Device Independent Quantum Key Activation

Abstract

Device-independent quantum key distribution (DIQKD) allows two distant parties to establish a secret key, based only on the observed Bell nonlocal distribution. It remains however, unclear what the minimal resources for enabling DIQKD are and how to maximize the key rate from a given distribution. In the present work, we consider a scenario where several copies of a given quantum distribution are jointly processed via a local and classical wiring operation. We find that, under few assumptions, it is possible to activate device-independent key. That is, starting from a distribution that is useless in a DIQKD protocol, we obtain a positive key rate by wiring several copies together. We coin this effect device-independent key activation. Our analysis focuses on the standard DIQKD protocol with one-way post-processing, and we resort to semi-definite programming techniques for computing lower bounds on the key rate.

Figures (4)

• Figure 1: Consider an initial quantum nonlocal distribution $P(ab|xy)$ from which no DI key can be extracted. Here we ask whether by locally wiring several copies of $P(ab|xy)$, resulting in a different nonlocal distribution $P'(ab|xy)$, it becomes possible to implement DIQKD? We show that this is possible---under few assumptions in our analysis---leading to an effect of device-independent key activation.
• Figure 2: Sketch of the two-copy XOR-wiring Forster_2009 (with flipped output bit). Alice forwards her input $x$ into both nonlocal boxes (green lines), and combines their outputs via an XOR operation, where the final output is $a=a_1 \oplus a_2$. Bob proceeds analogously.
• Figure 3: We consider nonlocal boxes as in Eq. \ref{['dist']}, parametrized by $v$ and $\alpha$, and determine whether DIQKD is possible or not. In the single-copy regime, we get a positive key rate ($r>0$) above the red dashed curve. When wiring two (three) copies of the nonlocal box, we get $r>0$ above the red solid (dash-dotted) curve. Hence we see that DI key can be activated in the yellow region. The lower set of curves consider the case where Eve performs the specific attack in Ref. Farkas_2021. In the single-copy regime, no key can be extracted ($r\leq 0$) below the green dashed curve. When wiring two (three) copies, we get $r\leq0$ below the green solid (dash-dotted) curve. Hence, certain nonlocal boxes that were initially vulnerable to the attack now become robust to it after wiring several copies.
• Figure 4: Lower bounds on the key rate $r$ (via SDP) as a function of the noise parameter $v$, for nonlocal boxes of the form in Eq. \ref{['dist']}; with $\alpha=0.01$. Wiring several copies of the nonlocal box allows for higher rates. Note that here $r$ is normalized by the number of copies used in each round.