2016
May  

Marco Tomamichel SEMINAR Time: 4pm, Thursday 5 May Abstract: We prove several trace inequalities that extend the GoldenThompson and the ArakiLiebThirring inequality. to arbitrarily many matrices. As an example application of our four matrix extension of the GoldenThompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong subadditivity of the von Neumann entropy in terms of recoverability, improving on recent results in the literature. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.



Jonathan Gross Visit dates: SEMINAR Time: 4pm, Thursday 12 May Abstract: The quantum Fisher information (QFI) is a valuable tool on account of the achevable lower bound it provides for single parameter estimation. Due to the existence of incompatible quantum observables, however, the lower bound provided by the QFI cannot be saturated in the general multiparameter case. A bound demonstrated by Gill and Massar (GM) captures some of the limitations that incompatibility imposes in the multi parameter case. We further explore the structure of measurements allowed by quantum mechanics, identifying restrictions beyong those given by the QFI and GM bound. These addition restrictions give insight into the geometry of quantum state space and notions of measurement symmetry related to the QFI.


Andrew Ferguson Visit dates: SEMINAR Time: 4pm, Wednesday 18 May Abstract:


Simon Burton SEMINAR Time: 4pm, Thursday 19 May Abstract: We take a look at numerical algorithms such as matrix multiplication, fast fourier transform, and belief propagation. In each case we a find a message passing algorithm on some graphy. A physicist would call these path integrals, and this is most clearly seen considering message passing as a kind of Huygen's principle. When this works, a large sum over paths is replaced by a more efficient calculation that propagates over a wavefront. In each case, the decisive step is seen to be a kind of distributivity. The path space, and the wavefront space is different in each example and controlled by the particular structure of the problem. We review some of these applications and try to add some more.

Volker Scholz Visit dates: SEMINAR Time: 2pm, Monday 23 May Abstract: Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting manybody systems: ground states of gapped 1D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp., P08024 (2007)]. In contrast, whether MPS and more general tensor networks can accurately reproduce correlations in critical quantum systems, respectively quantum field theories, has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable Ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions. Here we provide a complete positive answer to this question in the case of MPS and 2D conformal field theory: we give quantitative estimates for the approximation error when approximating correlation functions by MPS. Our work is constructive and yields an explicit MPS, thus providing both suitable initial values as well as a rigorous justification of variational methods.


Esteban Martinez & Martin VanMourik Visit dates: SEMINAR Time: 10am, Wednesday 25 May Abstract: In the first park of the talk, we will introduce a trappedion quantum information processing setup in Innsbruck, and discuss recent results on quantum simulation of gauge field theories. Gauge theories are at the core of our current understanding of fundamental interactions, and notoriously challening to investigate using classical numerical methods. In our work, we investigate the real time dyanmics of quantum electrodynamics in one spatial dimension (the Schwinger model) and investigate phenomena such as particleantiparticle creation as a result of vacuum fluctuations and entanglement generation. In the second part of the talk, we will discuss a new setup that aims to perform similar types of algorithm, but with the prospect of scaling up to several tens to hundreds of qubits. We employ a planar slotted trap, placed in a cryogenic environment and capable of trapping multiple species of ions. In the talk we will discuss some of the challenges and solutions involved in setting up a system that meets the requirements for scalable quantum information processing. Finally, we will share a few of our first results of trap characterization.


Mario Berta Visit dates: SEMINAR Time: 4:30pm, Thursday 26 May Abstract: Shannon entropy and its multipartite extensions conditional entropy, mutual information, as well as conditional mutual information are well understood quantities in classical probability theory with manifold operational applications. Noncommutative extensions of entropy for the quantum setting are usually defined in terms of the von Neumann entropy, again leading to multipartite extensions in the form of quantum conditional entropy, quantum mutual information, and quantum conditional mutual information. In this talk I will give an axiomatic approach to quantum entropy, characterising possible noncommutative extensions of classical entropy. In particular, I will discuss when the noncommunicative entropy measure can be understood as optimising the commutative entropy measure over all measurement statistics that can be obtained from the respective quantum states. If time permits I will discuss possible applications for studying additivity problems in quantum Shannon theory.

