Converging State Distributions for Discrete Modulated CVQKD Protocols
- URL: http://arxiv.org/abs/2305.06484v2
- Date: Fri, 2 Jun 2023 01:59:21 GMT
- Title: Converging State Distributions for Discrete Modulated CVQKD Protocols
- Authors: Micael Andrade Dias and Francisco Marcos de Assis
- Abstract summary: We show that the loss of secret key rate quickly falls below $10-5$ as the distance increases.
By using a 256-QAM with Gauss-Hermite shaping, the loss of secret key rate quickly falls below $10-5$ as the distance increases.
- Score: 2.4366811507669124
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Consider the problem of using a finite set of coherent states to distribute
secret keys over a quantum channel. It is known that computing the exact secret
key rate in this scenario is intractable due to the infinite dimensionality of
the Hilbert spaces and usually one computes a lower bound using a Gaussian
equivalent bipartite state in the entangled based version of the protocol,
which leads to underestimating the actual protocol capability of generating
secret keys for the sake of security. Here, we define the QKD protocol's
non-Gaussianity, a function quantifying the amount of secret key rate lost due
to assuming a Gaussian model when a non-Gaussian modulation was used, and
develop relevant properties for it. We show that if the set of coherent states
is induced by a random variable approaching the AWGN channel capacity, then the
protocol's non-Gaussianity vanishes, meaning that there is no loss of secret
key rate due to the use of a Gaussian model for computing bound on the secret
key rate. The numerical results show that by using a 256-QAM with Gauss-Hermite
shaping, the loss of secret key rate quickly falls below $10^{-5}$ as the
distance increases.
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