12th Central European Quantum Information Processing Workshop
1821 June 2015, Telč, Czech Republic
List of posters

ShinLiang Chen
Quantifying temporal and spatiotemporal steering provides a practical measure of strong nonMarkovianity

Mikolaj Czechlewski
Asymmetric Bell Experiment with Inefficient Detectors
The main aim of the research was finding a solution of the following experimental problem. In the practical realisation of Bell experiment for two parties it is hard to ensure the same conditions in Alice and Bob’s laboratories. For instance, a source of photons can be closer Alice’s laboratory then Bob’s or vice versa. Therefore efficiencies of Alice and Bob’s detectors of are different. Indeed, one can say that avoiding the asymmetry in the real Bell experiment is impossible. Taking into account the asymmetry arising in a laboratory, an experimentalist, who wants to perform device independent Bell’s test of chosen inequality, must decide which detector should each party receive. In other words, which laboratory should belong to Alice and which to Bob. Moreover he must know, which representation of the selected Bell inequality should he consider. As an object of study the I3322 inequality was chosen because of its natural asymmetry. For this inequality two postselection strategies was considered: discard strategy and assignment strategy.

Giacomo De Palma
Normal form decomposition for GaussiantoGaussian superoperators
We explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these GaussiantoGaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of onemode mappings we also show that any GaussiantoGaussian superoperator can be expressed as a concatenation of a phasespace dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition. While a similar decomposition is shown to fail in the multimode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.

Giuseppe Florio
Sampling entangled states: polarized ensembles of random states and entanglement spectrum
We investigate the generation and properties of random quantum pure states using polarized ensembles. These ensembles are obtained by linear superposition of two random pure states with suitable distributions. We will use the obtained results for two purposes: on the one hand we will be able to derive an efficient strategy for sampling states from isopurity manifolds. On the other, we will characterize the deviation of a pure quantum state from separability under the influence of noise. Moreover, we discuss the spectral properties of the reduced states of one of the parties. Our analysis suggests that these polarized random states exhibit some interesting phase transitions in the entanglement spectrum.

Piotr Gawron
Generalized open quantum walks on Apollonian networks
We introduce the model of generalized open quantum walks on networks using the Transition Operation Matrices formalism. We focus our analysis on the mean first passage time and the average return time in Apollonian networks. These results differ significantly from a classical walk on these networks. We show a comparison of the classical and quantum behaviour of walks on these networks.

Adam Glos
Inference in quantum Bayesian networks
Belief propagation algorithm is a popular method for deriving inference amongst large number of random variables. We present a quantum version of the algorithm which is used to reasoning in quantum Bayesian networks (QBN). Classical probability theory can be generalized by quantum information theory, where probability distributions and conditional probability distributions can be described by density operators and conditional density operators, which are fundamental in describing quantum Bayesian network. We show method of transition from the structure of QBN to junction tree corresponded with set of quantum potentials and the algorithm of inference amongst the potentials.

Aurel Gabris
Discrete time quantum walks on dynamically changing graphs
Quantum simulators are advanced quantum systems that can be used to answer challenging questions about complex systems. Among emerging candidates for analysing quantum transport phenomena are quantum walks. In particular, quantum walks on percolation structures constitute an attractive platform for studying open system dynamics of random media. We present an implementation of quantum walks differing from the previous experiments by achieving dynamical control of the underlying graph structure. We demonstrate the evolution of an optical timemultiplexed quantum walk over six double steps, revealing the intricate interplay between the internal and external degrees of freedom. The observation of clear nonMarkovian signatures in the coin space testifies the high coherence of the implementation and the extraordinary degree of control of all system parameters. Our work is the proofofprinciple experiment of a quantum walk on a dynamical percolation graph, paving the way towards complex simulation of quantum transport in random media.

Zeynep Nilhan Gurkan
Energy Localization and Geometric Phase in Maximally Entangled Two Qubit Phase Space
In the present work, motivated by Möbius transformation and its action on symmetric points of the generalized circle in complex plane, the system of symmetrical spin coherent states corresponding to antipodal qubit states is introduced. It implies the maximally entangled spin coherent states basis, which in the limiting cases reduces to the Bell basis. A specific property of our symmetric image coherent states is that they never become unentangled for any value from complex plane. By the reduced density matrix and the concurrence determinant methods, it is shown that our basis is maximally entangled. In addition we find that the average of spin operators in these states vanish, as it must be according to another, operational definition of completely entangled states. Universal one qubit and two qubit gates in this new basis are calculated and time evolution of these states for some spin systems is derived. We find that in maximally entangled two qubit phase space, the average energy for XYZ model in two qubit case shows regular finite energy localized structure with characteristic extremum points. Also geometric phase is calculated for these maximally entangled states.

Anna Jenčová
Optimal input states for discrimination of quantum channels
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum states. For discrimination of two channels, we get a simple condition for existence of an optimal tester with any given input state with maximal Schmidt rank, in particular with a maximally entangled input state. These results are applied to some examples, including covariant families of channels, qubit channels, unitary channels and measurements.

