From Geometry and Chaos
to Quantum Information and Neurobiology

Symposium in honour of Marek Kuś 60th birthday

Warsaw, April 24-25, 2015

Schedule

Friday (24 April)
Session 1 (Student's life)
chair: I. Białynicki-Birula
900 - 940M. Lewenstein
A Portrait of the Physicists as a Young Man Marek at the Frontiers of Quantum Theory ≫
In my lecture I review the history of my friendship with Marek Kuś from the high school years till today from the perspective of our joint scientific encounters. Stochastic processes, exact solutions, chaos and randomness, quantum dynamics, entanglement, quantum correlations and mathematics played particular role in these events. I will try place our joint works in the context of the seminal achievements of Marek and others.
940 - 1020K. Rzążewski
Stochastic processes in physics of cold bosons ≫
My two joint papers with Marek were devoted to the applications of stochastic processes in quantum physics. Now, with a number of coworkers, we apply the methods of random variables to describe various experiments in the theory of cold quantum gases
1020 - 1050Coffee break
Session 2 (Chaotic life)
chair: J. Zakrzewski
1050 - 1130F. Haake
Different paths to spectral universality ≫
Numerical case studies reveal that dynamics with full chaos in their classical limit show universal fluctuations in their two-point function of the quantum level density, at least within the window(s) of (quasi-)energies where correlations persist above some small noise level. Good understanding of such universality has by now been reached by four different methods: (i) Random matrix theory provides ensembles of (Hermitian and unitary) matrices phenomenologically describing symmetry classes of Hamiltonians of Floquet maps and predicts closed-form expressions for the two-point function within certain symmetry classes; moreover, the variances of that function are shown to be inversely proportional to the matrix size N such that for large N all matrices have the same (universal) spectral fluctuations. (ii) 'Level dynamics' maps the dependence of quantum levels on some control parameter to the time evolution of some fictitious classical many-partical system whose equilibrium statistics is equivalent to random-matrix theory. (iii) Gutzwiller's periodic-orbit theory allows to calculate spectral characteristics like the two-point function as the sum of contributions from bunches of near action degenerate orbits, thus recovering the RMT results for individual quantum systems. (iv) The field theoretic method known as supersymmetric sigma model reveals the periodic-orbit sums as perturbation expansions and even comes with more powerful non-perturbative procedures. I shall briefly describe the relative status of the four approaches.
1130 - 1210L. Sirko
Can one hear the shape of a network? ≫
Can one hear the shape of a network? This is a modification of the famou question of Mark Kac "Can one hear the shape of a drum?" which can be asked in the case of scattering systems such as microwave networks and quantum graphs. It addresses an important mathematical problem whether scattering properties of such systems are uniquely connected to theirshapes?
1210 - 1250K. Życzkowski
Extreme value statistics for random unitary matrices and quantum entanglement ≫
To describe statistical properties of unitary evolution operators we propose to consider the distributionsof the smallest and the largest spacing between the neighbouring eigenphases. Expected valuesof the extreme spacings are found for three canonical ensembles of random unitary matrices of order N and their distributions are discussed in the asymptotic case. Furthermore, we analyze the distribution of quantum entanglement for random pure states of quantum  multipartite systems and identify states for which certain measures of entanglement achieve extremal values.
1250 - 1420Lunch break
Session 3 (Geometric life)
chair: M. Gajda
1420 - 1500G. Marmo
The Geometry of Density States,Observables and Evolution ≫
In this talk I shall discuss the differential manifold structure of the quantum states and describe in geometrical terms the Lie-Jordan algebra associated with observables. I will also discuss the geometrical version of the Kossakowski-Lindblad operator and provide an interpretation in terms of the geometrical structures associated with the Lie-Jordan algebra.
1500 - 1540J. Grabowski
Entanglement in arbitrary parastatistics ≫
We analyze the concept of entanglement for multipartite system with bosonic and fermionic constituents and its generalization to systems with arbitrary parastatistics. We use the representation theory of symmetry groups to formulate a unified approach to this problem in terms of simple tensors with appropriate symmetry. For an arbitrary parastatistics, we define the S-rank, generalizing the notion of the Schmidt rank, which serves for distinguishing entanglement of pure states.
1540 - 1610Coffee break
Session 4 (Information life)
chair: K. Banaszek
1610 - 1650B. Englert
Sampling from the quantum state space ≫
Various applications need random samples of quantum states of good quality. For example, Monte Carlo integration over regions in the state space is needed in the context of quantum state estimation; or one may wonder whether a randomly chosen state has certain properties, such as being entangled; or one wishes to check a conjecture about quantum states on many randomly chosen states. I'll discuss various sampling strategies and algorithms.
1650 - 1730A. Buchleitner
Benchmarking BosonSamplers ≫
BosonSampling currently enjoys some popularity as an incident of the quantum simulation of "complex" many particle quantum dynamics. Since the number of interfering many-particle amplitudes rapidly increases with the number of input and output modes of a many-particle scattering device (as well as with the number of injected particles), classical computing devices are easily saturated when it comes to fully characterize the many particle state upon transmission. This immediately raises the question of how to certify the reliability of such quantum simulators, and we here propose an efficient statistical solution to this problem.
1730 - 1810F. Mintert
Complete positivity of non-Markovian quantum dynamics ≫
Truncated hierarchical equations of motion describe the dynamics of non-Markovian systems very well. Approximations in microscopic derivations, however, typically result in loss of complete positivity. We derive sufficient conditions for truncated hierarchical equations of motion to induce valid quantum channels.
1900Dinner (Restaurant Vivandier)
Saturday (25 April)
Session 5 (Offspring's life)
chair: J. Mostowski
900 - 940D. Wójcik
Common kinematics for neural activity and mice behavior (or what a theoretical physicists does in experimental biology) ≫
Neural cells - the neurons - are complex analog computers encoding incoming information into sequences of unitary events called action potentials or spikes. To understand computations performed by the brain we first need a precise language to discuss these spike trains. The accepted language is that of point processes. Interestingly, it is also useful in description of mice behavior in IntelliCages, modern cages housing multiple mice for studies of social behavior. In my talk I will describe briefly these two remote levels of animal functioning illustrating them with examples from specific experiments. I will show how increasing language precision can provide biologically interesting results.
940 - 1020R. Demkowicz-Dobrzański
Coherence and decoherence - on fundamental sensitivity limits of quantum probes in metrology and computation ≫
The extent to which quantum features such as coherence and entanglement can be utilized in practical measurement or computation protocols crucially depends on the ability to reduce detrimental effects of decoherence. I will show how to derive fundamental limitations on quantum enhancement in general quantum metrological protocols and based on this how to infer the performance of Grover algorithm in the presence of noise.
1020 - 1050Coffee break
1050 - 1130A. Sawicki
Universality of beamsplitters and control theory ≫
I will show how one can prove universality of a real beamsplitter in quantum optics using some fundamental theorems from control theory and a few magic formulas valid for SO(N) group. This is unpublished work in progress.
1130 - 1210M. Oszmaniec
Creation of superposition of unknown quantum states ≫
The existence of superpositions of pure quantum states is one of the most intriguing features of quantum mechanics.  In the talk I will systematically study the problem of creation of superpositions of unknown quantum states.  First, I will present a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, I will show a unique probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the referential pure state. Thirdly, I will discuss quantum channels that give the optimal performance for the approximate creation of superpositions of two unknown quantum states.
1210Happy birthday (birthday cake :-) )

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