Eigenstates of fully many-body localized (FMBL) systems are described by quasilocal operators $\tau_i^z$ (l-bits), which are conserved exactly under Hamiltonian time evolution. The algebra of the operators $\tau_i^z$ and $\tau_i^x$ associated with l-bits ($\boldsymbol{\tau}_i$) completely define the eigenstates and the matrix elements of local operators between eigenstates at all energies. We develop a non-perturbative construction of the full set of l-bit algebras in the many-body localized phase for the canonical model of MBL. Our algorithm to construct the Pauli-algebra of l-bits combines exact diagonalization and a tensor network algorithm developed for efficient diagonalization of large FMBL Hamiltonians. The distribution of localization lengths of the l-bits is evaluated in the MBL phase and used to characterize the MBL-to-thermal transition.

Non-Hermitian Hamiltonians with the equidistant spectrum of the harmonic oscillator are studied in terms of a bi-orthogonal system that behaves as a complete set of orthonormal vectors. The approach permits to work with these non-Hermitian Hamiltonians as if they were Hermitian operators. Some of the criteria that are useful to identify nonclassicality in Hermitian systems are adapted to test the pure states of the non-Hermitian oscillators. Several nonclassical states are uniquely constructed as bi-orthogonal superpositions of the corresponding eigenstates.

The exponential speedups promised by Hamiltonian simulation on a quantum computer depends crucially on structure in both the Hamiltonian $\hat{H}$, and the quantum circuit $\hat{U}$ that encodes its description. In the quest to better approximate time-evolution $e^{-i\hat{H}t}$ with error $\epsilon$, we motivate a systematic approach to understanding and exploiting structure, in a setting where Hamiltonians are encoded as measurement operators of unitary circuits $\hat{U}$ for generalized measurement. This allows us to define a \emph{uniform spectral amplification} problem on this framework for expanding the spectrum of encoded Hamiltonian with exponentially small distortion. We present general solutions to uniform spectral amplification in a hierarchy where factoring $\hat{U}$ into $n=1,2,3$ unitary oracles represents increasing structural knowledge of the encoding. Combined with structural knowledge of the Hamiltonian, specializing these results allow us simulate time-evolution by $d$-sparse Hamiltonians using $\mathcal{O}\left(t(d \|\hat H\|_{\text{max}}\|\hat H\|_{1})^{1/2}\log{(t\|\hat{H}\|/\epsilon)}\right)$ queries, where $\|\hat H\|\le \|\hat H\|_1\le d\|\hat H\|_{\text{max}}$. Up to logarithmic factors, this is a polynomial improvement upon prior art using $\mathcal{O}\left(td\|\hat H\|_{\text{max}}+\frac{\log{(1/\epsilon)}}{\log\log{(1/\epsilon)}}\right)$ or $\mathcal{O}(t^{3/2}(d \|\hat H\|_{\text{max}}\|\hat H\|_{1}\|\hat H\|/\epsilon)^{1/2})$ queries. In the process, we also prove a matching lower bound of $\Omega(t(d\|\hat H\|_{\text{max}}\|\hat H\|_{1})^{1/2})$ queries, present a distortion-free generalization of spectral gap amplification, and an amplitude amplification algorithm that performs multiplication on unknown state amplitudes.

In recent decades, a great variety of researches and applications concerning Bell nonlocality have been developed with the advent of quantum information science. Providing that Bell nonlocality can be revealed by the violation of a family of Bell inequalities, finding maximal Bell violation (MBV) for unknown quantum states becomes an important and inevitable task during Bell experiments. In this paper we introduce a self-guide method to find MBVs for unknown states using a stochastic gradient ascent algorithm (SGA), by parameterizing the corresponding Bell operators. For all the investigated systems (2-qubit, 3-qubit and 2-qutrit), this method can ascertain the MBV accurately within 100 iterations. Moreover, SGA exhibits significant superiority in efficiency, robustness and versatility compared to other possible methods.

A geometric interpretation for quantum correlations and entanglement according to a particular framework of emergent quantum mechanics is developed. The mechanism described is based on two ingredients: 1. At an hypothetical sub-quantum level description of physical systems, the dynamics has a regime where it is partially ergodic and 2. A formal projection from a two-dimensional time mathematical formalism of the emergent quantum theory to the usual one-dimensional time formalism of quantum dynamics. Observable consequences of the theory are obtained. Among them we show that quantum correlations must be instantaneous from the point of view of the spacetime description, but the spatial distance up to which they can be observed must be bounded. It is argued how our mechanism avoids Bell theorem and Kochen-Specken theorem. Evidence for non-signaling faster than the speed of light in our proposal is discussed.

