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.

VL - 118 ER - TY - CONF T1 - Information Theoretic Principles of Universal Discrete Denoising T2 - 2017 {INTERNATIONAL} {SYMPOSIUM} {ON} {WIRELESS} {COMMUNICATION} {SYSTEMS} ({ISWCS}) Y1 - 2017 A1 - Noetzel, Janis A1 - Winter, Andreas AB -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).

JF - 2017 {INTERNATIONAL} {SYMPOSIUM} {ON} {WIRELESS} {COMMUNICATION} {SYSTEMS} ({ISWCS}) T3 - International {Symposium} on {Wireless} {Communication} {Systems} SN - 978-1-5386-2913-0 ER - TY - JOUR T1 - Interferometric visibility and coherence JF - PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Y1 - 2017 A1 - Biswas, Tanmoy A1 - Garcia Diaz, Maria A1 - Winter, Andreas AB - 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. VL - 473 ER - TY - ICOMM T1 - Implementing unitary 2-designs using random diagonal-unitary matrices Y1 - 2015 A1 - Yoshifumi Nakata A1 - Christoph Hirche A1 - Ciara Morgan A1 - Winter, Andreas UR - http://arxiv.org/abs/1502.07514 ER - TY - JOUR T1 - Individual Quantum Probes for Optimal Thermometry JF - Physical Review Letters Y1 - 2015 A1 - Correa, Luis A. A1 - Mehboudi, Mohammad A1 - Adesso, Gerardo A1 - Sanpera, Anna VL - 114 IS - 22 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Inequalities for the ranks of multipartite quantum states JF - Linear Algebra and its Applications Y1 - 2014 A1 - Josh Cadney A1 - Huber, Marcus A1 - Noah Linden A1 - Winter, Andreas AB - 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,∞) 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. VL - 452 JO - Linear Algebra and its Applications ER - TY - JOUR T1 - Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information JF - Nature Communications Y1 - 2014 A1 - Robert Fickler A1 - Radek Lapkiewicz A1 - Huber, Marcus A1 - Lavery, Martin P.J. A1 - Padgett, Miles J. A1 - Anton Zeilinger AB - 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. VL - 5 JO - Nat Comms ER - TY - CHAP T1 - Identification via Quantum Channels T2 - Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede Y1 - 2013 A1 - Winter, Andreas ED - Aydinian, Harout ED - Cicalese, Ferdinando ED - Deppe, Christian JF - Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede T3 - Lecture Notes in Computer Science PB - Springer Berlin Heidelberg CY - Berlin, Heidelberg VL - LNCS 7777 SN - 978-3-642-36899-8 ER - TY - JOUR T1 - Ion-trap simulation of the quantum phase transition in an exactly solvable model of spins coupled to bosons JF - Phys. Rev. A Y1 - 2010 A1 - Giorgi, Gian Luca A1 - Paganelli, Simone A1 - Galve, Fernando KW - Quantum Physics AB - 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. VL - 81 ER -