Switching off the reservoir through nonstationary quantum systems

In this paper, we demonstrate that the inevitable action of the environment can be substantially weakened when considering appropriate nonstationary quantum systems. Beyond protecting quantum states against decoherence, an oscillating frequency can be engineered to make the system-reservoir coupling almost negligible. Differently from the program for engineering reservoir and similarly to the schemes for dynamical decoupling of open quantum systems, our technique does not require previous knowledge of the state to be protected. However, differently from the previously-reported schemes for dynamical decoupling, our technique does not rely on the availability of tailored external pulses acting faster than the shortest timescale accessible to the reservoir degree of freedom.

Combinatorial identities and quantum state densities of supersymmetric sigma models on N-folds

There is a remarkable connection between the number of quantum states of conformal theories and the sequence of dimensions of Lie algebras. In this paper, we explore this connection by computing the asymptotic expansion of the elliptic genus and the microscopic entropy of black holes associated with (supersymmetric) sigma models. The new features of these results are the appearance of correct prefactors in the state density expansion and in the coefficient of the logarithmic correction to the entropy.

Quantum state density and critical temperature in M-theory

We discuss the asymptotic properties of quantum states density for fundamental p-branes which can yield a microscopic interpretation of the thermodynamic quantities in M-theory. The matching of the BPS part of spectrum for superstring and supermembrane gives the possibility of getting membrane's results via string calculations. In the weak coupling limit of M-theory, the critical behavior coincides with the first-order phase transition in the standard string theory at temperature less than the Hagedorn's temperature T-H. The critical temperature at large coupling constant is computed by considering M-theory on manifold with topology R-9 circle times T-2. Alternatively we argue that any finite temperature can be introduced in the framework of membrane thermodynamics.

Photodissociation dynamics of tert-butylnitrite following excitation to the S(1) and S(2) states. A study by velocity-map ion-imaging and 3D-REMPI spectroscopy

Excitation of tert-butylnitrite into the first and second UV absorption bands leads to efficient dissociation into the fragment radicals NO and tert-butoxy in their electronic ground states (2)Π and (2)E, respectively. Velocity distributions and angular anisotropies for the NO fragment in several hundred rotational and vibrational quantum states were obtained by velocity-map imaging and the recently developed 3D-REMPI method. Excitation into the well resolved vibronic progression bands (k = 0, 1, 2) of the NO stretch mode in the S(1) ← S(0) transition produces NO fragments mostly in the vibrational state with v = k, with smaller fractions in v = k - 1 and v = k - 2. It is concluded that dissociation occurs on the purely repulsive PES of S(1) without barrier. All velocity distributions from photolysis via the S(1)(nπ*) state are monomodal and show high negative anisotropy (β ≈ -1). The rotational distributions peak near j = 30.5 irrespective of the vibronic state S(1)(k) excited and the vibrational state v of the NO fragment. On average 46% of the excess energy is converted to kinetic energy, 23% and 31% remain as internal energy in the NO fragment and the t-BuO radical, respectively. Photolysis via excitation into the S(2) ← S(0) transition at 227 nm yields NO fragments with about equal populations in v = 0 and v = 1. The rotational distributions have a single maximum near j = 59.5. The velocity distributions are monomodal with positive anisotropy β ≈ 0.8. The average fractions of the excess energy distributed into translation, internal energy of NO, and internal energy of t-BuO are 39%, 23%, and 38%, respectively. In all cases ∼8500 cm(-1) of energy remain in the internal degrees of freedom of the t-BuO fragment. This is mostly assigned to rotational energy. An ab initio calculation of the dynamic reaction path shows that not only the NO fragment but also the t-BuO fragment gain large angular momentum during dissociation on the purely repulsive potential energy surface of S(2).

Tunable molecular resonances of a double quantum dot Aharonov-Bohm interferometer

We investigate resonant tunnelling through molecular states of an Aharonov-Bohm (AB) interferometer composed of two coupled quantum dots. The conductance of the system shows two resonances associated with the bonding and the antibonding quantum states. We predict that the two resonances are composed of a Breit-Wigner resonance and a Fano resonance, of which the widths and Fano factor depend on the AB phase very sensitively. Further, we point out that the bonding properties, such as the covalent and ionic bonding, can be identified by the AB oscillations.

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed quantum nonlocality without entanglement. We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.

Production of superpositions of coherent states in traveling optical fields with inefficient photon detection

We develop an all-optical scheme to generate superpositions of macroscopically distinguishable coherent states in traveling optical fields. It nondeterministically distills coherent-state superpositions (CSS's) with large amplitudes out of CSS's with small amplitudes using inefficient photon detection. The small CSS's required to produce CSS's with larger amplitudes are extremely well approximated by squeezed single photons. We discuss some remarkable features of this scheme: it effectively purifies mixed initial states emitted from inefficient single-photon sources and boosts negativity of Wigner functions of quantum states.

Continuous-variable quantum-state sharing via quantum disentanglement

Quantum-state sharing is a protocol where perfect reconstruction of quantum states is achieved with incomplete or partial information in a multipartite quantum network. Quantum-state sharing allows for secure communication in a quantum network where partial information is lost or acquired by malicious parties. This protocol utilizes entanglement for the secret-state distribution and a class of quantum disentangling protocols for the state reconstruction. We demonstrate a quantum-state sharing protocol in which a tripartite entangled state is used to encode and distribute a secret state to three players. Any two of these players can collaborate to reconstruct the secret state, while individual players obtain no information. We investigate a number of quantum disentangling processes and experimentally demonstrate quantum-state reconstruction using two of these protocols. We experimentally measure a fidelity, averaged over all reconstruction permutations, of F=0.73 +/- 0.02. A result achievable only by using quantum resources.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

A quantum Jensen-Shannon graph kernel for unattributed graphs

In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Memory effects and geometrical considerations in open quantum systems

This thesis discusses memory effects in open quantum systems with an emphasis on the Breuer, Laine, Piilo (BLP) measure of non-Markovianity. It is shown how the calculation of the measure can be simplifed and how quantum information protocols can bene t from memory e ects. The superdense coding protocol is used as an example of this. The quantum Zeno effect will also be studied from the point of view of memory e ects. Finally the geometric ideas used in simplifying the calculation of the BLP measure are applied in studying the amount of resources needed for detecting bipartite quantum correlations. It is shown that to decide without prior information if an unknown quantum state is entangled or not, an informationally complete measurement is required. The first part of the thesis contains an introduction to the theoretical ideas such as quantum states, closed and open quantum systems and necessary mathematical tools. The theory is then applied in the second part of the thesis as the results obtained in the original publications I-VI are presented and discussed.