of secret keys over an untrusted network with uncharacterized devices1, whose security is guaranteed by certification of quantum correlations between remote, legitimate parties through violation of Bell inequalities2. However, implementations of DI-QKD protocols in practice are impeded by the detection loophole, imposing stringent detection efficiency thresholds, preventing practical realizations of DI-QKD. To overcome this limitation, the novel concept of routed Bell tests was recently introduced3,4,5. Here, we propose a DI-QKD protocol based on the routed Bell tests with only standard quantum optical tools, namely two-mode squeezed states, displacement-based measurements and on/off detectors. Fig. 1(a) illustrates this in more detail. Two honest, distant parties, Alice and Bob, each receive one mode of a two-mode squeezed state, and perform displacement-operations, D(α) and D(β_L ), on their received mode and detect it with an on/off detector with detection efficiencies η_A and η_(B_L ), where Alice has her input choices x∈{0,1}, and Bob has his input choices y∈{0,1,2}, obtaining classical outputs a,b∈{0,1}. In addition, Bob can route his mode via a switch with input z∈{S,L} towards another displacement-based measurement device with displacement operation D(β_S ), with input choices and classical outputs denoted by y ̂∈{0,1} and b ̂∈{0,1} respectively, and detection efficiency η_(B_S ), where η_(B_S )≥η_(B_L ). It is crucial that Bob’s routing choice z should not have an influence on Alice’s measurement input and outcomes. We denote (x,y,z)=(0,2,L) as key generation rounds where some rounds are used for estimating error correction cost, and others to construct their keys, and all other input combinations are used to certify their correlations. We optimize for Alice and Bob’s displacement operation D(α),D(β_S ) and D(β_L) and compute the lower bounds on the key rate using numerical optimization6, setting η_A=η_(B_L ). In Fig. 1(b), we observe that our protocol allows us to relax the detection efficiency requirements and see improved key rates against an unrouted protocol, facilitating the possibility of realizing long-distance DI-QKD in the future.

We propose a long-distance device-independent conference key agreement (DI-CKA) protocol. We use an efficient GHZ state distribution protocol based on entanglement swapping. We calculate a key rate of our protocol from violation of a multipartite Bell inequality and show that our protocol can distribute a secret key over longer distance than a direct transmission DI-CKA protocol. We also consider practical displacement-based measurement and show experimental feasibility of our protocol.