Quantum counterfeit coin problems

AbstractThe counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only “balanced” or “tilted” information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k<N/2, Q(k,N)=O(k1/4), contrasting with the classical query complexity, Ω(klog(N/k)), that depends on N. So our quantum algorithm achieves a quartic speed-up for this problem. We do not have a matching lower bound, but we show some evidence that the upper bound is tight: any algorithm, including our algorithm, that satisfies certain properties needs Ω(k1/4) queries

Signing Perfect Currency Bonds

We propose the idea of a Quantum Cheque Scheme, a cryptographic protocol in which any legitimate client of a trusted bank can issue a cheque, that cannot be counterfeited or altered in anyway, and can be verified by a bank or any of its branches. We formally define a Quantum Cheque and present the first Unconditionally Secure Quantum Cheque Scheme and show it to be secure against any no-signaling adversary. The proposed Quantum Cheque Scheme can been perceived as the quantum analog of Electronic Data Interchange, as an alternate for current e-Payment Gateways.Comment: 6 pages, 2 figure

Brief History of Quantum Cryptography: A Personal Perspective

Quantum cryptography is the only approach to privacy ever proposed that allows two parties (who do not share a long secret key ahead of time) to communicate with provably perfect secrecy under the nose of an eavesdropper endowed with unlimited computational power and whose technology is limited by nothing but the fundamental laws of nature. This essay provides a personal historical perspective on the field. For the sake of liveliness, the style is purposely that of a spontaneous after-dinner speech.Comment: 14 pages, no figure

How to make unforgeable money in generalised probabilistic theories

We discuss the possibility of creating money that is physically impossible to counterfeit. Of course, "physically impossible" is dependent on the theory that is a faithful description of nature. Currently there are several proposals for quantum money which have their security based on the validity of quantum mechanics. In this work, we examine Wiesner's money scheme in the framework of generalised probabilistic theories. This framework is broad enough to allow for essentially any potential theory of nature, provided that it admits an operational description. We prove that under a quantifiable version of the no-cloning theorem, one can create physical money which has an exponentially small chance of being counterfeited. Our proof relies on cone programming, a natural generalisation of semidefinite programming. Moreover, we discuss some of the difficulties that arise when considering non-quantum theories.Comment: 27 pages, many diagrams. Comments welcom

Quantum Computers and Quantum Coherence

If the states of spins in solids can be created, manipulated, and measured at the single-quantum level, an entirely new form of information processing, quantum computing, will be possible. We first give an overview of quantum information processing, showing that the famous Shor speedup of integer factoring is just one of a host of important applications for qubits, including cryptography, counterfeit protection, channel capacity enhancement, distributed computing, and others. We review our proposed spin-quantum dot architecture for a quantum computer, and we indicate a variety of first generation materials, optical, and electrical measurements which should be considered. We analyze the efficiency of a two-dot device as a transmitter of quantum information via the ballistic propagation of carriers in a Fermi sea.Comment: 13 pages, latex, one eps figure. Prepared for special issue of J. Mag. Magn. Matl., "Magnetism beyond 2000". Version 2: small revisions and correction