This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform topologically protected operations on this encoding. In particular, we introduce a new and general computational primitive of topological charge measurement and present a symmetry-protected implementation of this primitive. Throughout the Letter, a concrete physical example, the $\mathbb{Z}_3$ toric code ($\mathfrak{D}(\mathbb{Z}_3)$), is discussed. For this example, we have a qutrit encoding and an abstract universal gate set. Physically, gapped boundaries of $\mathfrak{D}(\mathbb{Z}_3)$ can be realized in bilayer fractional quantum Hall $1/3$ systems. If a practical implementation is found for the required topological charge measurement, these boundaries will give rise to a direct physical realization of a universal quantum computer based on a purely abelian topological phase.

We show how to implement a Rindler transformation of coordinates with an embedded quantum simulator. A suitable mapping allows to realise the unphysical operation in the simulated dynamics by implementing a quantum gate on an enlarged quantum system. This enhances the versatility of embedded quantum simulators by extending the possible in-situ changes of reference frames to the non-inertial realm, paving the way to the analysis of new phenomena, from twin-paradox experiments to black hole physics.

One of the fundamental issues in the field of open quantum systems is the classification and quantification of non-Markovianity. In the contest of quantity-based measures of non-Markovianity, the intuition of non-Markovianity in terms of information backflow is widely discussed. However, it is not clear how to explicitly define the information flux for a given system state and how it connects to non-Markovianity. Here, by the using concepts from thermodynamics and information theory, we discuss a potential definition of information flux of an open quantum system, valid for static environments. We present a simple protocol to show how a system attempts to share information with its environment and how it builds up system-environment correlations. We also show that the information returned from the correlations characterizes the non-Markovianity and a hierarchy of indivisibility of the system dynamics.

We study the dynamics of the biased sub-Ohmic spin-boson model by means of a Time-Dependent Variational Matrix Product State (TDVMPS) algorithm. The evolution of both the system and the environment is obtained in the weak and the strong coupling regimes, characterized respectively by damped spin oscillations and by a non-equilibrium process where the spin freezes near its initial state, which are explicitly shown to arise from a variety of reactive environmental quantum dynamics. We also explore the rich phenomenology of the intermediate coupling case, a nonperturbative regime where the system shows a complex dynamical behaviour, combining features of both the weakly and the strongly coupled case in a sequential, time-retarded fashion. Our work demonstrates the potential of TDVMPS methods for exploring otherwise elusive, nonperturbative regimes of complex open quantum systems, and points to the possibilities of exploiting the qualitative, real-time modification of quantum properties induced by non-equilibirum bath dynamics in ultrafast transient processes.

We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not restricted. Although our result follows the idea of splitting the network into two parts developed by Azuma et al. [Nat. Comm. 7, 13523 (2016)], our approach relaxes their strong restriction on the use of a single entanglement measure in the quantification of the maximum amount of entanglement generated by the channels. In particular, in our bound the measure can be chosen on a channel-by-channel basis, in order to make our bound as tight as possible. This enables us to apply the relative entropy of entanglement, known to give a state-of-the-art upper bound, on every Choi-stretchable channel in the network, even when the other channels do not satisfy this property. We also develop tools to compute, or bound, the max-relative entropy of entanglement for qubit channels that are invariant under phase rotations.

We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this concept to the many-particle scenario and determine the influence of the exchange symmetry. Moreover, we characterize the relation of multiparticle coherence to the entanglement of the compound quantum system. To support our general treatment with examples, we consider the quantum correlations of a collection of qudits. The impact of local and global quantum superpositions on the different forms of quantum correlations are discussed. For differently correlated states in the bipartite and multipartite scenarios, we provide a comprehensive characterization of the various forms and origins of quantum correlations.

