Abstract
We consider continuous-variable quantum key distribution with discrete-alphabet encodings. In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states. In this setting, we provide a composable security analysis in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks. Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.
Highlights
Quantum key distribution (QKD) [1,2,3,4] allows two remote authenticated parties to establish a shared secret key without any assumption on the computational power of the eavesdropper, the security being based on fundamental laws of quantum mechanics, such as the no-cloning theorem [5,6]
We study the finite-size composable security of a discrete-alphabet CV-QKD protocol under the assumption of collective Gaussian attacks
This assumption is realistic because the standard model of loss and noise in optical quantum communications is the memoryless thermal-loss channel, which is dilated into a collective entangling cloner attack, i.e., a specific type of collective Gaussian attack [40]
Summary
Quantum key distribution (QKD) [1,2,3,4] allows two remote authenticated parties to establish a shared secret key without any assumption on the computational power of the eavesdropper, the security being based on fundamental laws of quantum mechanics, such as the no-cloning theorem [5,6]. [34] considered four coherent states and, later, other works studied alphabets with arbitrary number of states under pure-loss [35] and thermal-loss [36] attacks All these security proofs were limited to the asymptotic case of infinite signals exchanged by the parties. We depart from the asymptotic security assumption and study the finite-size composable security of discrete-alphabet CV-QKD protocols. This extension comes with the price of another restriction.
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