We study weak ergodicity breaking in a one-dimensional, non-integrable spin-1 XY model. We construct for it an exact, highly excited eigenstate, which despite large energy density, can be represented analytically by a finite bond-dimension matrix product state (MPS) with area-law entanglement. Upon a quench to a finite Zeeman field, the state undergoes periodic dynamics with perfect many-body revivals, in stark contrast to other generic initial states which instead rapidly thermalize. This dynamics can be completely understood in terms of the evolution of entangled virtual spin-1/2 degrees of freedom, which in turn underpin the presence of an $O(L)$ tower of strong-eigenstate thermalization hypothesis (ETH)-violating many-body eigenstates. The resulting quantum many-body scars are therefore of novel origin. Our results provide important insights into the nature and entanglement structure of quantum many-body scars.

In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by using the connection between the hydrodynamic variables and the Schr\"odinger wave function. One of the main purposes of the present paper is to overcome the need to postulate the a priori existence of a wave function that generates the hydrodynamic data. Moreover, we introduce a novel functional, related to the chemical potential in the quantum probability density $\rho\,dx$, which allow us to obtain stability properties for a large class of weak solutions in the finite energy space.

Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum computers. These systems will require codes which utilize the full computational space. In this paper we show that codes for these systems can be derived from already known codes, a result which could prove to be very useful.

With the emergence of quantum computing and quantum networks, many communication protocols that take advantage of the unique properties of quantum mechanics to achieve a secure bidirectional exchange of information, have been proposed. In this study, we propose a new quantum communication protocol, called Continuous Quantum Secure Dialogue (CQSD), that allows two parties to continuously exchange messages without halting while ensuring the privacy of the conversation. Compared to existing protocols, CQSD improves the efficiency of quantum communication. In addition, we offer an implementation of the CQSD protocol using the Qiskit framework. Finally, we conduct a security analysis of the CQSD protocol in the context of several common forms of attack.

In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also relate to the already existing theory for the former. This makes it clear what the similarities and differences between the two geometric phases are. We discuss and motivate constraints on the two phases. Furthermore, we discuss some topological properties of the holonomy of `real' quantum systems, and we introduce higher-order geometric phases for not necessarily cyclic dynamical systems of mixed states. In a final chapter, we apply the theory developed for the geometric phase of Sj\"{o}qvist et al. to geometric uncertainty relations, including some new "quantum speed limits".

We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy for scalar fields propagating under the influence of a one-dimensional crystal represented by a periodic potential formed by an infinite array of identical potentials with compact support.

Strong coupling between a single quantum emitter and an electromagnetic mode is one of the key effects in quantum optics. In the cavity QED approach to plasmonics, strongly coupled systems are usually understood as single-transition emitters resonantly coupled to a single radiative plasmonic mode. However, plasmonic cavities also support non-radiative (or "dark") modes, which offer much higher coupling strengths. On the other hand, realistic quantum emitters often support multiple electronic transitions of various symmetry, which could overlap with higher order plasmonic transitions -- in the blue or ultraviolet part of the spectrum. Here, we show that vacuum Rabi splitting with a single emitter can be achieved by leveraging dark modes of a plasmonic nanocavity. Specifically, we show that a significantly detuned electronic transition can be hybridized with a dark plasmon pseudomode, resulting in the vacuum Rabi splitting of the bright dipolar plasmon mode. We develop a simple model illustrating the modification of the system response in the "dark" strong coupling regime and demonstrate single photon non-linearity. These results may find important implications in the emerging field of room temperature quantum plasmonics.

Quantum cryptography promises security based on the laws of physics with proofs of security against attackers of unlimited computational power. However, deviations from the original assumptions allow quantum hackers to compromise the system. We present a side channel attack that takes advantage of ventilation holes in optical devices to inject additional photons that can leak information about the secret key. We experimentally demonstrate light injection on an ID~Quantique Clavis2 quantum key distribution platform and show that this may help an attacker to learn information about the secret key. We then apply the same technique to a prototype quantum random number generator and show that its output is biased by injected light. This shows that light injection is a potential security risk that should be addressed during the design of quantum information processing devices.

We discuss pretty good state transfer of multiple qubit states and provide a model for considering state transfer of arbitrary states on unmodulated XX-type spin chains. We then provide families of paths and initial states for which we can determine whether there is pretty good state transfer based on the eigenvalue support of the initial state.

