Continuous-Variable Quantum Computing and its Applications to Cryptography
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Continuous-Variable Quantum Computing and its Applications to Cryptography Do Ngoc Diep1,2 · Koji Nagata3
· Renata Wong4
Received: 11 June 2020 / Accepted: 8 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a quantum cryptography based on an algorithm for determining a function using continuous-variable entangled states. The security of our cryptography is based on the Ekert 1991 protocol, which uses an entangled state. Eavesdropping destroys the entangled state. Alice selects a secret function from the very large number of possible function types. Bob’s aim is to determine the selected function (a key) without an eavesdropper learning it. In order for both Alice and Bob to be able to select the same function classically, in the worst case Bob requires a very large number of queries to Alice. In the quantum case however, Bob requires just a single query. By measuring the single entangled state, which is sent to him by Alice, Bob can obtain the function that Alice has selected. This quantum key distribution method is faster than the very large number of classical queries that would be required in the classical case. Keywords Quantum cryptography and communication security · Quantum communication · Quantum algorithms · Quantum computation · Formalism
1 Introduction Continuous-variable quantum information is the area of quantum information science that makes use of physical observables, such as the strength of an electromagnetic field, whose numerical values belong to continuous intervals. In 1998, Braunstein studied error correction for continuous quantum variables [1] and quantum error correction for communication with linear optics [2]. In 1999, Lloyd and Braunstein proposed quantum computation
Koji Nagata
ko mi [email protected] 1
TIMAS, Thang Long University, Nghiem Xuan Yem Road, Hoang Mai District, Hanoi, Vietnam
2
Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Cau Giay District, Hanoi, Vietnam
3
Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea
4
Department of Computer Science and Technology, Nanjing University, 163 Xianlin Road, 210093, Nanjing, Jiangsu, China
International Journal of Theoretical Physics
over continuous variables [3]. The same year, Ralph considered continuous-variable quantum cryptography [4]. In 2000, Hillery discussed quantum cryptography with squeezed states [5], while Reid described quantum cryptography with a predetermined key using continuous-variable Einstein-Podolsky-Rosen correlations [6]. In 2001, secure quantum key distribution using squeezed states was studied by Gottesman and Preskill [7]. A year later, continuous-variable quantum cryptography using coherent states was first proposed by Grosshans and Grangier [8]. Efficient classical simulation of continuous-variable quantum information processes has been studied by Bartlett et al. [9]. More recently, there has been developement with regards to applying quantum algorithms to quantum cryptography. In 2015,
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