April  

Carlton Caves Home institution: University of New Mexico Visit dates: 3/4/16  6/4/16
SEMINAR
Abstract:



Glen Evenbly Home institution: California Institute of Technology Visit dates: 11/4/16  14/4/16
SEMINAR
Abstract:

Time: 4pm, Thursday 21 April Abstract: Theoretical tools, such as the Fisher information, can reveal the ultimate performance limits of sensing devices in a variety of scenarios including optical and solidstate setups. Using these tools, one can design protocols that enable very high precision estimation, exploiting (for example) quantum phenomena such as squeezing or entanglement to great advantage. The issue of realising such an advantage in the laboratory, however, is crucial if the theoretical results are to have any meaning. The first half of my talk will concentrate on the estimation of transverse optical beam displacements [1], and will involve a foray into the controversial field of weakvalue amplification [2]. The second half of my talk will report on experimental results pushing toward sub femtosecond precision estimation of photonic time delays using a HongOuMandel interferometer. The third half (!) of my talk (time permitting) will discuss a far more ambitious proposal towards quantum sensing of magnetic fields using a hybrid device: namely, a superconducting fluxqubit coupled to a an ensemble of NV centers in diamond. [1] http://journals.aps.org/pra/abstract/10.1103/PhysRevA.92.012130 [2] http://arxiv.org/abs/1410.6252 [3] http://arxiv.org/abs/1512.03436




March  

SEMINAR Time: 4pm, Thursday 10 March Abstract: The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. I will demonstrate that the existence of symmetry breaking is a consequence of the geometric structure of the convex set of reduced density matrices of all possible many body wavefunctions of a physical system. The surfaces of these convex bodies exhibit certain features, which signal the emergence of symmetry breaking and of an associated order parameter. I will illustrate this with a few paradigmatic examples of many body systems exhibiting symmetry breaking: the quantum Ising model, the classical Ising and Potts model in 2D at finite temperature and the ideal Bose gas in three dimensions at finite temperature. This state based viewpoint on phase transitions provides a very intuitive and informative new way of drawing phase diagrams and constitutes a unique novel tool for studying exotic many body phenomena.




Kitaev Toric Code is a $Z_2$gauge invariant quantum model which has very special properties such as degenerated ground states and anyonic excitations. These are all characteristic of topologically ordered systems. The $G$quantum double (QD) models represent a generalization of the TC model with $G$ being any finite group. These models are exactly solvable models with more complicated anyonic excitations, but still topologically ordered. One way to identify the topological order in these models is by looking at their quasiparticle excitations properties as fusion rules and braiding statistics. However there is also a way to identify it by showing the QD ground state degeneracy is described by a nonlocal orderparameter which is a topological invariant of the surface $\Sigma$ on which the system lives. In this talk I will show how the the QD ground state degeneracy can be realized as a topological invariant without even looking at its quasiparticle excitations properties.



February  

Antony Milne Home institution: Imperial College London Visit dates: 24/2/16  26/2/16
SEMINAR Time: 3pm, Thursday 25 February
Abstract: The quantum steering ellipsoid formalism naturally extends the Bloch vector picture to provide a visualisation of twoqubit systems. If Alice and Bob share an entangled state then a local measurement by Bob steers Alice’s Bloch vector; given all possible measurements by Bob, the set of states to which Alice can be steered forms her steering ellipsoid inside the Bloch sphere. This gives us a novel geometric perspective on a number of quantum correlation measures such as entanglement, CHSH nonlocality and singlet fraction. In particular, by analysing a tripartite scenario we find that steering ellipsoid volumes obey a simple monogamy relation from which one can derive the wellknown CKW (CoffmanKunduWootters) inequality for the monogamy of entanglement. Following a number of recent results on the steerability of twoqubit states, we are now exploring how the steering ellipsoid formalism relates to EPRsteerability and local hidden variablelocal hidden state models. 

