Nonclassical correlations from random measurements
Yeong-Cherng Liang National Cheng Kung University
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Purity and reversibility as a paradigm for Quantum Information Processing
Giulio Chiribella University of Hong Kong (HKU)
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Unified approach to classical and quantum dualities
Gerardo Ortiz Indiana University - Bloomington
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Why Does Nature Like the Square Root of Negative One?
William Wootters Williams College
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What's Wrong with 'Measurement'?
Richard Healey University of Arizona
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Reduction and Emergence in Bose-Einstein Condensates
Richard Healey University of Arizona
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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. -
Purity and reversibility as a paradigm for Quantum Information Processing
Giulio Chiribella University of Hong Kong (HKU)
In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded. From the purification principle one can also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamiolkowski isomorphism in Quantum Mechanics. Such an isomorphism allows one to prove most of the basic features of Quantum Information Processing, like e.g. no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, complementarity between correctable and deletion channels, no programming, and no bit commitment, without resorting to the mathematical framework of Hilbert spaces. -
Quantum Money
Scott Aaronson The University of Texas at Austin
Ever since there's been money, there have been people trying to counterfeit it, and governments trying to stop them. In 1969, the physicist Stephen Wiesner raised the remarkable possibility of money whose authenticity would be guaranteed by the laws of quantum mechanics. However, the question of whether one can have secure quantum money that anyone (not only the bank) can verify has remained open for forty years. In this talk, I'll tell you about progress on the question over the last two years. (1) I'll show that no publicly-verifiable quantum money scheme can have security based on quantum physics alone: like in most cryptography, one also needs a computational hardness assumption. (2) I'll show that one can have quantum money that remains hard to counterfeit, even if a counterfeiter gains access to a "black box" for verifying the money. (3) I'll describe a candidate quantum money scheme I proposed last spring, and how that scheme was recently broken by Lutomirski et al. I'll also discuss a new class of schemes that might evade the existing attacks -- schemes with the bizarre property that not even the bank can prepare the same bill twice. The talk is designed to be accessible to those without a quantum information background. Reference for (1)-(2): S. Aaronson, "Quantum copy-protection and quantum money," in Proceedings of CCC'2009, http://www.scottaaronson.com/papers/noclone-ccc.pdf. Reference for (3): A. Lutomirski, S. Aaronson, E. Farhi, D. Gosset, A. Hassidim, J. Kelner, and P. Shor. Breaking and making quantum money: toward a new quantum cryptographic protocol, Proceedings of Innovations in Computer Science (ICS), 2010. http://arxiv.org/abs/0912.3825. -
Weak Gravity and the Arrow of Time
Simon Judes Columbia University
CMB measurements reveal a very smooth early universe. We propose a mech- anism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy. -
Symmetric informationally complete measurements: Can we make big ones out of small ones?
William Wootters Williams College
For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure. In this talk I give one example showing how a SIC for three qubits can be constructed from SICs for the individual qubits. I ask whether the strategy used in this example might apply to other composite cases. -
Unified approach to classical and quantum dualities
Gerardo Ortiz Indiana University - Bloomington
Dualities appear in nearly all disciplines of physics and play a central role in statistical mechanics and field theory. I will discuss in a pedagogical way our recent findings motivated by a quest for a simple unifying framework for the detection and treatment of dualities. I will explain how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories (i.e. emergent dualities), can be unveiled, and systematically established. Our method relies on the use of morphisms of the "bond algebra" of a quantum Hamiltonian. Dualities are characterized as unitary mappings implementing such morphisms, whose even powers become symmetries of the quantum problem. Dual variables (non-local mappings between the elementary degrees of freedom of the theory) which were guessed in the past can be derived in our formalism. New self-dualities for four-dimensional Abelian gauge field theories will be discussed. -
Why Does Nature Like the Square Root of Negative One?
William Wootters Williams College
Is there a theory yet to be discovered that underlies quantum theory and explains its structure? If there is such a theory, one of the features it will have to explain is the central role of complex numbers as probability amplitudes. In this talk I explore the physical meaning of the statement “probability amplitudes are complex” by comparing ordinary complex-vector- space quantum theory with the real-vector-space theory having the same basic structure. Specifically, I discuss three questions that bring out qualitative differences between the two theories: (i) Is information about a preparation expressed optimally in the outcomes of a measurement? (ii) Are multipartite states locally accessible? (iii) Is entanglement “monogamous”? -
What's Wrong with 'Measurement'?
Richard Healey University of Arizona
In his brilliant article "Against 'Measurement'", John Bell famously argued that the word has had such a damaging effect on the discussion, that it should now be banned altogether in quantum mechanics. But in the beginning was the word, and the word is still with us. Indeed, David Mermin responded In Praise of Measurement that within the field of quantum computer science the concept of measurement is precisely defined, unproblematic, and forms the foundation of the entire subject, a verdict reaffirmed by the development of measurement-based quantum computation. Bell's arguments deserve a more direct response: I shall try to give one. -
Quantum computational phases of matter: measurement-based quantum computing in the Haldane phase
Stephen Bartlett University of Sydney
A recent breakthrough in quantum computing has been the realization that quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state. One exciting prospect is that the ground or low-temperature thermal state of an interacting quantum many-body system can serve as such a resource state for quantum computation. The system would simply need to be cooled sufficiently and then subjected to local measurements. It would be unfortunate, however, if the usefulness of a ground or low-temperature thermal state for quantum computation was critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterized by the ability to perform measurement-based quantum computation. I’ll discuss some recent results on the existence of such a computational phase of matter. I’ll first outline some positive results on a phase of a toy model that contains the cluster state. Then, in a realistic model of coupled spin-1 particles, I’ll demonstrate the existence of a computational phase. This result is obtained by using a local measurement sequence to “renormalize” the state to a computationally-universal fixed point. Together, these results reveal that the characterization of computational phases of matter has a rich, complex structure – one which is still poorly understood. Joint work with Gavin Brennen, Akimasa Miyake, and Joseph Renes. -
Reduction and Emergence in Bose-Einstein Condensates
Richard Healey University of Arizona
A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.