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International Journal of Quantum Information

ON THE SECURITY OF DECOHERENCE-FREE SUBSPACES AND SUBSYSTEMS FOR CLASSICAL INFORMATION CONVEYING THROUGH QUANTUM CHANNELS

Elloá B. Guedes, Francisco de Assis

Published Mar 1, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749913500226

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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.
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.
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.
Quantum cryptography is a promising way to secure communication in the era of quantum information technologies (Nx-ICT). However, ensuring the confidentiality and authenticity of quantum communication is challenging in the presence of noisy quantum channels and a lack of trust between communicating parties. Unconditional mistrustful quantum cryptography protocols address these challenges by providing security guarantees even when parties do not trust each other. This paper explores the fundamental concepts and methodologies behind unconditional mistrustful quantum cryptography protocols in Nx-ICT scenarios. We examine the theoretical underpinnings of these protocols, which are based on cryptographic techniques from quantum mechanics, such as quantum key distribution (QKD) and entanglement-based protocols. We also review the latest experimental developments and achievements in the implementation of unconditional mistrustful quantum cryptography protocols. We discuss the progress that has been made in mitigating noise-induced vulnerabilities, as noisy quantum channels are common in practical quantum communication systems. Finally, we discuss the future prospects and open research questions in this field. We emphasize the importance of continuous research to improve the efficiency, scalability, and security of unconditional mistrustful quantum cryptography protocols in the face of evolving Nx-ICT applications and advancements.
Quantum cryptography promises information theoretic security of several cryptographic primitives. Most of the proposed security proofs work in an ideal communication scenario where all messages are correctly delivered after the first attempt. However, real networks are subject to message losses and require retransmissions to cope with them. While the latter is hardly ever a problem in classical cryptography, with quantum communication copy-and-retransmit could be impossible due to the famous no-cloning theorem. In this work, we analyze some quantum cryptoschemes such as public-key encryption, authentication and quantum money, assuming that quantum messages may be lost as they travel through the communication medium. Although all these schemes are theoretically secure, we show that this degree of realism renders some protocols insecure or impractical, while others are completely unaffected. When possible, we provide mitigations such as teleportation or protocol modifications to circumvent these challenges.
The need for secrecy and security is essential in communication. Secret sharing is a conventional protocol to distribute a secret message to a group of parties, who cannot access it individually but need to cooperate in order to decode it. While several variants of this protocol have been investigated, including realizations using quantum systems, the security of quantum secret sharing schemes against eavesdroppers and dishonest participants remained unproven. Here we establish an unconditional security proof for continuous variable entanglement-based quantum secret sharing schemes, in the limit of asymptotic keys and for an arbitrary number of players, by utilizing ideas from the recently developed one-sided device-independent approach to quantum key distribution. We demonstrate the practical feasibility of our scheme, which can be implemented by Gaussian states and homodyne measurements, with no need for ideal single-photon sources or quantum memories. Our results establish quantum secret sharing as a viable and practically relevant primitive for quantum communication technologies.