Waldemar Kłobus
Violation of monogamy relations and communication strength of signalling boxes
In any theory satisfying the nosignalling principle correlations generated among spatially separated parties in a Belltype experiment are subject to certain constraints known as monogamy relations. Violation of such a relation implies that correlations arising in the experiment must be signalling, and, as such, they can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this aim, we first provide a framework associating them with classical channels whose capacities are then used to quantify the usefulness of these correlations in sending information. Finally, we determine the minimal amount of information that can be sent using signalling correlations violating the monogamy relation associated to the chained Bell inequalities.

Dariusz Kurzyk
Quantum Bayesian networks
This paper presents a generalization of probability theory in a field of quantum information theory, where random distributions and conditional random distributions are generalized by density operators and conditional density operators, respectively. Introduced generalized probability distributions are fundamental in describing quantum Bayesian networks, which describes an acausal relationship between quantum systems. The result of reasoning performance over the networks was presented in a Monty Hall game.

Justyna Łodyga
Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defectedlattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phaseflip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for two other codes. We show that the fidelity of the protected qubit in the noisy scenario in a large code size limit is of 1O(p), where p is a probability of error on a single qubit per time step. Regarding Haah code we provide noiseless scheme, leaving the noisy case as an open problem.

Edgar A Aguilar Lozano
No External Randomness is Needed to Send Private Messages
Randomness is a highly valuable resource which is difficult to come by, especially in a world where we regard everyone as an adversary. Recent advances in the field of Randomness Extraction and Expansion have given the needed mathematical tools to prove that it is possible for two parties to establish a secret cryptographic key when randomness is not available as a resource. Instead of requiring the parties to have initial random seeds, we are able to show that it is sufficient for the message they want to communicate to be (partially) unknown to the adversaries. Hence, this article minimizes the assumptions needed to perform secure Device Independent Quantum Key Distribution (DIQKD).

Kimmo Luoma
Adaptive joint measurements and EPR steering

Nikolay Nahimov
Quantum walks on twodimensional grids with multiple marked locations
Although quantum walks have been studied for more than a decade, many questions are still open. One such very basic question is the dependence of the running time of a quantum walk algorithm on the number and the placement of marked locations. We study search by quantum walks on twodimensional grids according to [Proceedings of SODA’05, 10991108, 2005
]. The original paper analyses the behaviour of the algorithm for one or two marked locations. We move beyond two marked locations and study the behaviour of the algorithm for an arbitrary configuration (the number and the placement) of marked locations. We show that the placement of marked locations has much bigger effect on the running time and probability than the number of marked locations. We present two extreme examples. The first example is two configurations  one of k2 marked locations and another of k marked locations  having the same number of steps and probability to find a marked location. The second example is two configurations of k marked locations having asymptotically different number of steps – O(sqrt{N}/sqrt{k}) and O(sqrt{N}), respectively. Additionally, we study the dependence of the algorithm on the coin transformation. We show what the most natural coin  Grover's diffusion transformation  has a wide class of exceptional configurations of marked locations, for which the probability to find any of marked locations does not grow over time. Until now the only known exceptional configuration was the "diagonal configuration".

Mateusz Ostaszewski
Quantum image classification using principal component analysis
In this paper we present a novel quantum algorithm for classiﬁcation of images. The algorithm is constructed using principal component analysis and von Neuman quantum measurements. The input of the algorithm is a quantum representation of an grayscale image which we want to test. Algorithm requires a set of principal components. The output is “yes” or “no” and answers the question whether the image exhibits features represented by principal components.

Łukasz Pawela
Asymptotic behavior of trace distance
In this work we study the distinguishably of large quantum states. Helstrom theorem gives us that the proba
bility of the correct distinction with the usage of measurements is bounded by the trace distance.
The above bound can be achieved for measurements being the projections. In this work we will show, that for large dimensions and
random states this probability stabilizes on a nontrivial
value 0,784155.

Carlos Pineda
Measuring and using nonmarkovianity
We construct measures for the nonMarkovianity of quantum evolution with a physically meaningful interpretation. We first provide a general setting in the framework of channel capacities and propose two families of meaningful quantitative measures, based on the largest revival of a channel capacity, avoiding some drawbacks of other nonMarkovianity measures. We relate the proposed measures to the task of information screening. This shows that the nonMarkovianity of a quantum process may be used as a resource. Under these considerations, we analyze two paradigmatic examples, a qubit in a quantum environment with classically mixed dynamics and the JaynesCummings model.

Zbigniew Puchała
Mutually coherent states, mutually entangling gates and nondisplacable manifolds
An equator of a sphere is nondisplacable as any two great circles do interset. Such a statement can be generalized for a great torus embedded in complex projective space. This fact implies that for any choice of two orthogonal measurements of a pure state of an arbitrary size N there exist a mutually coherent state, such that the sum of the entropies characterizing its measurements in both basis is maximal. If the number of measurements L=N+1, the sum of entropies becomes minimal for a collection of mutually unbiased bases. Analogous approach is used to study entanglement with respect to L different splittings of the composite system, linked by bipartite quantum gates. For any twoqubit unitary gate there exist mutually separable states and mutually entangled states with respect to both splittings of the system. The latter statement follows from the fact that real projective space RP3 < CP3 is nondisplacable. For L=3 splittings the maximal sum of L entanglement entropies achieves its minimum for a collection of three mutually entangled bases, formed by two mutually entangling gates.