SEMINAR Time: 4pm, Thursday 25 February
Abstract: Fundamental laws of Nature often take the form of restrictions: nothing can move faster than light in vacuum, energy cannot be created from nothing, there are no perpetuum mobiles. It is due to these limitations that we can ascribe value to different objects and phenomena, e.g., energy would not be treated as a resource if we could create it for free. The mathematical framework developed to study the influence of such constraints on the possible transformations of quantum states is known under the collective name of resource theories. The first and second laws of thermodynamics are such fundamental constraints that force thermodynamic processes to conserve the overall energy and forbid free conversion of thermal energy into work. Thus, a natural question to ask is: what amounts to a resource when we are restricted by these laws? It has been recently identified that apart from athermality (the property of a state of having a distribution over energy levels that is not thermal), also coherence can be viewed as a second, independent resource in thermodynamics [1]. This stems from the fact that energy conservation implied by the first law restricts processing of coherence, and so possessing a state with coherence allows for otherwise impossible transformations. It also enforces a modification of the traditional Szilard argument: both athermality and coherence contribute to the free energy, however coherence remains "locked" and cannot be extracted as work. Since coherence is a thermodynamic resource, an open question is what kind of coherence processing is allowed by thermodynamic means. The aim of this presentation is to address this problem and ask: what are the allowed transformations of quantum states that are consistent with the first and second laws of thermodynamics? Our approach employs the underlying energyconservation within thermodynamics that constrains all thermodynamic evolutions to be "symmetric" under time translations. This in turn allows us to make use of harmonic analysis techniques, developed in [2], to track the evolution of coherence under thermodynamic transformations in terms of the "mode components" of the system. This constitutes a natural framework to understand coherence and allows us to separate out the constraints that stem solely from symmetry arguments from those particular to thermodynamics. This approach also implies that the existing singleshot results applicable to blockdiagonal results, constrained by thermomajorization [3], can be viewed as particular cases of our analysis when only the zeromode is present. Beyond this regime, every nonzero mode obeys independent constraints, and displays thermodynamic irreversibility similar to the zeromode. Exploiting these tools we arrive at the upper bounds on final coherences in the energy eigenbasis for quantum states undergoing timetranslation symmetric and thermodynamic processing [4]. A rich dynamics is allowed, in which coherence can be transferred among different energy levels within each mode. We show that similarly to heat flows, coherence flows show directionality due to the limitations imposed by the second law. This new kind of irreversibility adds up to the ones identified in work extraction [3] and coherence distillation. Finally, we analyse the process of converting quantum coherence to work, emphasizing the need of an external source of coherence and connecting its quality with the efficiency of the conversion process[5].
[1] M. Lostaglio, D. Jennings, and T. Rudolph, Nat. Commun. 6, 6383 (2015).



SEMINAR Time: 4pm, Thursday 18 February
Abstract: It is believed that quantum computers can perform certain tasks faster than their classical counterparts. Identifying the resource that enables this speedup is of particular interest in quantum information science. Attempts to identify the elusive quantum feature are generally backdoor attacks, studying not what is essential for speedup, but rather what is lacking in quantum circuits that can be efficiently simulated classically. In this talk, by using the welldeveloped theory of phasespace quasiprobability distributions, I will introduce two sufficient conditions for efficient classical simulation of generic quantum optics experiments: M bosonic modes prepared in an arbitrary state undergo an Mmode (trace preserving) quantum process; one generates samples by making a measurement on the M output modes [1]. These conditions show that the negativity is a necessary resource for a generic quantumoptics experiment not to be efficiently classically simulatable. As an interesting application of these conditions, I will consider implementations of boson sampling, an intermediate model of quantum computation, that use singlephoton or spontaneousparametricdownconversion sources. We have shown that above some threshold for loss and noise, the bosonsampling experiments are classically simulatable [1]. [1] S. RahimiKeshari, T. C.Ralph, and C. M. Caves, arXiv:1511.06526.


Stephanie Wehner Home institution: Delft University of Technology Visit dates: 15/2/16  29/2/16 





Beni Yoshida Home institution: Perimeter Institute Visit dates: 8/2/16  12/2/16 

Aleksander Kubica Home institution: California Institute of Technology Visit dates: 8/2/16  12/2/16 





Event contact: Wicky West/ Fran Vega
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