Artificial quantum systems with synthetic dimensions enable exploring novel quantum phenomena difficult to create in conventional materials. These synthetic degrees of freedom increase the system's dimensionality without altering its physical structure, accessing higher-dimensional physics in lower-dimensional setups. However, synthetic quantum systems often suffer from intrinsic disorder, causing rapid decoherence that limits scalability, a major obstacle in quantum information science. Here, we show that introducing just a few long-range interactions can mitigate decoherence, creating persistent collective coherence in highly symmetric collective excited states. We term this universal phenomenon "supercoherence" and show its exceptional robustness against disorder up to a dynamical phase transition at critical interaction strength and disorder. Supercoherence stabilizes not only coherence but also all other quantum properties of the states, challenging traditional views on the inevitability of decoherence in disordered interacting quantum systems and suggesting new opportunities for quantum memory and information processing.

We describe the homotopy classes of loops in the space of 2 × 2 simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in R3/{0}. Since closed curves in R3/{0} can be readily visualized, no advanced tools of algebraic topology are needed. The matrices represent gapped Bloch Hamiltonians in 1D with a two dimensional Hilbert space per unit cell.

In a paper titled "Asking photons where they have been?" Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors. They argue that the experiment supports Aharonov-Vaidman's formulation of quantum mechanics where post-selected particles are assigned disconnected trajectories. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The standard view of interfering trajectories accounts for the experimental findings.

We discuss an apparent difficulty in computing the radiation emitted by a system undergoing Lindblad evolution. The difficulty is resolved by viewing the problem as Born rule for conserved currents defined by the appropriate terms in the adjoint Lindbladian. In Heralding Alice prepares Bob's system in a state that mirrors her test. We show that heralding is consistent with no-cloning. This follows from the observation that heralding is not a completely positive map.

We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell.

Distributed quantum computing can give substantial noise reduction due to shallower circuits. An experiment illustrates the advantages in the case of Grover search. This motivates studying the quantum advantage of the distributed version of the Simon and Deutsch-Jozsa algorithm. We show that the distributed Simon algorithm retains the exponential advantage, but the complexity deteriorates from O(n) to O(n^2), where n = log2(N). The distributed Deutsch-Jozsa deteriorates to being probabilistic but retains a quantum advantage over classical random sampling.

This is a review of the geometry of quantum states using elementary methods and pictures. Quantum states are represented by a convex body, often in high dimensions. In the case of n-qubits, the dimension is exponentially large in n. The space of states can be visualized, to some extent, by its simple cross sections: Regular simplexes, balls and hyper-octahedra. When the dimension gets large there is a precise sense in which the space of states resembles, almost in every direction, a ball. The ball turns out to be a ball of rather low purity states. We also address some of the corresponding, but harder, geometric properties of separable and entangled states and entanglement witnesses.

Pair collisions in atomic gases lead to decoherence and decay. Assuming that all the atoms in the gas are equally likely to collide one is led to consider Lindbladian of mean field type where the evolution in the limit of many atoms reduces to a single qudit Lindbladian with quadratic nonlinearity. We describe three smoking guns for nonlinear evolutions: power law decay and dephasing rates; dephasing rates that take a continuous range of values depending on the initial data and finally, anomalous flow of the Bloch ball towards a hemisphere.

An introduction to the theory of teleportation.

We derive the relativistically exact eikonal equation for ring interferometers undergoing deformation. For ring interferometers that undergo slow deformation we describe the two leading terms in the adiabatic expansion of the phase shift. The leading term is independent of the refraction index n and is given by a line integral generalizing results going back to Sagnac for nondeforming interferometers to all orders in beta = |v|/c. In the nonrelativistic limit this term is O(beta). The next term in the adiabaticity has the form of a double integral, it is of order beta(0) and depends on the refractive index n. It accounts for nonreciprocity due to changing circumstances in the fiber. The adiabatic correction is often comparable to the Sagnac term. In particular, this is the case in Fizeau's interferometer. Besides providing a mathematical framework that puts all ring interferometers under a single umbrella, our results strengthen earlier results and generalize them to fibers with chromatic dispersion.

