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The software project kdotpy provides a Python application for simulating electronic band structures of semiconductor devices with $\mathbf{k}\cdot\mathbf{p}$ theory on a lattice. The application implements the widely used Kane model, capable of reliable predictions of transport and optical properties for a large variety of topological and non-topological materials with a zincblende crystal structure. The application automates the tedious steps of simulating band structures. The user inputs the relevant physical parameters on the command line, for example materials and dimensions of the device, magnetic field, and temperature. The program constructs the appropriate matrix Hamiltonian on a discretized lattice of spatial coordinates and diagonalizes it. The physical observables are extracted from the eigenvalues and eigenvectors and saved as output. The program is highly customizable with a large set of configuration options and material parameters., Comment: 143 pages, submission to SciPost Physics Codebases

We present overlapping top gate electrodes for the formation of gate defined lateral junctions in semiconducting layers as an alternative to the back gate/top gate combination and to the split gate configuration. The optical lithography microfabrication of the overlapping top gates is based on multiple layers of low-temperature atomic layer deposited hafnium oxide, which acts as a gate dielectric and as a robust insulating layer between two overlapping gate electrodes exhibiting a large dielectric breakdown field of > 1E9 V/m. The advantage of overlapping gates over the split gate approach is confirmed in model calculations of the electrostatics of the gate stack. The overlapping gate process is applied to Hall bar devices of mercury telluride in order to study the interaction of different quantum Hall states in the nn', np, pn and pp' regime., Comment: 7 pages, 3 figures

QBism has long recognized quantum states, POVM elements, Kraus operators, and even unitary operations to be cut from the same cloth: They express aspects of an agent's belief system concerning the consequences (for her) of actions she might take upon her external world. Such action-consequence pairs have conventionally been called "quantum measurements." The calculus of quantum theory is then viewed as an empirically motivated addition to Bayesian decision theory when brought to this notion of measurement. This radical approach has allowed QBism to eliminate conceptual problems that plague other interpretations of quantum mechanics. However, one issue has remained elusive: If a QBist does not believe in the existence of an ontic (agent-independent) dynamical variable evolving over time, why would there be any constraints on her quantum-state assignment in the absence of performing a measurement? Why would she introduce unitary or open-system quantum dynamics at all? Here, we present a representation theorem based on van Fraassen's reflection principle to answer these questions. Simply put, an agent's assignment of quantum dynamics represents her belief that a measurement action she is contemplating would not change her current odds for future gambles. A corollary to this approach is that one can make sense of "open-system dynamics" without the need to introduce an "environment with a measurement record," as is common in decoherence accounts of quantum measurement. QBism's understanding instead rests more fundamentally on an agent's beliefs about the system of interest (not system plus environment) and her judgments about measurements she might perform on that system. More broadly, this result establishes QBism's contention that measurement itself is the central concept of quantum theory and thus the framework upon which any future QBist ontology must hang., Comment: 32 pages, 2 figures. v2: Substantial additions to existing sections and a new section added. v3: Significant revisions and addition of material. To appear in Physical Review A

This paper expresses what a breath of fresh air it has been since a few phenomenological philosophers have started to engage with QBism. In service of the newfound discussion, the aim of this exposition is to lay out the structure of QBism as clearly as possible for that audience. In the process, we arrive at eight tenets for QBism: 1) A quantum state is an agent's personal judgment. 2) A quantum measurement is an agent's action upon its external world. 3) Quantum measurement outcomes are personal to the agent performing the action. 4) The quantum formalism is normative rather than descriptive. 5) Unitary evolution too expresses an agent's degrees of belief. 6) Even probability-one assignments are judgments without ontic content. 7) Subjective certainty about what an outcome will be does not negate that unperformed measurements have no outcomes. And, 8) quantum theory is a single-user theory for each of us. We then analyze the Wigner's friend thought experiment in light of the eight tenets and indicate that a still more extended analysis is potentially QBism's surest path to uncovering an ontology to go with quantum theory's normative structure. We conclude with a small discussion of how the philosophy of Maurice Merleau-Ponty may be relevant to this quest., Comment: 53 pages (but just barely), 5 figures, a version of this to appear in a Routledge volume on QBism and Phenomenology edited by H. A. Wiltsche and P. Berghofer; v2 corrects some infelicities

QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit experiment. This establishes the meaning of the Born Rule from a QBist perspective. Moreover it suggests that the best way to formulate the Born Rule for foundational discussions is with respect to an informationally complete reference device. Recent work [DeBrota, Fuchs, and Stacey, Phys. Rev. Res. 2, 013074 (2020)] has demonstrated that reference devices employing symmetric informationally complete POVMs (or SICs) achieve a minimal quantumness: They witness the irreducible difference between classical and quantum. In this paper, we attempt to answer the analogous question for real-vector-space quantum theory. While standard quantum mechanics seems to allow SICs to exist in all finite dimensions, in the case of quantum theory over the real numbers it is known that SICs do not exist in most dimensions. We therefore attempt to identify the optimal reference device in the first real dimension without a SIC (i.e., $d=4$) in hopes of better understanding the essential role of complex numbers in quantum mechanics. In contrast to their complex counterparts, the expressions that result in a QBist understanding of real-vector-space quantum theory are surprisingly complex., Comment: 25 pages, 6 figures, 3 tables, 1 really ugly equation; in v2 we got the spellings right

From the Text: How shall I tribute Andrei Khrennikov in this volume? With an email collection of course! But with what theme? It ought to be something big. One of the troubles of QBism's ontological program is that it is so sideways to the ways most run-of-the-mill philosophers of physics think, they don't even have the tools to parse its sentences. They simply can't see it as having to do with ontology at all. Maybe there is no remedy for this except to wait for the generation to die away. But QBism can and must move forward. Here we select some emails that might inspire a young researcher to throw in on the QBist ontological project, to help develop it on its own terms. The road to a proper, detailed QBist ontology is sure to be a hard one, but one has to start somewhere., Comment: 38 pages, no figures, to appear in The Quantum-Like Revolution: A Festschrift in Honor of Andrei Khrennikov, edited by E. Haven and A. Plotnitsky (Springer, Berlin, 2021). arXiv admin note: substantial text overlap with arXiv:1405.2390

We remark on John Earman's paper ``Quantum Bayesianism Assessed'' [The Monist 102 (2019), 403--423], illustrating with a number of examples that the quantum ``interpretation'' Earman critiques and the interpretation known as QBism have almost nothing to do with each other., Comment: 12 pages

The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series of monetary transactions based on those probabilities would lead them to expect a sure loss. Similarly, the subjective Bayesian interpretation of quantum mechanics (QBism) asserts that the Born rule is a normative rule in analogy to Dutch-book coherence, but with the addition of one or more empirically based assumptions -- i.e., the "only a little more" that connects quantum theory to the particular characteristics of the physical world. Here we make this link explicit for a conjectured representation of the Born rule which holds true if symmetric informationally complete POVMs (or SICs) exist for every finite dimensional Hilbert space. We prove that an agent who thinks they are gambling on the outcomes of measurements on a sufficiently quantum-like system, but refuses to use this form of the Born rule when placing their bets is vulnerable to a Dutch book. The key property for being sufficiently quantum-like is that the system admits a symmetric reference measurement, but that this measurement is not sampling any hidden variables., Comment: 13 pages, 35 references, 3 appendices, 1 miserable year finally over and done with; v2: title change to match journal version

According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences of the same agent. Wigner's conundrum of the friend, in which two agents ostensibly have different accounts of whether or not there is a measurement outcome, thus poses no paradox for QBism. Indeed the resolution of Wigner's original thought experiment was central to the development of QBist thinking. The focus of this paper concerns two very instructive modifications to Wigner's puzzle: One, a recent no-go theorem by Frauchiger and Renner, and the other a thought experiment by Baumann and Brukner. We show that the paradoxical features emphasized in these works disappear once both friend and Wigner are understood as agents on an equal footing with regard to their individual uses of quantum theory. Wigner's action on his friend then becomes, from the friend's perspective, an action the friend takes on Wigner. Our analysis rests on a kind of quantum Copernican principle: When two agents take actions on each other, each agent has a dual role as a physical system for the other agent. No user of quantum theory is more privileged than any other. In contrast to the sentiment of Wigner's original paper, neither agent should be considered as in "suspended animation." In this light, QBism brings an entirely new perspective to understanding Wigner's friend thought experiments., Comment: 15 pages, 1 figure

