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Register a new userRepeatable classical one-time-pad crypto-system with quantum mechanics
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Added by
Gui-Lu Long Prof Dr
Publication date
2019
fields
Physics
and research's language is
English
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Classical one-time-pad key can only be used once. We show in this Letter that with quantum mechanical information media classical one-time-pad key can be repeatedly used. We propose a specific realization using single photons. The reason why quantum mechanics can make the classical one-time-pad key repeatable is that quantum states can not be cloned and eavesdropping can be detected by the legitimate users. This represents a significant difference between classical cryptography and quantum cryptography and provides a new tool in designing quantum communication protocols and flexibility in practical applications. Note added: This work was submitted to PRL as LU9745 on 29 July 2004, and the decision was returned on 11 November 2004, which advised us to resubmit to some specialized journal, probably, PRA, after revision. We publish it here in memory of Prof. Fu-Guo Deng (1975.11.12-2019.1.18), from Beijing Normal University, who died on Jan 18, 2019 after two years heroic fight with pancreatic cancer. In this work, we designed a protocol to repeatedly use a classical one-time-pad key to transmit ciphertext using single photon states. The essential idea was proposed in November 1982, by Charles H. Bennett, Gilles Brassard, Seth Breidbart, which was rejected by Fifteenth Annual ACM Symposium on Theory of Computing, and remained unpublished until 2014, when they published the article, Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP, Natural Computing (2014) 13:453-458, DOI 10.1007/s11047-014-9453-6. We worked out this idea independently. This work has not been published, and was in cooperated into quant-ph 706.3791 (Kai Wen, Fu Guo Deng, Gui Lu Long, Secure Reusable Base-String in Quantum Key Distribution), and quant-ph 0711.1642 (Kai Wen, Fu-Guo Deng, Gui Lu Long, Reusable Vernam Cipher with Quantum Media).
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We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while quantum systems can be considered the ones where the internal dynamics cannot be accessed at all. As information entropy can be used to characterize how much the state of the whole system identifies the state of its parts, classical systems can have arbitrarily small information entropy while quantum systems cannot. This provides insights that allow us to understand the analogies and differences between the two theories.
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Out-of-time-order correlator (OTOC) $langle [x(t),p]^2 rangle $ in an inverted harmonic oscillator (IHO) in one-dimensional quantum mechanics exhibits remarkable properties. The quantum Lyapunov exponent computed through the OTOC precisely agrees with the classical one. Besides, it does not show any quantum fluctuations for arbitrary states. Hence, the OTOC may be regarded as ideal indicators of the butterfly effect in the IHO. Since IHOs are ubiquitous in physics, these properties of the OTOCs might be seen in various situations too. In order to clarify this point, as a first step, we investigate the OTOCs in one dimensional quantum mechanics with polynomial potentials, which exhibit butterfly effects around the peak of the potential in classical mechanics. We find two situations in which the OTOCs show exponential growths reproducing the classical Lyapunov exponent of the peak. The first one, which is obvious, is using suitably localized states near the peak and the second one is taking a double scaling limit akin to the non-critical string theories.
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