Quantum Versus Classical Noise Cryptography

Abstract

Quantum money is the task of verifying the validity of banknotes while ensuring that they cannot be counterfeited. Public-key quantum money allows anyone to perform verification, while the private-key setting restricts the ability to verify to banks, as in Wiesner's original scheme. The current state of technological progress means that errors are impossible to entirely suppress, hence the requirement for noise-tolerant schemes. We show for the first time how to achieve noise-tolerance in the public-key setting. Our techniques follow Aaronson and Christiano's oracle model, where we use the ideas of quantum error correction to extend their scheme: a valid banknote is now a subspace state possibly affected by noise, and verification is performed by using classical oracles to check for membership in "larger spaces." Additionally, a banknote in our scheme is minted by preparing conjugate coding states and applying a unitary that permutes the standard basis vectors.

Security of classical noise-based cryptography

“…Bob should reduce system noise as possible to guarantee the security, by cooling the receiver, for example. If he can suppress all the thermal noise, the SNR of his system will be limited by shot noise, the standard quantum limit [18]. The mean photon number transmitted in this system should be reduced to unity, because the SNR of 0 dB refers to mean photon number of unity in the shot noise limited systems.…”

Communication and Measurement with Squeezed States

“…A major problem of the quantum cryptographic schemes is that they cannot be amplified to compensate for the loss without disrupting the operation of the scheme. In [58] a new quantum cryptographic scheme is introduced that allows amplification, which greatly extends the distance over a fiber for which the scheme works.…”

“…The optimum performance ideally achievable with a measurement system is of course an important piece of design information, but more importantly I would like to assess the potential of such systems, and ways to realize them in principle, in order to explore the feasibility of developing ultrahigh precision measurement systems important in many applications, especially scientific ones. My approach [58] is based on the communication characterization of measurement discussed so far, especially in section 2.3, while adopting quantum and classical communication theory to provide the answers. Since the correspondence between communication and measurement is not exactly isomorphic, we will find that it is possible to obtain limits on the measurement accuracy, but not always possible to be assured that those limits are attainable.…”

Secure Communication Using Mesoscopic Coherent States

“…In the presence of noise, it has been shown information theoretically [2] that new shared secret keys can be created between two users. A specific protocol has been proposed by Yuen, [3,4] which has been called the YK protocol. A particular implementation of this YK protocol has been demonstrated, [5] in which detector noise is utilized and hence it is not unconditionally secure.…”