In the last five years of his life Itamar Pitowsky developed the idea that the formal structure of quantum theory should be thought of as a Bayesian probability theory adapted to the empirical situation that Nature's events just so happen to conform to a non-Boolean algebra. QBism too takes a Bayesian stance on the probabilities of quantum theory, but its probabilities are the personal degrees of belief a sufficiently-schooled agent holds for the consequences of her actions on the external world. Thus QBism has two levels of the personal where the Pitowskyan view has one. The differences go further. Most important for the technical side of both views is the quantum mechanical Born Rule, but in the Pitowskyan development it is a theorem, not a postulate, arising in the way of Gleason from the primary empirical assumption of a non-Boolean algebra. QBism on the other hand strives to develop a way to think of the Born Rule in a pre-algebraic setting, so that it itself may be taken as the primary empirical statement of the theory. In other words, the hope in QBism is that, suitably understood, the Born Rule is quantum theory's most fundamental postulate, with the Hilbert space formalism (along with its perceived connection to a non-Boolean event structure) arising only secondarily. This paper will avail of Pitowsky's program, along with its extensions in the work of Jeffrey Bub and William Demopoulos, to better explicate QBism's aims and goals., Comment: 32 pages; Appendix B contains extracts that were formerly buried deep within arXiv:1405.2390

Minimal Informationally Complete quantum measurements, or MICs, illuminate the structure of quantum theory and how it departs from the classical. Central to this capacity is their role as tomographically complete measurements with the fewest possible number of outcomes for a given finite dimension. Despite their advantages, little is known about them. We establish general properties of MICs, explore constructions of several classes of them, and make some developments to the theory of MIC Gram matrices. These Gram matrices turn out to be a rich subject of inquiry, relating linear algebra, number theory and probability. Among our results are some equivalent conditions for unbiased MICs, a characterization of rank-1 MICs through the Hadamard product, several ways in which immediate properties of MICs capture the abandonment of classical phase space intuitions, and a numerical study of MIC Gram matrix spectra. We also present, to our knowledge, the first example of an unbiased rank-1 MIC which is not group covariant. This work provides further context to the discovery that the symmetric informationally complete quantum measurements (SICs) are in many ways optimal among MICs. In a deep sense, the ideal measurements of quantum physics are not orthogonal bases., Comment: 23 pages, 4 figures, 4 open conjectures; v5: title change to journal version, minor updates

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 pages

We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule. Such representations are motivated by QBism, where the Born Rule is understood as a consistency condition between probabilities assigned to the outcomes of one experiment in terms of the probabilities assigned to the outcomes of other experiments. In this setting, the difference between quantum and classical physics is the way their physical assumptions augment bare probability theory: Classical physics corresponds to a trivial augmentation -- one just applies the Law of Total Probability (LTP) between the scenarios -- while quantum theory makes use of the Born Rule expressed in one or another of the forms of our general procedure. To mark the irreducible difference between quantum and classical, one should seek the representations that minimize the disparity between the expressions. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses -- the first to do with unitarily invariant distance measures between the rules, and the second to do with available volume in a reference probability simplex (roughly speaking a new kind of uncertainty principle). Both of these arise from a significant majorization result. This work complements recent studies in quantum computation where the deviation of the Born Rule from the LTP is measured in terms of negativity of Wigner functions., Comment: 10 pages, 2 figures; v4: corrected error in the last step of Theorem 1, strangely enough making the theorem stronger than we had believed

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 figure

The appearance of negative terms in quasiprobability representations of quantum theory is known to be inevitable, and, due to its equivalence with the onset of contextuality, of central interest in quantum computation and information. Until recently, however, nothing has been known about how much negativity is necessary in a quasiprobability representation. Zhu proved that the upper and lower bounds with respect to one type of negativity measure are saturated by quasiprobability representations which are in one-to-one correspondence with the elusive symmetric informationally complete quantum measurements (SICs). We define a family of negativity measures which includes Zhu's as a special case and consider another member of the family which we call "sum negativity." We prove a sufficient condition for local maxima in sum negativity and find exact global maxima in dimensions $3$ and $4$. Notably, we find that Zhu's result on the SICs does not generally extend to sum negativity, although the analogous result does hold in dimension $4$. Finally, the Hoggar lines in dimension $8$ make an appearance in a conjecture on sum negativity., Comment: 21 pages. v2: journal version, added references

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 844. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott's code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research., Comment: 16 pages, 1 figure, many references; v3: updating bibliography, dimension eight hundred forty four