The renormalization conditions of inhomogeneous systems of a quantum field under an external potential are studied, for both equilibrium and nonequilibrium scenarios and based on Thermo Field Dynamics. Extending the concept of the on-shell self-energies to these systems, we impose the renormalization conditions upon them. All the matrix elements of the energy counter term are determined. In the nonequilibrium case, in which the field operator is expanded to time-dependent wave functions so as to satisfy the appropriately chosen differential equation, the quantum transport equation is derived from the renormalization condition. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wave functions are relaxed to the correct equilibrium forms at the long-term limit.

We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the quantum world. Since these principles are to a large extent expressed in computational terminology, we argue that the hypothesis of "physics as computation", if suitably interpreted, attains surprising explanatory power. Similarly as Jeffrey Bub and others, we conclude that quantum theory should be understood as a "principle theory of information", and we regard this view as a partial interpretation of quantum theory. We outline three options for completion into a full-fledged interpretation of quantum theory, but argue that, despite their interpretational agnosticism, the principled reconstructions pose a challenge for existing psi-ontic interpretations. We also argue that continuous reversible time evolution can be understood as a characteristic property of quantum theory, offering a possible answer to Chris Fuchs' search for a "glimpse of quantum reality".

The aim of this work is to find exact solutions of the Dirac equation in 1+1 space-time beyond the already known class. We consider exact spin (and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus (and minus) the vector potential. We also include pseudo-scalar potentials in the interaction. The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis, which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric. This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.

Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable (NCHV) theory of our nature at the microscopic scale. The conflict between the NCHV theory and quantum mechanics is commonly revealed by Kochen-Specker (KS) sets of yes-no tests, represented by projectors (or rays), via either logical contradictions or noncontextuality inequalities in a state-(in)dependent manner. Here we propose a systematic and programmable construction of a state-independent proof from a given set of nonspecific rays according to their Gram matrix. Our approach not only brings us a greater convenience in the experimental arrangements but also yields a geometric proof for the KS theorem, which seems quite effective for some extreme cases and may be the most intuitive proof so far.

This paper is the first of several parts introducing a new powerful algebra: the algebra of the pseudo-observables. This is a C*-algebra whose set is formed by formal expressions involving observables. The algebra is constructed by applying the Occam's razor principle, in order to obtain the minimal description of physical reality. Proceeding in such a manner, every aspect of quantum mechanics acquires a clear physical interpretation or a logical explanation, providing, for instance, in a natural way the reason for the structure of complex algebra and the matrix structure of Werner Heisenberg's formulation of quantum mechanics. Last but not least, the very general hypotheses assumed, allow one to state that quantum mechanics is the unique minimal description of physical reality.

We consider energy-constrained infinite-dimensional quantum channels from a given system (satisfying a certain condition) to any other systems. We show that dealing with basic capacities of these channels we may assume (accepting arbitrarily small error $\epsilon$) that all channels have the same finite-dimensional input space -- the subspace corresponding to the $m(\epsilon)$ minimal eigenvalues of the input Hamiltonian.

By using this result we prove uniform continuity of basic capacities on the set of all quantum channels equipped with the strong (pointwise) convergence topology. For all the capacities we obtain continuity bounds depending only on the input energy and the energy-constrained-diamond-norm distance between quantum channels (generating the strong convergence on the set of quantum channels).

Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical ensemble, quantum systems formally can not. Recent theoretical breakthroughs and, in particular, the eigenstate thermalization hypothesis (ETH) however indicate that quantum systems can also thermalize. In fact ETH provided us with a framework connecting microscopic models and macroscopic phenomena, based on the notion of highly entangled quantum states. Such thermalization was beautifully demonstrated experimentally by A. Kaufman et. al. who studied relaxation dynamics of a small lattice system of interacting bosonic particles. By directly measuring the entanglement entropy of subsystems, as well as other observables, they showed that after the initial transient time the system locally relaxes to a thermal ensemble while globally maintaining a zero-entropy pure state.

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

We propose a new implementation of real-space renormalization group (RG) transformations for quantum states on a lattice. Key to this approach is the removal of short-ranged entanglement, similar to Vidal's entanglement renormalization (ER), which allows a proper RG flow to be achieved. However, our proposal only uses operators that act locally within each block, such that the use of disentanglers acting across block boundaries is not required. By avoiding the use of disentanglers we argue many tensor network algorithms for studying quantum many-body systems can be significantly improved. The effectiveness of this RG approach is demonstrated through application to the ground state of a 1D system at criticality, which is shown to reach a scale-invariant fixed point.