We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schr\"odinger cat states, defined as orthonormalized eigenstates of $k$-th powers of nonlinear $f$-oscillator annihilation operators, with $f$ of hypergeometric type. These "$k$-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states $|z_l\rangle, l=0,1,\dots,k-1$, with $z_l=z e^{2\pi i l/k}$ a $k$-th root of $z^k$, and they interpolate between number and coherent states. This fact motivates a continuous circle representation for high $k$. We also extend our study to truncated hypergeometric functions (finite dimensional Hilbert spaces) and a discrete exact circle representation is provided. We also show how to generate $k$-hypercats by amplitude dispersion in a Kerr medium and analyze their generalized Husimi $Q$-function in the super- and sub-Poissonian cases at different fractions of the revival time.

The Quantum Approximate Optimization Algorithm (QAOA) is a general-purpose algorithm for combinatorial optimization problems whose performance can only improve with the number of layers $p$. While QAOA holds promise as an algorithm that can be run on near-term quantum computers, its computational power has not been fully explored. In this work, we study the QAOA applied to the Sherrington-Kirkpatrick (SK) model, which can be understood as energy minimization of $n$ spins with all-to-all random signed couplings. There is a recent classical algorithm by Montanari that can efficiently find an approximate solution for a typical instance of the SK model to within $(1-\epsilon)$ times the ground state energy, so we can only hope to match its performance with the QAOA. Our main result is a novel technique that allows us to evaluate the typical-instance energy of the QAOA applied to the SK model. We produce a formula for the expected value of the energy, as a function of the $2p$ QAOA parameters, in the infinite size limit that can be evaluated on a computer with $O(16^p)$ complexity. We found optimal parameters up to $p=8$ running on a laptop. Moreover, we show concentration: With probability tending to one as $n\to\infty$, measurements of the QAOA will produce strings whose energies concentrate at our calculated value. As an algorithm running on a quantum computer, there is no need to search for optimal parameters on an instance-by-instance basis since we can determine them in advance. What we have here is a new framework for analyzing the QAOA, and our techniques can be of broad interest for evaluating its performance on more general problems.

A novel approach to quantum communication has demonstrated that placing communication channels in a quantum superposition of alternative configurations can boost the amount of transmissible information beyond the limits of conventional quantum Shannon theory. Instances of this paradigm are the superposition of different causal orderings of communication devices [Ebler et al., Phys. Rev. Lett. 120, 120502 (2018); Salek et al., arXiv:1809.06655 (2018); Chiribella et al., arXiv:1810.10457 (2018)], or the superposition of information carriers' trajectories [Chiribella and Kristj\'ansson, Proc. R. Soc. A 475, 20180903 (2019); Gisin et al., Phys. Rev. A 72, 012338 (2005); Abbott et al., arXiv:1810.09826 (2018)]. Recently, it was argued that the communication advantages presented in the first three references above are not a genuine consequence of indefinite causal order but can be reproduced by the coherent control of devices [Abbott et al., arXiv:1810.09826 (2018); Gu\'erin et al., Phys. Rev. A 99, 062317 (2019)]. Here, we point out that these arguments set up an uneven comparison between different types of quantum superpositions. To shed light on the discussion, we study communication as a resource theory, formally specifying the communication resources and the allowed operations on them. We argue that any reasonable resource theory of communication must prohibit the use of side-channels, which allow a sender and a receiver to communicate independently of the communication channels initially available to them. We show that the communication paradigms introduced in the first six references above are compatible with such a resource-theoretic framework, while the counterexamples proposed in [Gu\'erin et al., Phys. Rev. A 99, 062317 (2019)] create side-channels.

We investigate the implications of a string-theory modified propagator in the high-precision regime of quantum mechanics. In particular, we examine the situation in which string theory is compactified at the T-duality self-dual radius. The corresponding propagator is closely related to the one derived from the path integral duality.

Our focus is on the hydrogen ground state energy and the $1\text{S}_{1/2}-2\text{S}_{1/2}$ transition frequency as they are the most precisely explored properties of the hydrogen atom. In our analysis, the T-duality propagator affects the photon field leading to a modified Coulomb potential. Thus, our study is complementary to investigations where the electron evolution is modified as in studies of a minimal length in the context of the generalized uncertainty principle.

The first manifestation of the T-duality propagator arises at fourth order in the fine-structure constant, including a logarithmic term. The constraints on the underlying parameter, the zero-point length, reach down to $3.9 \times 10^{-19}\, \text{m}$ and are in full agreement with previous studies on black holes.

We present an efficient method to generate a Greenberger-Horne-Zeilinger (GHZ) entangled state of three cat-state qubits (cqubits) via circuit QED. The GHZ state is prepared with three microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the operation, decoherence caused by the energy relaxation and dephasing of the qutrit is greatly suppressed. The GHZ state is created deterministically because no measurement is involved. Numerical simulations show that high-fidelity generation of a three-cqubit GHZ state is feasible with present circuit QED technology. This proposal can be easily extended to create a $N$-cqubit GHZ state ($N\geq 3$), with $N$ microwave or optical cavities coupled to a natural or artificial three-level atom.

