Quantum Physics

The relation between manifold topology, observables and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated to positions and displacements on the manifold. The guiding, physically motivated, principles are i) locality, i.e. the generating role of the algebras localized in small, topological trivial, regions, ii) diffeomorphism covariance, which guarantees the intrinsic character of the analysis, iii) the exclusion of additional local degrees of freedom with respect to the Schroedinger representation. The locally normal representations of the resulting observable algebra are classified by unitary representations of the fundamental group of the manifold, which actually generate an observable, "topological", subalgebra. The result is confronted with the standard approach based on the introduction of the universal covering M ~ of M and on the decomposition of L 2 ( M ~ ) according to the spectrum of the fundamental group, which plays the role of a gauge group. It is shown that in this way one obtains all the representations of the observables iff the fundamental group is amenable. The implications on the observability of the Permutation Group in Particle Statistics are discussed.

Recent experimental progress in the field of cavity quantum electrodynamics allows to study the regime of strong interaction between quantized light and complex matter systems. Due to the coherent coupling between photons and matter-degrees of freedom, polaritons -- hybrid light-matter quasiparticles -- emerge, which can significantly influence matter properties and complex processes such as chemical reactions (strong coupling). In this thesis we propose a way to overcome these problems by reformulating the coupled electron-photon problem in an exact way in a different, purpose-build Hilbert space, where no longer electrons and photons are the basic physical entities but the polaritons. Representing an N-electron-M-mode system by an N-polariton wave function with hybrid Fermi-Bose statistics, we show explicitly how to turn electronic-structure methods into polaritonic-structure methods that are accurate from the weak to the strong-coupling regime. We elucidate this paradigmatic shift by a comprehensive review of light-matter coupling, as well as by highlighting the connection between different electronic-structure methods and quantum-optical models. This extensive discussion accentuates that the polariton description is not only a mathematical trick, but it is grounded in a simple and intuitive physical argument: when the excitations of a system are hybrid entities a formulation of the theory in terms of these new entities is natural. Finally, we discuss in great detail how to adopt standard algorithms of electronic-structure methods to adhere to the new hybrid Fermi-Bose statistics. Guaranteeing the corresponding nonlinear inequality constraints in practice requires a careful development, implementation and validation of numerical algorithms. This extra numerical complexity is the price we pay for making the coupled matter-photon problem feasible for first-principle methods.

We present a map from the travelling salesman problem (TSP), a prototypical NP-complete combinatorial optimisation task, to the ground state associated with a system of many-qudits. Conventionally, the TSP is cast into a quadratic unconstrained binary optimisation (QUBO) problem, that can be solved on an Ising machine. The size of the corresponding physical system's Hilbert space is 2 N 2 , where N is the number of cities considered in the TSP. Our proposal provides a many-qudit system with a Hilbert space of dimension 2 N log 2 N , which is considerably smaller than the dimension of the Hilbert space of the system resulting from the usual QUBO map. This reduction can yield a significant speedup in quantum and classical computers. We simulate and validate our proposal using variational Monte Carlo with a neural quantum state, solving the TSP in a linear layout for up to almost 100 cities.

Thermodynamics of quantum systems and associated quantum technologies are rapidly developing fields, which have already delivered several promising results, as well as raised many intriguing questions. Many-body quantum technologies present new opportunities stemming from many-body effects. At the same time, they pose new challenges related to many-body physics. In this short review we discuss some of the recent developments on technologies based on many-body quantum systems. We mainly focus on many-body effects in quantum thermal machines. We also briefly address the role played by many-body systems in the development of quantum batteries and quantum probes.

The purpose of this article is to derive a Markovian approximation of the reduced time dynamics of observables for the Pauli-Fierz Hamiltonian with a precise control of the error terms. In that aim, we define a Lindblad operator associated to the corresponding quantum master equation. In a particular case, this allows to study the transition probability matrix.

In early 90's Mandel and coworkers performed an experiment \cite{mandel} to examine the significance of quantum phase operators by measuring the phase between two optical fields. We show that this type of quantum mechanical phase measurement is possible for matter-waves of ultracold atoms in a double well. In the limit of low number of atoms quantum and classical phases are drastically different. However, in the large particle number limit, they are quite similar. We assert that the matter-wave counterpart of the experiment \cite{mandel} is realizable with the evolving technology of atom optics.

We demonstrate how to create maximal entanglement between two qubits that are encoded in two spectrally distinct solid-state quantum emitters embedded in a waveguide interferometer. The optical probe is provided by readily accessible squeezed light, generated by parametric down-conversion. By continuously probing the emitters, the photon scattering builds up entanglement with a concurrence that reaches its maximum after O(10^1) photo-detection events. Our method does not require perfectly identical emitters, and accommodates spectral variations due to the fabrication process. It is also robust enough to create entanglement with a concurrence above 99% for 10% scattering photon loss, and can form the basis for practical entangled networks.

Two important results of quantum physics are the \textit{no-cloning} theorem and the \textit{monogamy of entanglement}. The former forbids the creation of an independent and identical copy of an arbitrary unknown quantum state and the latter restricts the shareability of quantum entanglement among multiple quantum systems. For distinguishable particles, one of these results imply the other. In this Letter, we show that in qubit systems with indistinguishable particles (where each particle cannot be addressed individually), a maximum violation of the monogamy of entanglement is possible by the measures that are monogamous for distinguishable particles. To derive this result, we formulate the degree of freedom trace-out rule for indistinguishable particles corresponding to a spatial location where each degree of freedom might be entangled with the other degrees of freedom. Our result removes the restriction on the shareability of quantum entanglement for indistinguishable particles, without contradicting the no-cloning theorem.

We present a genuine coherence measure based on a quasi-relative entropy as a difference between quasi-entropies of the dephased and the original states. The measure satisfies non-negativity and monotonicity under genuine incoherent operations (GIO). It is strongly monotone under GIO in two- and three-dimensions, or for pure states in any dimension, making it a genuine coherence monotone. We provide a bound on the error term in the monotonicity relation in terms of the trace distance between the original and the dephased states. Moreover, the lower bound on the coherence measure can also be calculated in terms of this trace distance.

We generalize the quantum Fisher information flow proposed by Lu \textit{et al}. [Phys. Rev. A \textbf{82}, 042103 (2010)] to the multi-parameter scenario from the information geometry perspective. A measure named the \textit{intrinsic density flow} (IDF) is defined with the time-variation of the intrinsic density of quantum states (IDQS). IDQS measures the local distinguishability of quantum states in state manifolds. The validity of IDF is clarified with its vanishing under the parameter-independent unitary evolution and outward-flow (negativity) under the completely positive-divisible map. The temporary backflow (positivity) of IDF is thus an essential signature of the non-Markovian dynamics. Specific for the time-local master equation, the IDF decomposes according to the channels, and the positive decay rate indicates the inwards flow of the sub-IDF. As time-dependent scalar fields equipped on the state space, the distribution of IDQS and IDF comprehensively illustrates the distortion of state space induced by its environment. As example, a typical qubit model is given.