We consider quantum metrology with arbitrary prior knowledge of the parameter. We demonstrate that a single sensing two-level system can act as a virtual multilevel system that offers increased sensitivity in a Bayesian single-shot metrology scenario, and that allows one to estimate (arbitrary) large parameter values by avoiding phase wraps. This is achieved by making use of additional degrees of freedom or auxiliary systems not participating in the sensing process. The joint system is manipulated by intermediate control operations in such a way that an effective Hamiltonian, with an arbitrary spectrum, is generated that mimics the spectrum of a multisystem interacting with the field. We show how to use additional internal degrees of freedom of a single trapped ion to achieve a high-sensitivity magnetic field sensor for fields with arbitrary prior knowledge.

}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.118.170801}, author = {Sekatski, P. and Skotiniotis, M. and Duer, W.} } @conference {noetzel_information_2017, title = {Information Theoretic Principles of Universal Discrete Denoising}, booktitle = {2017 {INTERNATIONAL} {SYMPOSIUM} {ON} {WIRELESS} {COMMUNICATION} {SYSTEMS} ({ISWCS})}, series = {International {Symposium} on {Wireless} {Communication} {Systems}}, year = {2017}, pages = {205{\textendash}210}, abstract = {Social media platforms make tremendous amounts of data available. Often times, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, one may assume such a distorted image to be corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA).

}, isbn = {978-1-5386-2913-0}, author = {Noetzel, Janis and Winter, Andreas} } @article {biswas_interferometric_2017, title = {Interferometric visibility and coherence}, journal = {PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, volume = {473}, number = {2203}, year = {2017}, abstract = {Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. (Phys. Rev. Lett. 113, 140401. (doi: 10.1103/PhysRevLett.113.140401)), following Aberg (http://arxiv.org/abs/quant-ph/0612146), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.}, issn = {1364-5021}, doi = {10.1098/rspa.2017.0170}, author = {Biswas, Tanmoy and Garcia Diaz, Maria and Winter, Andreas} } @article {702, title = {Implementing unitary 2-designs using random diagonal-unitary matrices}, year = {2015}, url = {http://arxiv.org/abs/1502.07514}, author = {Yoshifumi Nakata and Christoph Hirche and Ciara Morgan and Winter, Andreas} } @article {708, title = {Individual Quantum Probes for Optimal Thermometry}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {6/2015}, issn = {1079-7114}, doi = {10.1103/PhysRevLett.114.220405}, author = {Correa, Luis A. and Mehboudi, Mohammad and Adesso, Gerardo and Sanpera, Anna} } @article {567, title = {Inequalities for the ranks of multipartite quantum states}, journal = {Linear Algebra and its Applications}, volume = {452}, year = {2014}, month = {07/2014}, pages = {153 - 171}, abstract = {We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We show that there exist inequalities constraining the possible distribution of ranks. This is analogous to the case of von Neumann entropy (\alpha-R\'enyi entropy for \alpha=1), where nontrivial inequalities constraining the distribution of entropies (such as e.g. strong subadditivity) are known. It was also recently discovered that all other \alpha-R\'enyi entropies for α∈(0,1)∪(1,$\infty$) satisfy only one trivial linear inequality (non-negativity) and the distribution of entropies for α∈(0,1) is completely unconstrained beyond non-negativity. Our result resolves an important open question by showing that also the case of \alpha=0 (logarithm of the rank) is restricted by nontrivial linear relations and thus the cases of von Neumann entropy (i.e., \alpha=1) and 0-R\'enyi entropy are exceptionally interesting measures of entanglement in the multipartite setting.}, issn = {00243795}, doi = {10.1016/j.laa.2014.03.035}, author = {Josh Cadney and Huber, Marcus and Noah Linden and Winter, Andreas} } @article {560, title = {Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information}, journal = {Nature Communications}, volume = {5}, year = {2014}, month = {7/2014}, abstract = {Photonics has become a mature field of quantum information science, where integrated optical circuits offer a way to scale the complexity of the setup as well as the dimensionality of the quantum state. On photonic chips, paths are the natural way to encode information. To distribute those high-dimensional quantum states over large distances, transverse spatial modes, like orbital angular momentum (OAM) possessing Laguerre Gauss modes, are favourable as flying information carriers. Here we demonstrate a quantum interface between these two vibrant photonic fields. We create three-dimensional path entanglement between two photons in a non-linear crystal and use a mode sorter as the quantum interface to transfer the entanglement to the OAM degree of freedom. Thus our results show a novel, flexible way to create high-dimensional spatial mode entanglement. Moreover, they pave the way to implement broad complex quantum networks where high-dimensionally entangled states could be distributed over distant photonic chips.}, doi = {10.1038/ncomms5502}, author = {Robert Fickler and Radek Lapkiewicz and Huber, Marcus and Lavery, Martin P.J. and Padgett, Miles J. and Anton Zeilinger} } @inbook {464, title = {Identification via Quantum Channels}, booktitle = {Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede}, series = {Lecture Notes in Computer Science}, volume = {LNCS 7777}, year = {2013}, pages = {217 - 233}, publisher = {Springer Berlin Heidelberg}, organization = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, isbn = {978-3-642-36899-8}, issn = {1611-3349}, doi = {10.1007/978-3-642-36899-8_9}, author = {Winter, Andreas}, editor = {Aydinian, Harout and Cicalese, Ferdinando and Deppe, Christian} } @article {giorgi2010, title = {Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons}, journal = {Phys. Rev. A}, volume = {81}, year = {2010}, month = {2010}, pages = {052118}, abstract = {It is known that arrays of trapped ions can be used to efficiently simulate a variety of many-body quantum systems. Here we show how it is possible to build a model representing a spin chain interacting with bosons that is exactly solvable. The exact spectrum of the model at zero temperature and the ground-state properties are studied. We show that a quantum phase transition occurs when the coupling between spins and bosons reaches a critical value, which corresponds to a level crossing in the energy spectrum. Once the critical point is reached, the number of bosonic excitations in the ground state, which can be assumed as an order parameter, starts to be different from zero. The population of the bosonic mode is accompanied by a macroscopic magnetization of the spins. This double effect could represent a useful resource for phase transition detection since a measure of the phonon can give information about the phase of the spin system. A finite-temperature phase diagram is also given in the adiabatic regime.}, keywords = {Quantum Physics}, doi = {10.1103/PhysRevA.81.052118}, author = {Giorgi, Gian Luca and Paganelli, Simone and Galve, Fernando} }