Related papers: Connections and Metrics Respecting Standard Purifi…
We consider the problem of improving noisy quantum measurements by suitable preprocessing strategies making many noisy detectors equivalent to a single ideal detector. For observables pertaining to finite-dimensional systems (e.g. qubits or…
Embedding calculations that find approximate solutions to the Schr\"{o}dinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective…
Starting from the observation that reversible processes cannot increase the purity of any input state, we study deterministic physical processes, which map a set of states to a set of pure states. Such a process must map any state to the…
Quantisation on spaces with properties of curvature, multiple connectedness and non orientablility is obtained. The geodesic length spectrum for the Laplacian operator is extended to solve the Schroedinger operator. Homotopy fundamental…
Common measures of neural representational (dis)similarity are designed to be insensitive to rotations and reflections of the neural activation space. Motivated by the premise that the tuning of individual units may be important, there has…
Distillation, or purification, is central to the practical use of quantum resources in noisy settings often encountered in quantum communication and computation. Conventionally, distillation requires using some restricted 'free' operations…
The original purpose of measurements is to provide us with information about a previously unknown physical property of the system observed. In the Hilbert space formalism of quantum mechanics, this physical meaning of measurement…
We present a novel method to purify quantum states, i.e. purification through Zeno-like measurements, and show an application to entanglement purification.
We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible…
For Hermitian connections on a Hermitian complex line bundle over a Riemannian manifold $(X,g)$, we can define the ``volume", which can be considered to be the ``mirror" of the standard volume for submanifolds. We call the critical points…
To any metric spaces there is an associated metric profile. The rectifiability of the metric profile gives a good notion of curvature of a sub-Riemannian space. We shall say that a curvature class is the rectifiability class of the metric…
The problem of Hamiltonian purification introduced by Burgarth et al. [D. K. Burgarth et al., Nat. Commun. 5, 5173 (2014)] is formalized and discussed. Specifically, given a set of non-commuting Hamiltonians {h1, . . ., hm} operating on a…
We explore the landscape of the decoherence effect in mixed-state ensembles from a purification perspective. We analyze the spontaneous strong-to-weak symmetry breaking (SSSB) in mixed states triggered by local quantum channels by mapping…
We consider the results of combining two approaches developed for the design of Riemannian metrics on curves and surfaces, namely parametrization-invariant metrics of the Sobolev type on spaces of immersions, and metrics derived through…
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned…
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…
Purifying noisy entanglement is a protocol which can increase the entanglement of a mixed state (as a source)at expense of the entanglement of others(as an ancilla)by collective measurement. A protocol with which one can get a pure…
This paper treats the isometries of metric spaces of quantum states. We consider two metrics on the set all quantum states, namely the Bures metric and the one which comes from the trace-norm. We describe all the corresponding (nonlinear)…
We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the…
I describe a concrete and efficient real-space renormalization approach that provides a unifying perspective on interface states in a wide class of Hermitian and non-Hermitian models, irrespective of whether they obey a traditional…