02409nas a2200193 4500008004100000245006700041210006700108260001500175490000700190520183800197100002002035700001902055700002302074700001802097700002402115700002002139700001902159856003702178 2020 eng d00aContinuous symmetries and approximate quantum error correction0 aContinuous symmetries and approximate quantum error correction c10/26/20200 v103 a

Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the error correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W-states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.

1 aFaist, Philippe1 aNezami, Sepehr1 aAlbert, Victor, V.1 aSalton, Grant1 aPastawski, Fernando1 aHayden, Patrick1 aPreskill, John uhttps://arxiv.org/abs/1902.0771402203nas a2200205 4500008004100000245008000041210006900121260001500190520157300205100002001778700002101798700002401819700001901843700001901862700001801881700002201899700001901921700002001940856003701960 2019 eng d00aQuantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes0 aQuantum Gravity in the Lab Teleportation by Size and Traversable c2019/11/143 a

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. 

1 aBrown, Adam, R.1 aGharibyan, Hrant1 aLeichenauer, Stefan1 aLin, Henry, W.1 aNezami, Sepehr1 aSalton, Grant1 aSusskind, Leonard1 aSwingle, Brian1 aWalter, Michael uhttps://arxiv.org/abs/1911.0631402354nas a2200157 4500008004100000245007000041210006900111520185900180100001902039700002002058700002402078700001802102700001902120700002002139856003702159 2017 eng d00aEntanglement Wedge Reconstruction via Universal Recovery Channels0 aEntanglement Wedge Reconstruction via Universal Recovery Channel3 a

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

1 aCotler, Jordan1 aHayden, Patrick1 aPenington, Geoffrey1 aSalton, Grant1 aSwingle, Brian1 aWalter, Michael uhttps://arxiv.org/abs/1704.05839