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Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
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In this paper, the authors introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics, and keep the writing in a self-consistent way, requiring minimum background in quantum information sciences.Abstract:
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.read more
Citations
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Quantum-enhanced measurements without entanglement
Daniel Braun,Gerardo Adesso,Fabio Benatti,Roberto Floreanini,Ugo Marzolino,Morgan W. Mitchell,Stefano Pirandola +6 more
TL;DR: In this article, a review of quantum-enhanced measurements can be found, including the use of more general quantum correlations such as quantum discord, identical particles, or non-trivial hamiltonians, and the estimation of thermodynamical parameters or parameters characterizing non-equilibrium states.
Journal ArticleDOI
Quantum coherence and geometric quantum discord
TL;DR: This aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states.
Posted Content
Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
TL;DR: The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems, and the syntax is provided by tensor networks as mentioned in this paper, where the tensor network enables the construction of real-space renormalization group flows and fixed points.
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Measurement-induced topological entanglement transitions in symmetric random quantum circuits
TL;DR: In this paper, a class of (1+1)D symmetric random quantum circuits with two competing types of measurements in addition to random unitary dynamics was studied, where the transitions are hidden to expectation values of operators and can only be accessed through the entanglement entropy averaged over quantum trajectories.
Journal ArticleDOI
The randomized measurement toolbox
Andreas Elben,Steven T. Flammia,Hsin-Yuan Huang,Richard Kueng,John Preskill,Benoît Vermersch,Peter Zoller +6 more
TL;DR: In this article , the authors present protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms, such as programmable quantum simulators and quantum computers.
References
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Book
Quantum Computation and Quantum Information
TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.
Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Journal ArticleDOI
Quantum spin Hall effect in graphene
Charles L. Kane,Eugene J. Mele +1 more
TL;DR: Graphene is converted from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator and the spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.
Journal ArticleDOI
Density matrix formulation for quantum renormalization groups
TL;DR: A generalization of the numerical renormalization-group procedure used first by Wilson for the Kondo problem is presented and it is shown that this formulation is optimal in a certain sense.
Journal ArticleDOI
New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance
TL;DR: In this article, the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field effect transistor, was measured and it was shown that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device.