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Journal of the Optical Society of America B

Quantum key distribution with Einstein–Podolsky–Rosen pairs associated with weak cross-Kerr nonlinearities

Xiao‐Ming Xiu, Li Dong, Yajun Gao, X. X. Yi

Published Sep 21, 2012• 9 citations
Publisher

Abstract

We propose a protocol sharing Einstein–Podolsky–Rosen pairs based on weak cross-Kerr nonlinearities and the coherent state at first. If the security check is passed, the checked photons can be applied in the next communication process due to the application of quantum nondemolition measurements, which improves the efficiency and the security of the distribution process. As its applications, we present two quantum key distribution protocols. A random key can be transmitted using the path analyzers based on the idea of BBM92-QKD protocol. Moreover, the sender performs the parity measurement and publicizes the measurement outcomes, and thus the recipient performs computational basis measurements to obtain a deterministic key.

DOI
10.1364/josab.29.002869

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We propose a protocol sharing Einstein–Podolsky–Rosen pairs based on weak cross-Kerr nonlinearities and the coherent state at first. If the security check is passed, the checked photons can be applied in the next communication process due to the application of quantum nondemolition measurements, which improves the efficiency and the security of the distribution process. As its applications, we present two quantum key distribution protocols. A random key can be transmitted using the path analyzers based on the idea of BBM92-QKD protocol. Moreover, the sender performs the parity measurement and publicizes the measurement outcomes, and thus the recipient performs computational basis measurements to obtain a deterministic key.
We propose a quantum secure direct communication protocol via a collective noise channel, exploiting polarization-entangled Bell states and the nondemolition parity analysis based on weak cross-Kerr nonlinearities. The participant Bob, who will receive the secret information, sends one of two photons in a polarization-entangled Bell state exploiting the transmission circuit against the collective noise to the participant Alice, who will send the secret information, by the means of photon block transmission. If the first security check employing the nondemolition parity analysis is passed, the task of securely distributing the quantum channel is fulfilled. Encoding secret information on the photons sent from Bob by performing single-photon unitary transformation operations, Alice resends these photons to Bob through the transmission circuit against the collective noise. Exploiting the nondemolition parity analysis to distinguish Bell states, Bob can obtain the secret information from Alice after the second security check is passed, and the resulting Bell states can be applied to other tasks of quantum information processing. Under the condition of the secure quantum channel being confirmed, the photons that are utilized in the role of the security check can be applied to the function of secure direct communication, thus enhancing the efficiency of transmitting secret information and saving a lot of resources.
Quantum key distribution (QKD) is used in quantum cryptographic systems to exchange secret key between parties who need to communicate secretly. According to the structure of European Secoqc QKD network, a QKD protocol is proposed. Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used to exchange message bits in two remote places. Based on this idea, n + 1 EPR pairs are used as logical quantum channel (for n nodes per routing), while measurements of Bell operator are transmitted by classical channel. Random space quantum channel selection is exploited in our protocol to improve the probability of revealing Eve. Compared with traditional EPR protocol, the proposed protocol exhibits many features, which are minutely described.
Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used to generate the same sequence of random bits in two remote places. A quantum key distribution protocol based on this idea is described. The scheme exhibits the following features. (a) It does not require that Alice and Bob choose between alternative measurements, therefore improving the rate of generated bits by transmitted qubit. (b) It allows Alice and Bob to generate a key of arbitrary length using a single quantum system (three EPR pairs), instead of a long sequence of them. (c) Detecting Eve requires the comparison of fewer bits. (d) Entanglement is an essential ingredient. The scheme assumes reliable measurements of the Bell operator.
We propose a protocol of quantum privacy comparison with polarization-entangled Einstein-Podolsky-Rosen (Bell) states and the coherent states. One of two legitimate participants, Alice, prepares polarization-entangled Bell states and keeps one photon of each photon pair and sends the other photons to the third party, Charlie. Receiving the photons, Charlie performs single-photon transformation operations on them and then sends them to the other legitimate participant, Bob. Three participants adopt parity analysis method to check the distribution security of Bell states. Exploiting polarization beam splitters and nonlinear interactions mediated by the probe coherent states in Kerr media, Alice and Bob check the parities of their photons using the bases of {∣H⟩,∣V⟩}\{\ket H, \ket V\}{∣H⟩,∣V⟩} or {∣+⟩,∣−⟩}\{\ket +, \ket -\}{∣+⟩,∣−⟩}. On the basis of the parity analysis outcomes and Charlie's publicized information, they can analyze the security of the distributed quantum channel. Confirming secure distribution of the shared Bell states, two participants perform respective parity measurements on the privacy photons and own photons of Bell states, and then send the results to Charlie. According to information provided by two legitimate participants and his single-qubit transformation operations, Charlie compares the privacy information of Alice and Bob and publicizes the conclusion.
This work presents a new concept in quantum key distribution called the probabilistic quantum key distribution (PQKD) protocol, which is based on the measurement uncertainty in quantum phenomena. It allows two mutually untrusted communicants to negotiate an unpredictable key that has a randomness guaranteed by the laws of quantum mechanics. In contrast to conventional QKD (e.g., BB84) in which one communicant has to trust the other for key distribution or quantum key agreement (QKA) in which the communicants have to artificially contribute subkeys to a negotiating key, PQKD is a natural and simple method for distributing a secure random key. The communicants in the illustrated PQKD take Einstein-Podolsky-Rosen (EPR) pairs as quantum resources and then use entanglement swapping and Bell-measurements to negotiate an unpredictable key.