Ashutosh Rai
Limited preparation contextuality in quantum theory leads to Cirel'son bound
KochenSpecker (KS) theorem lies at the heart of quantum foundation. It establishes impossibility of explaining predictions of quantum theory by any noncontextual ontological model. The notion of KS contextuality has been generalized for arbitrary experimental procedures, viz., preparation procedure, measurement procedure, and transformation procedure. Interestingly, it has been shown that preparation contextuality powers parityoblivious multiplexing, a two party information theoretic game. Thus, using resources of a given operational theory, the maximum success probability achievable in such a game suffices as a bonafide measure of preparation contextuality for the underlying theory. In this work we show that preparation contextuality in quantum theory is more restricted compared to a general operational theory known as boxworld. Moreover, we find that this restricted feature of quantum theory implies the quantitative bound on quantum nonlocality as depicted by the Cirel'son bound.

Matteo Rosati
Achieving the Holevo bound via a bisection decoding protocol
We present a decoding protocol to realize transmission of classical information through a quantum channel at asymptotically maximum capacity, achieving the Holevo bound and thus the optimal communication rate. This method, in contrast to the Pretty Good Measurement and inspired by the sequential decoding protocol, previously proposed, makes use of “yesno” measurements in a bisection fashion, thus determining which codeword was sent in log2 N steps, N being the number of codewords. Our analysis shows that, as long as N is below the limit imposed by the Holevo bound, the error probability can be sent to zero asymptotically in the codewords’ length.

László Ruppert
Homodyning without local oscillator
We investigated the case of homodyne measurement where no local oscillator is available but only a bright thermal source is present instead. Our work shows that we can estimate the covariance matrix of the signal state even in this case, which can lead to some interesting applications in quantum optics.

Krishnakumar Sabapathy
Quantum optical channels that output only 'classical' states
The GlauberSudarshan diagonal weight function provides a natural divide between classical and nonclassical states of continuous variables systems. Based on this division, a channel is said to be classical (or nonclassicality breaking) if the output of the channel is always classical for any input state. We classify all multimode Bosonic Gaussian channels that are classical. This is achieved by introducing a new criterion that needs to be satisfied by the matrices representing the Bosonic Gaussian channels, which can be interpreted as a kind of quantum benchmark for Bosonic Gaussian channels. We then prove a striking duality between classical and entanglement breaking Bosonic Gaussian channels, namely, we show that every classical Bosonic Gaussian channel is entanglement breaking, whereas every entanglement breaking Bosonic Gaussian channel can be rendered classical by the action of a Gaussian unitary whose active component consists only of parallel singlemode canonical squeezing elements. Consequently, Bosonic Gaussian channels that are classical have additive classical capacity and zero quantum capacity.

Przemysław Sadowski
Arbitrarily large polynomial speedup in quantum search with prior knowledge
The aim of this paper is to develop a framework for realising quantum network algorithms with use of prior knowledge about the structure of the network. In particular we consider a network that consists of different types of edges such that the transitions between nodes result in extra edgedependent phase shift. We combine amplitude amplification and phase estimation to develop an algorithm for exploring such networks. We show that in such model one is able to perform quantum search algorithms with arbitrarily large polynomial speedup compared to the quantum search that neglects the extra phase shift. We get hyperbolic decay of the search complexity with exponential growth of the nodes degree.

Roope Uola
Joint measurability of generalized measurements implies classicality
The fact that not all measurements can be carried out simultaneously is a peculiar feature of quantum mechanics and responsible for many key phenomena in the theory, such as complementarity or uncertainty relations. For the special case of projective measurements quantum behavior can be characterized by the commutator but for generalized measurements it is not easy to decide whether two measurements can still be understood in classical terms or whether they show already quantum features. We prove that generalized measurements which do not fulfill the notion of joint measurability are nonclassical, as they can be used for the task of quantum steering. This shows that the notion of joint measurability is, among several definitions, the proper one to characterize quantum behavior. Moreover, the equivalence allows to derive novel steering inequalities from known results on joint measurability and new criteria for joint measurability from known results on the steerability of states.

Sabine Wölk
The width of entanglement in spin chains
Entanglement of multipartite system can be characterized with different variables such as the entanglement depth, which is equal to the number of entangled particles or the entanglement width, indicating how far apart entangled particles are. The entanglement width is a very good indicator for the type of interaction present in a system as well as for quantum phase transitions. However, the investigation of the entanglement width done so far required addressability of single subsystems. Here, we present new investigation tools to detect the width of entanglement based on global observables which makes addressing of single particles unnecessary. We apply the criteria to different examples and point out the difference between entanglement depth and entanglement width.
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