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arXiv:1204.3000

Unconditional Security with Decoherence-Free Subspaces

Elloá B. Guedes, Francisco de Assis

Published Apr 13, 2012• 1 citation
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Abstract

We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.

DOI
10.48550/arxiv.1204.3000

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We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized receiver is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which these secret communications take place is equal to the Holevo-Schumacher-Westmoreland capacity of the quantum channel.
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized third part is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which such secret communications take place is equal to the ordinary capacity of a quantum channel to convey classical information. As a consequence of these results, we show how some protocols for secure communication can be simplified, reducing significantly the number of communications performed.
We show how to use decoherence-free subspaces over collective-noise quantum channels to convey classical information in perfect secrecy. We argue that codes defined over decoherence-free subspaces are codes for quantum wiretap channels in which the gain of information by a non-authorized third part is zero. We also show that if some symmetry conditions are guaranteed, the maximum rate on which such secret communications take place is equal to the ordinary capacity of a quantum channel to convey classical information. As a consequence of these results, we show how some protocols for secure communication can be simplified, reducing significantly the number of communications performed.
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Decoherence is one of the main obstacles in quantum information processing. In cryptographic scenarios, in particular, decoherence is not only responsible for the loss of the quantum properties but also for information leakage out to a wiretapper. Given that decoherence must be fought in real-world quantum communication systems, we present a scheme, using decoherence-free subspaces and subsystems, to perform secure classical communications through noisy quantum channels. Using quantum information and wiretap theories, we establish a proof of unconditional security of our scheme. We illustrate our proposal with a non-trivial example and discuss some of its impacts on already existing quantum secure message exchange protocols. Furthermore, we present some up-to-date technologies that can be used for practical implementation of the scheme proposed.
Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.
We consider the problem of semantic security via classical-quantum and quantum wiretap channels and use explicit constructions to transform a non-secure code into a semantically secure code, achieving capacity by means of biregular irreducible functions. Explicit parameters in finite regimes can be extracted from theorems. We also generalize the semantic security capacity theorem, which shows that a strongly secure code guarantees a semantically secure code with the same secrecy rate, to any quantum channel, including the infinite-dimensional and non-Gaussian ones.