Quantum repeaters, which are indispensable for long-distance quantum communication, are necessary for extending the entanglement from short distance to long distance; however, high-rate entanglement distribution, even between adjacent repeater nodes, has not been realized. In a recent work by C. Jones, et al., New J. Phys. 18, 083015 (2016), the entanglement distribution rate between adjacent repeater nodes was calculated for a plurality of quantum dots, nitrogen-vacancy centers in diamond, and trapped ions adopted as quantum memories inside the repeater nodes. Considering practical use, arranging a plurality of quantum memories becomes so difficult with the state-of-the art technology. It is desirable that high-rate entanglement distribution is realized with as few memory crystals as possible. Here we propose new entanglement distribution scheme with one quantum memory based on the atomic frequency comb which enables temporal multimode operation with one crystal. The adopted absorptive type quantum memory degrades the difficulty of multimode operation compared with previously investigated quantum memories directly generating spin-photon entanglement. It is shown that the present scheme improves the distribution rate by nearly two orders of magnitude compared with the result in C. Jones, et al., New J. Phys. 18, 083015 (2016) and the experimental implementation is close by utilizing state-of-the-art technology.

What is it like to create a game for a quantum computer? With its ability to perform calculations and processing in a distinctly different way than classical computers, quantum computing has the potential for becoming the next revolution in information technology. Flying Unicorn is a game developed for a quantum computer. It is designed to explore the properties of superposition and uncertainty. In this paper, we explore the development of the game, using Python Qiskit. We detail the usage of qubits and an implementation of Grover's search. Finally, we compare and contrast a classical implementation of the game against the quantum computing design, including execution and performance on a physical quantum computer at IBMQ.

Hybrid qubits have recently drawn intensive attention in quantum computing. We here propose a method to implement a universal controlled-phase gate of two hybrid qubits via two three-dimensional (3D) microwave cavities coupled to a superconducting flux qutrit. For the gate considered here, the control qubit is a microwave photonic qubit (particle-like qubit), whose two logic states are encoded by the vacuum state and the single-photon state of a cavity, while the target qubit is a cat-state qubit (wave-like qubit), whose two logic states are encoded by the two orthogonal cat states of the other cavity. During the gate operation, the qutrit remains in the ground state; therefore decoherence from the qutrit is greatly suppressed. The gate realization is quite simple, because only a single basic operation is employed and neither classical pulse nor measurement is used. Our numerical simulations demonstrate that with current circuit QED technology, this gate can be realized with a high fidelity. The generality of this proposal allows to implement the proposed gate in a wide range of physical systems, such as two 1D or 3D microwave or optical cavities coupled to a natural or artificial three-level atom. Finally, this proposal can be applied to create a novel entangled state between a particle-like photonic qubit and a wave-like cat-state qubit.

A non-dispersing wave packet has been attracting much interest from various scientific and technological viewpoints. However, most quantum systems are accompanied by anharmonicity, so that retardation of quantum wave-packet dispersion is limited to very few examples only under specific conditions and targets. Here we demonstrate a conceptually new and universal method to retard or advance the dispersion of a quantum wave packet through programmable time shift induced by a strong non-resonant femtosecond laser pulse. A numerical simulation has verified that a train of such retardation pulses stops wave-packet dispersion.

In a recent paper [Phys. Lett. A 383 (2019) 2836; arXiv:1906.05121 [quant-ph]], Bagarello, Gargano, and Roccati have claimed that no square-integrable vacuum exists in quantizing the Bateman oscillator model. In this paper, we rebut their claim by actually deriving the square-integrable vacuum eigenfunction using a common procedure. We see that no problems occur in quantizing the Bateman oscillator model.

We analyze the continuous operation of the nine-qubit error correcting Bacon-Shor code with all noncommuting gauge operators measured at the same time. The error syndromes are continuously monitored using cross-correlations of sets of three measurement signals. We calculate the logical error rates due to $X$, $Y$ and $Z$ errors in the physical qubits and compare the continuous implementation with the discrete operation of the code. We find that both modes of operation exhibit similar performances when the measurement strength from continuous measurements is sufficiently strong. We also estimate the value of the crossover error rate of the physical qubits, below which continuous error correction gives smaller logical error rates. Continuous operation has the advantage of passive monitoring of errors and avoids the need for additional circuits involving ancilla qubits.