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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Unselected quantum information as an effective tool for quantum cryptography

Сыч Денис Васильевич, B. A. Grishanin, Victor N. Zadkov

Published Feb 3, 2004• 0 citations
Publisher

Abstract

A novel quantum key distribution (QKD) protocol, based on all unselected states of a quantum system, which set the alphabet with continuous set of letters, is proposed. Employing all states of the Hilbert space leads to the maximal quantum uncertainty of transmitted states and therefore an eavesdropper receives the minimal amount of information. For the case of two-dimensional Hilbert space, our protocol allows secure transmission at the error rate higher than that one for the BB84-protocol and comparable with the characteristics of the best known QKD-protocols. However, with increasing the dimensionality of the Hilbert space the critical error rate for our protocol increases and in the limit of infinite-dimensional space the protocol becomes non-threshold.

DOI
10.1117/12.505033

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A novel quantum key distribution (QKD) protocol, based on all unselected states of a quantum system, which set the alphabet with continuous set of letters, is proposed. Employing all states of the Hilbert space leads to the maximal quantum uncertainty of transmitted states and therefore an eavesdropper receives the minimal amount of information. For the case of two-dimensional Hilbert space, our protocol allows secure transmission at the error rate higher than that one for the BB84-protocol and comparable with the characteristics of the best known QKD-protocols. However, with increasing the dimensionality of the Hilbert space the critical error rate for our protocol increases and in the limit of infinite-dimensional space the protocol becomes non-threshold.
A novel quantum key distribution protocol (QKD) based on all unselected states of a quantum sys- tem that set the alphabet with a continuous set of letters is proposed. Employing all states of the Hilbert space leads to a maximum quantum uncertainty of transmitted states, and, therefore, an eavesdropper receives the minimum amount of information. For the case of a two-dimensional Hilbert space, our protocol allows secure transmission at an error rate better than that for the BB84-protocol and is comparable with the characteristics of the best known QKD protocols. However, with increasing the dimensionality of the Hilbert space, the critical error rate for our protocol increases and, in the limit of infinite-dimensional space, the protocol becomes non- threshold.
We present the scheme of compatible quantum information analysis of the quantum key distribution (QKD) protocols, which give answers to the following questions: is it possible to improve the quantum bit error rate (QBER) of the 6-state protocol by employing more states, up to infinity, and can we essentially improve the QBER if the multidimensional Hilbert space with dimensionality more than 3 is used? Also, a novel quantum key distribution (QKD) protocol, based on all unselected states of a quantum system, which set the alphabet with continuous set of letters, is proposed. Employing all states of the Hilbert space leads to the maximal quantum uncertainty of transmitted states and therefore an eavesdropper receives the minimal amount of information. For the case of two-dimensional Hilbert space, our protocol allows secure transmission at the error rate higher than that one for the BB84-protocol and comparable with the characteristics of the best known QKD-protocols. However, with increasing the dimensionality of the Hilbert space the critical error rate for our protocol increases and in the limit of infinite-dimensional space the protocol becomes non-threshold.
Like all of quantum information theory, quantum cryptography is traditionally based on two-level quantum systems. In this paper, a protocol for quantum key distribution based on higher-dimensional systems is presented. An experimental realization using an interferometric setup is also proposed. Analyzing this protocol from the practical side, one finds an increased key creation rate while keeping the initial laser pulse rate constant. Analyzing it for the case of intercept/resend eavesdropping strategy, an increased error rate is found compared to two-dimensional systems, hence an advantage for the legitimate users to detect an eavesdropper.
We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N -dimensional Hilbert space. In our protocol, we adopt asymmetric measurement scheme resulting in an efficiency higher than previous protocols and a generalized Bell inequality [Phys. Rev. Lett. 92 (2004) 130404] is employed to detect the presence of an eavesdropper Eve. We also derive the information gained by a potential eavesdropper Eve applying a cloning-based attack and the maximal error rate which measures the robustness of the protocol. The result shows that the security of our scheme increases with the dimension N .
Quantum cryptography is a well-stated field within quantum applications where quantum information is used to set secure communications, authentication, and secret keys. Now used in quantum devices with those purposes, particularly Quantum Key Distribution (QKD), which proposes a secret key between two parties free of effective eavesdropping, at least at a higher level than classical cryptography. The best-known quantum protocol to securely share a secret key is the BB84 one. Other protocols have been proposed as adaptations of it. Most of them are based on the quantum indeterminacy for non-orthogonal quantum states. Their security is commonly based on the large length of the key. In the current work, a BB84-like procedure for QKD based on double quantum teleportation allows the sharing of the key statement using several parties. Thus, the quantum bits of information are assembled among three parties via entanglement, instead of travelling through a unique quantum channel as in the traditional protocol. Asymmetry in the double teleportation plus post-measurement retains the secrecy in the process. Despite requiring more complex control and resources, the procedure dramatically reduces the probability of success for an eavesdropper under individual attacks, because of the ignorance of the processing times in the procedure. Quantum Bit Error Rate remains in the acceptable threshold and it becomes configurable. The article depicts the double quantum teleportation procedure, the associated control to introduce the QKD scheme, the analysis of individual attacks performed by an eavesdropper, and a brief comparison with other protocols.