This paper represents an elaboration of the lectures delivered by one of us (CAF) during "Course 197 -- Foundations of Quantum Physics" at the International School of Physics "Enrico Fermi" in Varenna, Italy, July 2016. Much of the material for it is drawn from arXiv:1003.5209, arXiv:1401.7254, and arXiv:1405.2390. However there are substantial additions of original material in Sections 4, 7, 8 and 9, along with clarifications and expansions of the older content throughout. Topics include the meaning of subjective probability; no-cloning, teleportation, and quantum tomography from the subjectivist Bayesian perspective; the message QBism receives from Bell inequality violations (namely, that nature is creative); the import of symmetric informationally complete (SIC) quantum measurements for the technical side of QBism; quantum cosmology QBist-style; and a potential meaning for the holographic principle within QBism., Comment: 39 pages, 8 figures (1 of a superhero); lectures based on arXiv:1003.5209, arXiv:1401.7254 and arXiv:1405.2390 plus new content; v3: bibliography glitch-fixes

We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres's dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, mutually exclusive experiments mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. Along the way, we derive a condition for the existence of a d-dimensional SIC., Comment: 30 pages, 4 figures, 3 appendices; v2: typos and notational glitches corrected

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 pages

We compare the standard 50%-efficient single beam splitter method for Bell-state measurement to a proposed 75%-efficient auxiliary-photon-enhanced scheme [W. P. Grice, Phys. Rev. A 84, 042331 (2011)] in light of realistic conditions. The two schemes are compared with consideration for high input state photon loss, auxiliary state photon loss, detector inefficiency and coupling loss, detector dark counts, and non-number-resolving detectors. We also analyze the two schemes when multiplexed arrays of non-number-resolving detectors are used. Furthermore, we explore the possibility of utilizing spontaneous parametric down-conversion as the auxiliary photon pair source required by the enhanced scheme. In these different cases, we determine the bounds on the detector parameters at which the enhanced scheme becomes superior to the standard scheme and describe the impact of the different imperfections on measurement success rate and discrimination fidelity. This is done using a combination of numeric and analytic techniques. For many of the cases discussed, the size of the Hilbert space and the number of measurement outcomes can be very large, which makes direct numerical solutions computationally costly. To alleviate this problem, all of our numerical computations are performed using pure states. This requires tracking the loss modes until measurement and treating dark counts as variations on measurement outcomes rather than modifications to the state itself. In addition, we provide approximate analytic expressions that illustrate the effect of different imperfections on the Bell-state analyzer quality., Comment: 14 pages, 5 figures, version accepted by PRA

This is a reply to Michael Nauenberg's arXiv:1502.00123, to be published in the American Journal of Physics, in which he comments critically on our paper "An introduction to QBism with an application to the locality of quantum mechanics", Am. J. Phys. 82, 749--754 (2014) and arXiv:1311.5253., Comment: 2 pages

In the quantum Bayesian (or QBist) conception of quantum theory, "quantum measurement" is understood not as a comparison of something pre-existent with a standard, but instead indicative of the creation of something new in the universe: Namely, the fresh experience any agent receives upon taking an action on the world. We explore the implications of this for any would-be ontology underlying QBism. The concept that presently stands out as a candidate "material for our universe's composition" is "experience" itself, or what John Wheeler called "observer-participancy"., Comment: 15 pages, 1 figure, published version of philosophical section in arXiv:0906.2187, but with new introductory material, published in The Pauli-Jung Conjecture and its Impact Today, edited by H. Atmanspacher and C. A. Fuchs, p. 93-108 (Imprint Academic, Exeter, 2014)

In QBism (or Quantum Bayesianism) a quantum state does not represent an element of physical reality but an agent's personal probability assignments, reflecting his subjective degrees of belief about the future content of his experience. In this paper, we contrast QBism with hidden-variable accounts of quantum mechanics and show the sense in which QBism explains quantum correlations. QBism's agent-centered worldview can be seen as a development of ideas expressed in Schr\"odinger's essay "Nature and the Greeks"., Comment: 11 pages, 1 figure, introduction clarified

This document is the second installment of three in the Cerro Grande Fire Series. Like its predecessor arXiv:quant-ph/0105039, "Notes on a Paulian Idea," it is a collection of letters written to various friends and colleagues, most of whom regularly circuit this archive. The unifying theme of all the letters is that each has something to do with the quantum. Particularly, the collection chronicles the emergence of Quantum Bayesianism as a robust view of quantum theory, eventually evolving into the still-more-radical "QBism" (with the B standing for no particular designation anymore), as it took its most distinctive turn away from various Copenhagen Interpretations. Included are many anecdotes from the history of quantum information theory: for instance, the story of the origin of the terms "qubit" and "quantum information" from their originator's own mouth, a copy of a rejection letter written by E. T. Jaynes for one of Rolf Landauer's original erasure-cost principle papers, and much more. Specialized indices are devoted to historical, technical, and philosophical matters. More roundly, the document is an attempt to provide an essential ingredient, unavailable anywhere else, for turning QBism into a live option within the vast spectrum of quantum foundational thought., Comment: CAUTION, do not unthinkingly print from a printer: 2,349 pages, 4 indices, 6 figures, with extensive hyperlinking. Foreword by M. Schlosshauer, edited by B. C. Stacey. v2: more footnotes, fewer typos

