Just Two Nonorthogonal Quantum States

From the perspective of quantum information theory, a system so simple as one restricted to just two nonorthogonal states can be surprisingly rich in physics. In this paper, we explore the extent of this statement through a review of three topics: (1) ``nonlocality without entanglement'' as exhibited in binary quantum communication channels, (2) the tradeoff between information gain and state disturbance for two prescribed states, and (3) the quantitative clonability of those states. Each topic in its own way quantifies the extent to which two states are ``quantum'' with respect to each other, i.e., the extent to which the two together violate some classical precept. It is suggested that even toy examples such as these hold some promise for shedding light on the foundations of quantum theory.Comment: 7 pages, no figures, requires myplenumQPH.st

Quantum Bayesianism at the Perimeter

The author summarizes the Quantum Bayesian viewpoint of quantum mechanics, developed originally by C. M. Caves, R. Schack, and himself. It is a view crucially dependent upon the tools of quantum information theory. Work at the Perimeter Institute for Theoretical Physics continues the development and is focused on the hard technical problem of a finding a good representation of quantum mechanics purely in terms of probabilities, without amplitudes or Hilbert-space operators. The best candidate representation involves a mysterious entity called a symmetric informationally complete quantum measurement. Contemplation of it gives a way of thinking of the Born Rule as an addition to the rules of probability theory, applicable when one gambles on the consequences of interactions with physical systems. The article ends by outlining some directions for future work.Comment: 6 pages, 2 figures; an abridged version of this will appear in Physics in Canada

Interview with a Quantum Bayesian

This paper collects into one place (most of) my answers to the questions Maximilian Schlosshauer posed in his interview volume, "Elegance and Enigma: The Quantum Interviews" (Springer, Frontiers Collection, 2011).Comment: 22 page

Copenhagen Interpretation Delenda Est?

This is a slightly extended version of a review of Adam Becker's book What is Real? The Unfinished Quest for the Meaning of Quantum Physics, to appear in American Journal of Physics. The key addition is the reference list.Comment: 6 page

Quantum Mechanics as Quantum Information (and only a little more)

In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part--but not all--of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding. This paper, though taking quant-ph/0106166 as its core, corrects one mistake and offers several observations beyond the previous version. In particular, I identify one element of quantum mechanics that I would not label a subjective term in the theory--it is the integer parameter D traditionally ascribed to a quantum system via its Hilbert-space dimension.Comment: 59 pages, 5 figures, 140 equations, one simple ide

On Participatory Realism

In the Philosophical Investigations, Ludwig Wittgenstein wrote, " 'I' is not the name of a person, nor 'here' of a place, .... But they are connected with names. ... [And] it is characteristic of physics not to use these words." This statement expresses the dominant way of thinking in physics: Physics is about the impersonal laws of nature; the "I" never makes an appearance in it. Since the advent of quantum theory, however, there has always been a nagging pressure to insert a first-person perspective into the heart of physics. In incarnations of lesser or greater strength, one may consider the "Copenhagen" views of Bohr, Heisenberg, and Pauli, the observer-participator view of John Wheeler, the informational interpretation of Anton Zeilinger and Caslav Brukner, the relational interpretation of Carlo Rovelli, and, most radically, the QBism of N. David Mermin, Ruediger Schack, and the present author, as acceding to the pressure. These views have lately been termed "participatory realism" to emphasize that rather than relinquishing the idea of reality (as they are often accused of), they are saying that reality is more than any third-person perspective can capture. Thus, far from instances of instrumentalism or antirealism, these views of quantum theory should be regarded as attempts to make a deep statement about the nature of reality. This paper explicates the idea for the case of QBism. As well, it highlights the influence of John Wheeler's "law without law" on QBism's formulation.Comment: 23 pages, to appear in "Information & Interaction: Eddington, Wheeler, and the Limits of Knowledge", edited by Ian T. Durham and Dean Rickles; v3 corrects word omissions from the Wheeler notebook page

