Security of device-independent quantum key distribution via monogamy relations from multipartite information causality

TL;DR

It is demonstrated that the IC is enough to ensure DI security on quantum key distribution (QKD) protocols, and it is demonstrated that the original bipartite formulation of IC fails to imply monogamy relations and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.

Abstract

Beyond the foundational significance, the problem of bounding nonlocal correlations by reasonable physical principles has meaningful practical consequences, particularly for device-independent (DI) cryptographic security. In this work, we advance in this direction, demonstrating that the IC is enough to ensure DI security on quantum key distribution (QKD) protocols. Security is proven for a range of theoretically quantum-attainable parameters against individual attacks by a potentially post-quantum eavesdropper. This result follows as a consequence of a strong form of monogamy of Bell's inequality violations, which we have proven to be implied by the recently proposed multipartite formulation for IC. Additionally, we demonstrated that the original bipartite formulation of IC fails to imply monogamy relations and hence, ensure security of DIQKD, thus stressing the necessity of the multipartite framework.

Figures (3)

• Figure 1: The graphic depicts the causal structure represented as a Directed Acyclic Graph (DAG) associated with the communication task for the multipartite $\mathcal{IC}$ criterion \ref{['eq:multipartite_IC']}, entailing $N-1$ senders and a receiver. The parties have access to a pre-shared entangled quantum state $\rho$ (green square). The senders $\{\mathcal{A}_k\}^{N-1}_{k=1}$ receive inputs $\{\{X^k_j\}^n_{j=1}\}^{N-1}_{k= 1}$ (blue disks), and transmit messages $\{M_k\}^{N-1}_{k=1}$ (pink disks) through binary-symmetric noisy classical channels with parameters $\{\epsilon_k\}^{N}_{k=1}$, to the receiver $\mathcal{B}$, respectively. Upon receiving the $N-1$ potentially noisy messages $\{M'_{k}\}^{N-1}_{k=1}$, the receiver computes guess $G_j$ (purple disk) about a joint function $f_j(\{X^k_j\}^{N-1}_{k= 1})$, based on a randomly selected input $j\in \{1,\ldots n\}$ (green disk).
• Figure 2: Wiring procedure that takes tripartite correlations $p(a,b,e|x,y,z)$ and produces a bipartite effective one $p_{eff}(a',b'|x',y')$.
• Figure 3: A plot of the maximum value of the CHSH functional $\beta(\mathcal{B},\mathcal{E})$ implied by the monogamy relations (of the form \ref{['eq:monogamy_T']}) considered in this work, against the CHSH functional $\beta(\mathcal{A},\mathcal{B})\in[1/2,1]$. The dashed and solid black lines represent the monogamy relations implied by the no-signaling condition \ref{['eq:monogamy_ns']} and quantum theory \ref{['eq:monogamy_q']}, respectively. The solid blue line represents monogamy relation implied by the bipartite $\mathcal{IC}$ criteria \ref{['eq:firstICnoisy']},\ref{['eq:recentIC']} taking into account all possible wiring of the form \ref{['eq:wiring']}. The solid orange line represents the monogamy relation implied by the tripartite $\mathcal{IC}$ criterion \ref{['eq:tripartite_IC']}. Finally, the solid gray line exhibits the security condition \ref{['eq:sec_mono']} for DIQKD. Notice that, in contrast to the bipartite criterion, the tripartite $\mathcal{IC}$ criterion implies a non-trivial monogamy relation for $\beta (\mathcal{A}, \mathcal{B}) \in [0.8333,\beta_Q=\frac{1}{2}(1+\frac{1}{\sqrt{2}})]$, and ensures security of DIQKD for $\beta (\mathcal{A}, \mathcal{B}) \in [0.8471,\beta_Q]$.

Theorems & Definitions (1)

• Lemma 1