We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multi-mode quantum memories and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss and noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle non-idealities, that this scheme achieves a secret key rate that surpasses the TGW bound---a recently-found fundamental limit to the rate-vs.-loss scaling achievable by any QKD protocol over a direct optical link---thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement distillation rate, as a function of the number of repeater nodes, total range, and various loss and noise parameters of the system. We extend our theoretical analysis to encompass sources with non-zero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols, and also to provide useful abstractions to seed analyses of quantum networks of complex topologies., Comment: 27 pages, 14 figures

Over the last 10 years there has been an explosion of "operational reconstructions" of quantum theory. This is great stuff: For, through it, we come to see the myriad ways in which the quantum formalism can be chopped into primitives and, through clever toil, brought back together to form a smooth whole. An image comes to mind of a brain-teaser puzzle, all sliding and interlocking pieces. There is no doubt that this is invaluable work, particularly for our understanding of the intricate connections between so many quantum information protocols. But to me, it seems to miss the mark for an ultimate understanding of quantum theory; I am left hungry. I still want to know what strange property of matter forces this formalism upon our information accounting. To play on something Einstein once wrote to Max Born, "The quantum reconstructions are certainly imposing. But an inner voice tells me that they are not yet the real thing. The reconstructions say a lot, but do not really bring us any closer to the secret of the `old one'." In this talk, I hope to expand on these points and convey some sense of why I am fascinated with the problem of the symmetric informationally complete POVMs to an extent greater than axiomatic reconstructions., Comment: Edited transcript of a talk given by one of us (CAF) at the Conceptual Foundations and Foils for Quantum Information Processing workshop, Perimeter Institute, 10 May 2011. v2: affiliations updated, broken URL removed

Although symmetric informationally complete positive operator valued measures (SIC POVMs, or SICs for short) have been constructed in every dimension up to 67, a general existence proof remains elusive. The purpose of this paper is to show that the SIC existence problem is equivalent to three other, on the face of it quite different problems. Although it is still not clear whether these reformulations of the problem will make it more tractable, we believe that the fact that SICs have these connections to other areas of mathematics is of some intrinsic interest. Specifically, we reformulate the SIC problem in terms of (1) Lie groups, (2) Lie algebras and (3) Jordan algebras (the second result being a greatly strengthened version of one previously obtained by Appleby, Flammia and Fuchs). The connection between these three reformulations is non-trivial: It is not easy to demonstrate their equivalence directly, without appealing to their common equivalence to SIC existence. In the course of our analysis we obtain a number of other results which may be of some independent interest., Comment: 36 pages, to appear in Quantum Inf. Comput

We give an introduction to the QBist interpretation of quantum mechanics. We note that it removes the paradoxes, conundra, and pseudo-problems that have plagued quantum foundations for the past nine decades. As an example, we show in detail how it eliminates quantum "nonlocality"., Comment: 11 pages, no figures

In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, we show how to view the Born Rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is seen particularly clearly by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete (SIC) measurement. We further explore the extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics., Comment: 31 pages, 3 figures; this is a compact, more straightforward, and less philosophical version of arXiv:0906.2187

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 pages

The probabilities a Bayesian agent assigns to a set of events typically change with time, for instance when the agent updates them in the light of new data. In this paper we address the question of how an agent's probabilities at different times are constrained by Dutch-book coherence. We review and attempt to clarify the argument that, although an agent is not forced by coherence to use the usual Bayesian conditioning rule to update his probabilities, coherence does require the agent's probabilities to satisfy van Fraassen's [1984] reflection principle (which entails a related constraint pointed out by Goldstein [1983]). We then exhibit the specialized assumption needed to recover Bayesian conditioning from an analogous reflection-style consideration. Bringing the argument to the context of quantum measurement theory, we show that "quantum decoherence" can be understood in purely personalist terms---quantum decoherence (as supposed in a von Neumann chain) is not a physical process at all, but an application of the reflection principle. From this point of view, the decoherence theory of Zeh, Zurek, and others as a story of quantum measurement has the plot turned exactly backward., Comment: 14 pages, written in memory of Itamar Pitowsky

