Explanation via Uncontrollable Idealization
Andrew Wayne Institut d'Astrophysique de Paris
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Adding entanglement to quantum error-correcting codes
Todd Brun University of Southern California
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Theories of Truth and Consequences for Quantum Theory
Nora Boyd University of Waterloo
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Quantum code with translation and scale symmetries
Beni Yoshida Perimeter Institute for Theoretical Physics
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Where is the quantum particle between two measurements
Lev Vaidman Tel Aviv University
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Quantum Bayesianism---Something Old, Something New
Chris Fuchs University of Massachusetts Boston
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The quantum world: from weird to wired
Joseph Emerson Institute for Quantum Computing (IQC)
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Nonclassical correlations from random measurements
Yeong-Cherng Liang National Cheng Kung University
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Explanation via Uncontrollable Idealization
Andrew Wayne Institut d'Astrophysique de Paris
Many putative explanations in physics rely on idealized models of physical systems. These explanations are inconsistent with standard philosophical accounts of explanation. A common view holds that idealizations can underwrite explanation nonetheless, but only when they are what have variously been called Galilean, approximative, traditional or controllable. Controllability is the least vague of these categories, and this paper focuses on the relation between controllability and explanation. Specifically, it argues that the common view is an untenable half-measure. It gives the example of a simple pendulum with quadratic damping, an uncontrollable idealization that makes use of singular limits and for which the behaviour at the limit is qualitatively new—but a system whose behaviour is fully explained in terms of the idealization. It shows that uncontrollable idealizations can have explanatory capacities (and in a way distinct from Batterman’s “asymptotic explanation”). -
Adding entanglement to quantum error-correcting codes
Todd Brun University of Southern California
Shared entanglement between sender and receiver can enable more errors to be corrected than with a standard quantum error-correcting code. This extra error correction can be used either to boost the rate of the code--commonly seen in quantum codes constructed from classical linear codes--or to increase the error-correcting power of the code (as represented by, for example, the code distance). We will see how adding extra entanglement to a given quantum code can increase its distance, and discuss the optimization problem in maximizing the effectiveness of a given amount of added entanglement. We will also briefly examine some applications of entanglement-assistance to particular types of codes, such as LDPC codes and convolutional codes. -
Theories of Truth and Consequences for Quantum Theory
Nora Boyd University of Waterloo
One might have hoped that philosophers had sorted out what ‘truth’ is supposed to be by now. After all, Aristotle offered what seems to be a clear and simple characterization in his Metaphysics. So perhaps it is surprising (and then again perhaps it isn’t), that contemporary philosophers have not settled on a consensus regarding the nature of truth to this day. In fact, the most obvious theory of truth, that truth consists in correspondence to the facts, seems to be steadily waning in popularity in technical circles, replaced instead by a perhaps puzzlingly austere minimalist theory that restricts its characterization of truth to the familiar equivalence schema:is true if and only if p. The differences between such deflationary theories and the ‘traditional’ correspondence theory of truth, and perhaps even more strikingly between these theories and epistemic theories of truth, call to mind counterpart features in different attitudes about the proper interpretation of quantum mechanics. By reviewing the most striking features of different theories of truth, as well as some of their most difficult objections, we can start to see where different interpretations seem to be reliant on (or at least quite congenial to) particular theories of truth and also where these theories begin to reveal themselves as variously helping and hindering the smooth functioning of different interpretations.
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CauCats: the backbone of a quantum relativistic universe of interacting processes
Bob Coecke Quantinuum
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. With very little structural effort (i.e. in very abstract terms) and in a very short time this categorical quantum mechanics research program has reproduced a surprisingly large fragment of quantum theory. Philosophically speaking, this framework shifts the conceptual focus from `material carriers' such as particles, fields, or other `material stuff', to `logical flows of information', by mainly encoding how things stand in relation to each other. These relations could, for example, be induced by operations. Composition of these relations is the carrier of all structure. Thus far the causal structure has been treated somewhat informally within this approach. In joint work with my student Raymond Lal, by restricting the capabilities to compose, we were able to formally encode causal connections. We call the resulting mathematical structure a CauCat, since it combines the symmetric monoidal stricture with Sorkin's CauSets within a single mathematical concept. The relations which now respect causal structure are referred to as processes, which make up the actual `happenings'. As a proof of concept, we show that if in a quantum teleportation protocol one omits classical communication, no information is transfered. We also characterize Galilean theories. Classicality is an attribute of certain processes, and measurements are special kinds of processes, defined in terms of their capabilities to correlate other processes to these classical attributes. So rather than quantization, what we do is classicization within our universe of processes. We show how classicality and the causal structure are tightly intertwined. All of this is still very much work in progress! -
Quantum code with translation and scale symmetries
Beni Yoshida Perimeter Institute for Theoretical Physics
Topological phases in spin systems are exciting frontiers of research with intimate connections to quantum coding theory. However, there is a disconnection between quantum codes and the idea of topology, in the absence of geometry and physical realizability. Here, we introduce a toy model, in which quantum codes are constrained to not only have a local geometric description, but also have translation and scale symmetries. These additional physical constraints enable us to assign topologically invariant properties to geometric shapes of logical operators of the code. Topological phases of the model are analyzed by geometrically classifying logical operators. The classification scheme also has topologically universal properties which are invariant under local unitary transformations and local perturbations, and may explain how global symmetries of a system Hamiltonian give rise to topological phases in correlated spin systems. -
Where is the quantum particle between two measurements
Lev Vaidman Tel Aviv University
