Southwest Quantum Information and Technology

Symmetric Extendability of Quantum States and the Extreme Limits of Quantum Key Distribution

Presenting Author: Sumeet Khatri, Louisiana State University

We investigate QKD protocols with two-way communication that are based on the quantum phase of the well-known BB84 and six-state protocols. The quantum phase consists of the source sending quantum signals to the receiver, who measures them, leaving only classical data on both sides. Our goal is to find the highest value of the quantum bit error rate $Q$ for which two-way classical post-processing protocols on the data can create secret keys. Using the BB84 quantum phase, such protocols currently exist for $Q\leq\frac{1}{5}$. On the other hand, for $Q\geq\frac{1}{4}$ no such protocol can exist as the observed data is compatible with an intercept-resend channel. This leaves the interesting question of whether successful protocols exist in the gap $\frac{1}{5}\leq Q\leq\frac{1}{4}$. For the six-state protocol, the corresponding gap is known to be $\frac{5-\sqrt{5}}{10}\leq Q\leq\frac{1}{3}$. The current lower bounds have previously been shown to come from the symmetric extendability of the underlying quantum state shared between Alice and Bob after a two-way protocol called advantage distillation. Our work looks more generally at two-way post-processing protocols within the gap and asks the question of symmetric extendability of the states after them, for if they are symmetrically extendable then no secret key is possible. We have analytically constructed a symmetric extension throughout the gap for a particular class of protocols using a two-step procedure. Numerical analysis shows that for other arbitrary protocols the states are also symmetrically extendable throughout the gap. Moreover, for a very large percentage of protocols tested, our two-step construction works. We thus have very strong evidence to believe that there does not exist a two-way classical post-processing protocol to create a secret key beyond the current bounds, so that there is a point beyond which classical correlations of quantum origin are no longer useful in creating a secret key.

(Session 5 : Thursday from 5:00pm - 7:00pm)