This article summarizes the Quantum Bayesian point of view of quantum mechanics, with special emphasis on the view's outer edges---dubbed QBism. QBism has its roots in personalist Bayesian probability theory, is crucially dependent upon the tools of quantum information theory, and most recently, has set out to investigate whether the physical world might be of a type sketched by some false-started philosophies of 100 years ago (pragmatism, pluralism, nonreductionism, and meliorism). Beyond conceptual issues, work at Perimeter Institute is focused on the hard technical problem of 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 an agent considers gambling on the consequences of his interactions with a newly recognized universal capacity: dimension (formerly Hilbert-space dimension). (The word "capacity" should conjure up an image of something like gravitational mass---a body's mass measures its capacity to attract other bodies. With hindsight one can say that the founders of quantum mechanics discovered another universal capacity, "dimension.") The article ends by showing that the egocentric elements in QBism represent no impediment to pursuing quantum cosmology and outlining some directions for future work., Comment: 30 pages, 6 figures

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.

Examples of symmetric informationally complete positive operator valued measures (SIC-POVMs) have been constructed in every dimension less than or equal to 67. However, it remains an open question whether they exist in all finite dimensions. A SIC-POVM is usually thought of as a highly symmetric structure in quantum state space. However, its elements can equally well be regarded as a basis for the Lie algebra gl(d,C). In this paper we examine the resulting structure constants, which are calculated from the traces of the triple products of the SIC-POVM elements and which, it turns out, characterize the SIC-POVM up to unitary equivalence. We show that the structure constants have numerous remarkable properties. In particular we show that the existence of a SIC-POVM in dimension d is equivalent to the existence of a certain structure in the adjoint representation of gl(d,C). We hope that transforming the problem in this way, from a question about quantum state space to a question about Lie algebras, may help to make the existence problem tractable., Comment: 56 pages

In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the usual probability rules as required by Dutch-book coherence, but quantum mechanics imposes additional constraints upon them. In this paper, we explore the question of deriving the structure of quantum-state space from a set of assumptions in the spirit of quantum Bayesianism. The starting point is the representation of quantum states induced by a symmetric informationally complete measurement or SIC. In this representation, the Born rule takes the form of a particularly simple modification of the law of total probability. We show how to derive key features of quantum-state space from (i) the requirement that the Born rule arises as a simple modification of the law of total probability and (ii) a limited number of additional assumptions of a strong Bayesian flavor., Comment: 7 pages, 1 figure, to appear in Foundations of Physics; this is a condensation of the argument in arXiv:0906.2187v1 [quant-ph], with special attention paid to making all assumptions explicit

Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication [1] advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset--quantum-state space--might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in [1], and all in conformity with quantum theory., Comment: 17 pages, 5 figures, a few additions in v2 on QBism ideas

In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, we show how to view the Born Rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is seen particularly clearly by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete (SIC) measurement. We further explore the extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics. It seems to get quite far., Comment: 62 pages, 3 figures, one special equation with a box around it

This pseudo-paper consists of excerpts drawn from two of my quantum-email samizdats. Section 1 draws a picture of a physical world whose essence is ``Darwinism all the way down.'' Section 2 outlines how quantum theory should be viewed in light of this, i.e., as being an expression of probabilism (in Bruno de Finetti or Richard Jeffrey's sense) all the way back up. Section 3 describes how the idea of ``identical'' quantum measurement outcomes, though sounding atomistic in character, nonetheless meshes well with a Jamesian style ``radical pluralism.'' Sections 4 and 5 further detail how quantum theory should not be viewed so much as a ``theory of the world,'' but rather as a theory of decision-making for agents immersed within a world of a particular character--the quantum world. Finally, Sections 6 and 7 attempt to sketch the very positive sense in which quantum theory is incomplete, but still just as complete is it can be. In total, I hope these heady speculations convey some of the excitement and potential I see for the malleable world quantum mechanics hints of., Comment: Stuffed away in a conference proceedings for years, I finally worked up the nerve to post this because I needed to cite it in a paper with some proper equations. Stay posted

In quantum Bayesian inference problems, any conclusions drawn from a finite number of measurements depend not only on the outcomes of the measurements but also on a prior. Here we show that, in general, the prior remains important even in the limit of an infinite number of measurements. We illustrate this point with several examples where two priors lead to very different conclusions given the same measurement data., Comment: 7 pages; published in AIP Conference Proceedings 1101: Foundations of Probability and Physics 5, edited by L. Accardi et al, p. 255 (2009)