We present a special-relativistic analysis of deformable interferometers where counter propagating beams share a common optical path. The optical path is allowed to change rather arbitrarily and need not be stationary. We show that, in the absence of dispersion the phase shift has two contributions. To leading order in $v/c$ one contribution is given by Wang empirical formula for deformable Sagnac interferometers. The second contribution is due to the stretching of the optical path and we give an explicit formula for this stretch term valid to first order in $v/c$. The analysis provides a unifying framework incorporating the Sagnac, Wang and Fizeau effects in a single scheme and gives a rigorous proof of Wang empirical formula.

We construct Lindbladians associated with controlled stochastic Hamiltonians in weak coupling. This allows to determine the power spectrum of the noise from measurements of dephasing rates; to optimize the control and to test numerical algorithms that solve controlled stochastic Schrodinger equations. A few examples are worked out in detail.

The introduction to the Winger Medal 2014, and laudatio for its recepient, can be viewed in the PDF.

Aharonov and Casher showed that Pauli Hamiltonians in two dimensions have gapless zero modes. We study the adiabatic evolution of these modes under the slow motion of N fluxons with fluxes Phi(a) is an element of R. The positions, r(a) is an element of R-2, of the fluxons are viewed as controls. We are interested in the holonomies associated with closed paths in the space of controls. The holonomies can sometimes be abelian, but in general are not. They can sometimes be topological, but in general are not. We analyse some of the special cases and some of the general ones. Our most interesting results concern the cases where holonomy turns out to be topological which is the case when all the fluxons are subcritical, Phi(a) < 1, and the number of zero modes is D = N - 1. If N >= 3 it is also non-abelian. In the special case that the fluxons carry identical fluxes the resulting anyons satisfy the Burau representations of the braid group. (C) 2014 Elsevier Inc. All rights reserved.

The Chern numbers for Hofstadter models with rational flux 2 pi p/q are partially determined by a Diophantine equation. A mod q ambiguity remains. The resolution of this ambiguity is only known for the rectangular lattice with nearest neighbors hopping where it has the form of a 'window condition'. We study a Hofstadter butterfly on the triangular lattice for which the resolution of ambiguity is open. In the model many pairs (p, q) satisfy a window condition which is shifted relative to the window of the square model. However, we also find pairs (p, q) where the Chern numbers do not belong to any contiguous window. This shows that the rectangular model and the one we study on the triangular lattice are not adiabatically connected: many gaps must close. Our results suggest the conjecture that the mod q ambiguity in the Diophantine equation generically reduces to a sign ambiguity.

When parameters are varied periodically, charge can be pumped through a mesoscopic conductor without applied bias.Here, we consider the inverse effect in which a transport current drives a periodic variation of an adiabatic degree of freedom.This provides a general operating principle for adiabatic quantum motors which we discuss here in general terms.We relate the work performed per cycle on the motor degree of freedom to characteristics of the underlying quantum pump and discuss the motors' efficiency.Quantum motors based on chaotic quantum dots operate solely due to quantum interference, and motors based on Thouless pumps have ideal efficiency.

The Chern numbers for Hofstadter models with rational flux 2*pi*p/q are partially determined by a Diophantine equation. A Mod q ambiguity remains. The resolution of this ambiguity is only known for the rectangular lattice with nearest neighbors hopping where it has the form of a "window condition". We study a Hofstadter butterfly on the triangular lattice for which the resolution of ambiguity is open. In the model many pairs (p,q) satisfy a window condition which is shifted relative to the window of the square model. However, we also find pairs (p,q) where the Chern numbers do not belong to any contiguous window. This shows that the rectangular model and the one we study on the triangular lattice are not adiabatically connected: Many gaps must close. Our results suggest the conjecture that the mod q ambiguity in the Diophantine equation generically reduces to a sign ambiguity.

We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.

We study the adiabatic response of open systems governed by Lindblad evolutions. In such systems, there is an ambiguity in the assignment of observables to fluxes (rates) such as velocities and currents. For the appropriate notion of flux, the formulas for the transport coefficients are simple and explicit and are governed by the parallel transport on the manifold of instantaneous stationary states. Among our results we show that the response coefficients of open systems, whose stationary states are projections, is given by the adiabatic curvature.