The Wheeler delayed choice experiment, Elitzur-Vaidman interaction-free measurement, and Hosten-Kwiat counterfactual computation will be discussed to answer Bohr's forbidden question: "Where is a quantum particle while it is inside a Mach-Zehnder Interferometer?". I will argue that the naive application of Wheeler's approach fails to explain a weak trace left by the particle and that the two-state vector description is required. -
Quantum Bayesianism---Something Old, Something New
Chris Fuchs University of Massachusetts Boston
Quantum Bayesianism is a point of view on quantum foundations that says that there is no such thing as a “measurement problem” because there is no such THING as a quantum state: Quantum states are not things---instead information. But the view doesn’t stop there; it starts there! Taking the idea seriously over the last 15 years has been the direct motivation for a number of theorems and objects in quantum information theory: from the no-broadcasting theorem, to the quantum de Finetti theorem, and even some quantum cryptographic alphabets. I will review some of this, and then move on to the holy grail of present efforts: Finding an efficient representation of quantum states in terms of a singular probability function. Doing so leads to the hard technical problem of demonstrating the existence of a certain very symmetric sets of quantum states, and holds out the hope of understanding the amount of “quantum stuff” in a physical system in terms of a single parameter. (I.e., there is the THING that the quantum state is not). -
Not altogether desperate: An exposition of Newton's Scholium Problem and the theoretical definition of duration
In the Scholium in Newton's Principia which contains the discussions about absolute space, time, and the bucket experiment, Newton also posed a problem that Julian Barbour has denoted the "Scholium problem". Newton writes there "But how are we to obtain the true motions from their causes, effects, and apparent differences, and the converse, shall be explained more at large in the following treatise. For to this end it was that I composed it". This problem was clearly considered very important by Newton who claims he wrote the Principia dedicated to this problem. Interestingly Newton never returned to the problem. In this talk we are going to give a mathematical precise formulation of the Scholium problem. A subpart of the Scholium problem consists of determining how accurate the observers clock is. We are going to start from that end and see that the problem of defining duration is inseparately intertwined with the full scholium problem. -
The quantum world: from weird to wired
Joseph Emerson Institute for Quantum Computing (IQC)
Does quantum mechanics really tell us that particles, molecules, and maybe even cats, can be in two places at once? Does it force us to deny a reality that is independent of our observation? How can scientists disagree about what quantum mechanics means and yet still agree that it is right? Joseph Emerson, co-writer of the award-winning documentary “The Quantum Tamers”, will address these questions and then describe, drawing on preview clips from the documentary, how the weirdness of the quantum world is now being harnessed for a ‘quantum information revolution’ that includes quantum teleportation, super-secure quantum communication, and the exponential power of quantum computation. -
Nonclassical correlations from random measurements
Yeong-Cherng Liang National Cheng Kung University
In this talk, I will demonstrate that correlations inconsistent with any locally causal description can be a generic feature of measurements on entangled quantum states. Specifically, spatially-separated parties who perform local measurements on a maximally-entangled state using randomly chosen measurement bases can, with significant probability, generate nonclassical correlations that violate a Bell inequality. For n parties using a Greenberger-Horne-Zeilinger state, this probability of violation rapidly tends to unity as the number of parties increases. Moreover, even with both a randomly chosen two-qubit pure state and randomly chosen measurement bases, a violation can be found about 10% of the time. Amongst other applications, our work provides a feasible alternative for the demonstration of Bell inequality violation without a shared reference frame. -
A Computational Grand-Unified Theory
Are Quantum Mechanics and Special Relativity unrelated theories? Is Quantum Field Theory an additional theoretical layer over them? Where the quantization rules and the Plank constant come from? All these questions can find answer in the computational paradigm: "the universe is a huge quantum computer". In my talk I'll take the computational-universe paradigm as genuine theoretical framework, and analyze some relevant implications. A new kind of quantum field theory emerges: "Quantum-Computational Field Theory" (QCFT). I will show how in QCFT Special Relativity unfolds from the fabric of the computational network, which also naturally embeds gauge-invariance, and even the quantization rule and the Planck constant, which thus resort to being properties of the underlying causal tapestry of space-time. In this way Quantum Mechanics remains the only theory needed to describe the computational-universe. I will analyze few simple toy-models in order to explore the mathematical structure of QCFT. The new QCFT has many advantages versus the customary field theoretical framework, solving a number of logical and mathematical problems that plague quantum field theory. One further advantage of QCFT is the possibility of changing the computational engine without changing the field-theoretical framework. One can thus consider different kind of engines, e.g. classical, quantum, super-quantum, and even input-output networks with no pre-established causal relations, which are very interesting for addressing the problem of Quantum Gravity. QCFT opens a large research line: I argue that this program should be addressed soon in the particle physics domain, before entering Quantum Gravity, notwithstanding the experimental success of the usual quantum field theory. It will also be the first test of the Lucien Hardy's program on Quantum Gravity. Reference: arXiv:1001.1088 (http://arxiv.org/abs/1001.1088)
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Switching boxes connections in operational theories and its consequence on causality
Paolo Perinotti University of Pavia
How can we describe a device that takes two unknown operational boxes and conditionally on some input variable connects them in different orders? In order to answer this question, I will introduce maps from transformations to transformations within operational probabilistic theories with purification, and show their characterisation in terms of operational circuits. I will then proceed exploring the hierarchy of maps on maps. A particular family of maps in the hierarchy are the ones whose output is in the set of transformations. These maps can be fully characterised by their correspondence with channels with memory, and it is exactly the family of transformations that can be implemented through operational circuits. I will then show the problems that arise in defining the remainder of the hierarchy, and the reason why we cannot avoid considering its elements. The main consequence of admitting the generalised transformations as possible within the operational theory is that we cannot describe them in terms of simple causal connection of transformations in a circuit with a fixed causal structure. In quantum theory, we can understand such higher order transformations in terms of superpositions of circuits with different causal structures. The problem whether computations exploiting higher-order transformations can be efficiently simulated by a conventional circuital computer is posed.