Commanding Heights? : The Strength and Fragility of Business Power in Global Politics

International relations urgently needs theoretical development that takes into the account the power of non-state actors, in particular business. The present paper aims to prepare the ground for such theoretical development by analysing the political power of business along three dimensions: its instrumental, structural, and discursive power. The paper discusses the extent to which business's political power has grown in each of the dimensions. While the analysis indicates that the political power of business in general and corporate actors in particular has increased in certain areas, it also highlights limits and challenges to this power. Specifically, the paper argues that the `commanding heights' to which business allegedly has climbed are built on shaky ground. This, in turn, implies the need for any IR theory that takes non-state actors into account to develop and include a new concept of vulnerability of political power

Notwithstanding Bohr, the Reasons for QBism

Without Niels Bohr, QBism would be nothing. But QBism is not Bohr. This paper attempts to show that, despite a popular misconception, QBism is no minor tweak to Bohr's interpretation of quantum mechanics. It is something quite distinct. Along the way, we lay out three tenets of QBism in some detail: 1) The Born Rule---the foundation of what quantum theory means for QBism---is a normative statement. It is about the decision-making behavior any individual agent should strive for; it is not a descriptive "law of nature" in the usual sense. 2) All probabilities, including all quantum probabilities, are so subjective they never tell nature what to do. This includes probability-1 assignments. Quantum states thus have no "ontic hold" on the world. 3) Quantum measurement outcomes just are personal experiences for the agent gambling upon them. Particularly, quantum measurement outcomes are not, to paraphrase Bohr, instances of "irreversible amplification in devices whose design is communicable in common language suitably refined by the terminology of classical physics." Finally, an explicit comparison is given between QBism and Bohr with regard to three subjects: a) The issue of the "detached observer" as it arose in a debate between Pauli and Bohr, b) Bohr's reply to Einstein, Podolsky, and Rosen, and c) Bohr's mature notion of "quantum phenomena." At the end, we discuss how Bohr's notion of phenomena may have something to offer the philosophy of William James: A physics from which to further develop his vision of the world---call it an ontology if you will---in which "new being comes in local spots and patches."Comment: 44 pages, 1 figur

Information Gain vs. State Disturbance in Quantum Theory

The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states) without disturbing the system in a statistically detectable way. This situation is often mistakenly described as a consequence of the ``Heisenberg uncertainty principle.'' A more accurate account is that it is a unique feature of quantum phenomena that rests ultimately on the Hilbert space structure of the theory along with the fact that time evolutions for isolated systems are unitary. In this paper I explore several aspects of the ``information / disturbance principle'' in an attempt to make it firmly quantitative for both pure and mixed states. The final section briefly explores the extent to which such a principle can be taken as a foundation for unitary dynamics rather than as a consequence.Comment: 5 pages LaTeX, Extended Abstract for PhysComp96, requires pac96sty.te

Quantum Foundations in the Light of Quantum Information

This paper reports three almost trivial theorems that nevertheless appear to have significant import for quantum foundations studies. 1) A Gleason-like derivation of the quantum probability law, but based on the positive operator-valued measures as the basic notion of measurement (see also Busch, quant-ph/9909073). Of note, this theorem also works for 2-dimensional vector spaces and for vector spaces over the rational numbers, where the standard Gleason theorem fails. 2) A way of rewriting the quantum collapse rule so that it looks almost precisely identical to Bayes rule for updating probabilities in classical probability theory. And 3) a derivation of the tensor-product rule for combining quantum systems (and with it the very notion of quantum entanglement) from Gleason-like considerations for local measurements on bipartite systems along with classical communication.Comment: 45 pages, 2 figures, a very slightly different version of this paper will appear in "Proceedings of the NATO Advanced Research Workshop on Decoherence and its Implications in Quantum Computation and Information Transfer," edited by A. Goni