TY - JOUR T1 - Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions Y1 - 2019 A1 - Freek Witteveen A1 - Volkher Scholz A1 - Brian Swingle A1 - Michael Walter AB -

The multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories. 

UR - https://arxiv.org/abs/1905.08821 ER - TY - JOUR T1 - Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes Y1 - 2019 A1 - Adam R. Brown A1 - Hrant Gharibyan A1 - Stefan Leichenauer A1 - Henry W. Lin A1 - Sepehr Nezami A1 - Grant Salton A1 - Leonard Susskind A1 - Brian Swingle A1 - Michael Walter AB -

With the long-term goal of studying quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in recent traversable wormhole constructions: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of "teleportation by size" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call "size winding". For more general setups (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. For example, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions. 

UR - https://arxiv.org/abs/1911.06314 ER - TY - JOUR T1 - Entanglement Wedge Reconstruction via Universal Recovery Channels Y1 - 2017 A1 - Jordan Cotler A1 - Patrick Hayden A1 - Geoffrey Penington A1 - Grant Salton A1 - Brian Swingle A1 - Michael Walter AB -

We apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra

UR - https://arxiv.org/abs/1704.05839 ER -