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arXiv:quant-ph/0408095

Quantum gloves: Physics and Information

Nicolas Gisin

Published Aug 14, 2004• 3 citations
arXivHTMLPDF

Abstract

The slogan information is physical has been so successful that it led to some excess. Classical and quantum information can be thought of independently of any physical implementation. Pure information tasks can be realized using such abstract c- and qu-bits, but physical tasks require appropriate physical realizations of c- or qu-bits. As illustration we consider the problem of communicating chirality.

DOI
10.48550/arxiv.quant-ph/0408095

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The slogan information is physical has been so successful that it led to some excess. Classical and quantum information can be thought of independently of any physical implementation. Pure information tasks can be realized using such abstract c- and qu-bits, but physical tasks require appropriate physical realizations of c- or qu-bits. As illustration we consider the problem of communicating chirality.
Communicating a physical quantity cannot be done using information only---i.e., using abstract cbits and∕or qubits. Rather one needs appropriate physical realizations of cbits and∕or qubits. We illustrate this by considering the problem of communicating chirality. We discuss in detail the physical resources this necessitates and introduce the natural concept of quantum gloves---i.e., rotationally invariant quantum states that encode as much as possible the concept of chirality and nothing more.
“All information is physical”, the slogan advocated over many years by Rolf Landauer of IBM, has recently led to some remarkable changes in the way we view communications, computing and cryptography. By employing quantum physics, several objectives that were thought impossible in a classical world have now proven to be possible. Quantum communications links, for example, become impossible to eavesdrop without detection. Quantum computers (were they to be realized) could turn some algorithms that are labelled “difficult” for a classical machine, no matter how powerful, into ones that become “simple”. The details of what constitutes “difficult” and what “easy” are the subject of mathematical complexity theory, but an example here will illustrate the point and the impact that quantum information processors will have on all of us. The security of many forms of encryption is predicated on the difficulty of factoring large numbers. Finding the factors of a 1024-digit number would take longer than the age of the universe on a computer designed according to the laws of classical physics, and yet can be done in the blink of an eye on a quantum computer were it to have a comparable clock speed. But only if we can build one, and that's the challenge! No one has yet realized a quantum register of the necessary size, or quantum gates with the prerequisite accuracy. Yet it is worth the chase, as a quantum computer with a modest-sized register could out-perform any classical machine.
Scientific progress in physics and mathematics has led to the development of efficient technology for communicating and distributing information in the 20th century. This technology forms one of the cornerstones of information society and our global economy, which are highly reliant on secure methods to transfer and distribute information quickly. To satisfy ever-increasing demands for speed and security, encryption and communication methods are constantly improved and there is an ongoing effort to develop corresponding technology further. Classical information theory is not usually part of a physics undergraduate degree course. The theory assumes simple classical properties of physical systems and based on those a largely mathematical theory of information is established. The obtained results are independent of the chosen implementation and its physical details. However, one still has to acknowledge that information is physical, that is information carriers, senders, and receivers obey the laws of physics. The notion of quantum information comes about since it turns out that the rules of quantum mechanics violate some of the basic physics assumptions in classical information theory. The consequences of this are many, ranging from improved channel capacities, the possibility of physically secure communication protocols, to invalidating some beliefs about the security of classical communication protocols. So far the approach followed in this book was to assume idealized physical systemswhich perfectly implement qubits and then demonstrate how quantum computing algorithms can be realized using perfect qubits. Error correction and fault tolerance were only mentioned briefly.
The use of quantum mechanical signals in communication opens up the opportunity to build new communication systems that accomplishes tasks that communication with classical signals structures cannot achieve. Prominent examples are Quantum Key Distribution Protocols, which allows the generation of secret keys without computational assumptions of adversaries. Over the past decade, protocols have been developed that achieve tasks that can also be accomplished with classical signals, but the quantum version of the protocol either uses less resources, or leaks less information between the involved parties. The gap between quantum and classical can be exponential in the input size of the problems. Examples are the comparison of data, the scheduling of appointments and others. Until recently, it was thought that these protocols are of mere conceptual value, but that the quantum advantage could not be realized. We changed that by developing quantum optical versions of these abstract protocols that can run with simple laser pulses, beam-splitters and detectors. [1–3] By now the first protocols have been successfully implemented [4], showing that a quantum advantage can be realized. The next step is to find and realize protocols that have a high practical value.