Quantum-Locked Key Distribution at Nearly the Classical Capacity Rate

Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper’s quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the $d$-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.

Figure 1

Comparison of several communication rates (in bits per channel use). Left panel: Asymptotic rates for the qudit erasure channel as a function of the erasure probability $p$. We show the QDL secret key generation rate (solid line), private capacity $P=(1-2p)\log d$ (dashed line), and classical capacity $C=(1-p)\log d$ (dash-dotted line). Right panel: Asymptotic rates for the qudit depolarizing channel as a function of the depolarizing probability $p$. We show the QDL secret key generation rate (solid line), the asymptotic secret key generation rate achieved by the protocol in [29] (we notice, incidentally, that this rate achieves the Hashing bound) (dashed line), and classical capacity (dash-dotted line).