Quantum information isomorphism: Beyond the dilemma of the Scylla of ontology and the Charybdis of instrumentalism

IBM Journal of Research and Development, Jan 2004 by Horodecki, R, Horodecki, M, Horodecki, P

In order to deal most effectively with the unanalyzable quantum whole, the Copenhagen interpretation takes as a "frame of reference" the preparation parameters and outcomes of measurements. It represents a passive, Ptolemaic-like instrumentalism directly related to "what we see in the sky," i.e., to the "surface" of reality. However, the notion of quantum information leads to an active, Copernican-like realism which involves an (intrinsic) ordering principle and the view that the quantum whole is analyzable. It is then possible to consider subsystems as localized in space, controlled individually, and communicated. This makes it natural to treat quantum information (quantum states) not merely as knowledge. Moreover, it involves complementarity between local and nonlocal information. To avoid the dilemma between the Scylla of ontology and the Charybdis of instrumentalism, we propose the concept of quantum information isomorphism, according to which the quantum description of nature is isomorphic to nature itself. By definition it is not just one-to-one mapping, but it preserves the full structure of nature. In particular, it allows the treatment of the wave function of isomorphic images of quantum systems in the laboratory, implying that quantum information is indeed carried by these quantum systems.

Introduction

In science many entangled paths lead to truth about nature. On one of them, we met Charles Bennett-a co-discoverer of the quantum information phenomena that have had a decisive influence on the development of quantum information theory [1-6]. During a visit several years ago to the IBM Thomas J. Watson Research Center, we got to know him as a renaissance man and a stimulating personality. It was a great pleasure for one of us (R. H.) to participate in the May 2003 IBM symposium commemorating Charles's sixtieth birthday.

The purpose of this paper is to point out that the quantum information revolution has had a considerable influence on our thinking about quantum formalism and its relation to physical reality. Quantum information theory (QIT) is a new approach that has a significant advantage-it allows us to ask new questions that would not be thought of in the old paradigm. This new way of thinking is more fruitful not only from a pragmatic point of view: We hope it will also lead to a new physical view of nature, as did the Copernican scheme. Although that scheme was initially conceived as only a change of reference frame, it led to the discovery of new laws of gravitation governing planetary motion.

The phrase "interpretation of quantum mechanics" has been associated with the interpretation of quantum measurements, commonly referred to as "the measurement problem." After decades, the discussions of this problem have become less and less fruitful and more and more tiresome-mainly because of a lack of connection with experimental results. The Copenhagen interpretation prevailed primarily because it was minimal. Now we ask, "Is it of use to undertake any new interpretational effort?" We believe it is still an important task. The goal of such an effort would be not to solve the measurement problem, but to provide a fresh view of quantum mechanics based on the new questions that are being asked within QIT. And on the other hand, one would hope to find an interpretation that would aid in the search for a deeper ordering principle of quantum mechanics. QIT provides a powerful notion of quantum information, which can be regarded as a new guiding principle in the current interpretive chaos, and thus as an alternative to the current principle of minimality of the Copenhagen interpretation.

Ptolemaic-like instrumentalism and Copernican-like realism in the description of quantum phenomena

There are historical reasons why an instrumental (Copenhagen) interpretation does not explicitly involve quantum entanglement at the root of the quantum formalism. However, we know that entanglement is a physical property of a compound quantum-mechanical system, and it cannot be ignored in the building of any consistent interpretation.

The other, even deeper, reason why the Copenhagen interpretation is now inefficient is that there previously existed no notion of quantum information. Information was treated only in classical terms, as knowledge rather than as a property of a physical system. In fact, the heart of this interpretation is a passive, Ptolemaic paradigm (Figure 1), taking as its reference frame the preparation parameters and outcomes of measurements, that is, the "surface" of reality.

This is similar to the Ptolemaic description that pertains directly to what we can see in the sky. However, while looking at the sky it is hard to perceive the order of planetary orbits that Copernicus proposed. The Ptolemaic description was artificial, as was known even in the time of Copernicus. At the Cracovian Academy, where Copernicus learned the Ptolemaic description, the lecturers giving the course on astronomy criticized the Ptolemaic approach.