We study a class of SYK-type models in large N limit from the gravity dual side in terms of Schwarzian action analytically. The quantum correction to two point correlation function due to the Schwarzian action produces transfer of degree of freedom from the quasiparticle peak to Hubbard band in density of states (DOS), a signature strong correlation. In Schwinger-Keldysh (SK) formalism, we calculate higher point thermal out-of-time order correlation (OTOC) functions, which indicate quantum chaos by having Lyapunov exponent. Higher order local spin-spin correlations are also calculated, which can be related to the dynamical local susceptibility of quantum liquids such as spin glasses, disordered metals.

A relation is established in the present paper between Dicke states in a d-dimensional space and vectors in the representation space of a generalized Weyl-Heisenberg algebra of finite dimension d. This provides a natural way to deal with the separable and entangled states of a system of N = d-1 symmetric qubit states. Using the decomposition property of Dicke states, it is shown that the separable states coincide with the Perelomov coherent states associated with the generalized Weyl-Heisenberg algebra considered in this paper. In the so-called Majorana scheme, the qudit (d-level) states are represented by N points on the Bloch sphere; roughly speaking, it can be said that a qudit (in a d-dimensional space) is describable by a N-qubit vector (in a N-dimensional space). In such a scheme, the permanent of the matrix describing the overlap between the N qubits makes it possible to measure the entanglement between the N qubits forming the qudit. This is confirmed by a Fubini-Study metric analysis. A new parameter, proportional to the permanent and called perma-concurrence, is introduced for characterizing the entanglement of a symmetric qudit arising from N qubits. For d=3 (i.e., N = 2), this parameter constitutes an alternative to the concurrence for two qubits. Other examples are given for d=4 and 5. A connection between Majorana stars and zeros of a Bargmmann function for qudits closes this article.

Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied to a wide variety of problems including detection of quantum entanglement. Resulting uncertainty relations are state-independent, semianalytical, bound-error and can be made arbitrarily tight. The advocated approach allows one to improve earlier numerical works and to derive semianalitical tight bounds for the uncertainty relation for the sum of variances constrained to finding roots of a polynomial of a single real variable. In several cases it is possible to solve the problem completely by establishing exact analytical bounds.

Starting from the many-body Schr\"odinger equation, we derive a new type of Lindblad Master equations describing a cyclic exciton/electron dynamics in the light harvesting complex and the reaction center. These equations resemble the Master equations for the electric current in mesoscopic systems, and they go beyond the single-exciton description by accounting for the multi-exciton states accumulated in the antenna, as well as the charge-separation, fluorescence and photo-absorption. Although these effects take place on very different timescales, their inclusion is necessary for a consistent description of the exciton dynamics. Our approach reproduces both coherent and incoherent dynamics of exciton motion along the antenna in the presence of vibrational modes and noise. We applied our results to evaluate energy (exciton) and fluorescent currents as a function of sunlight intensity.

We show that a linear term coupling the atoms of an ultracold binary mixture provides a simple method to induce an effective and tunable population imbalance between them. This term is easily realized by a Rabi coupling between different hyperfine levels of the same atomic species. The resulting effective imbalance holds for one-particle states dressed by the Rabi coupling and obtained diagonalizing the mixing matrix of the Rabi term. This way of controlling the chemical potentials applies for both bosonic and fermionic atoms and it allows also for spatially and temporally dependent imbalances. As a first application, we show that, in the case of two attractive fermionic hyperfine levels with equal chemical potentials and coupled by the Rabi pulse, the same superfluid properties of an imbalanced binary mixture are recovered. We finally discuss the properties of m-species mixtures in the presence of SU(m)-invariant interactions.

In the present study a particular case of Gross-Pitaevskii or non-linear Schr\"odinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.

The rapidly developing and converging fields of polaritonic chemistry and quantum optics necessitate a unified approach to predict strongly-correlated light-matter interactions with atomic-scale resolution. Combining concepts from both fields presents an opportunity to create a predictive theoretical and computational approach to describe cavity correlated electron-nuclear dynamics from first principles. Towards this overarching goal, we introduce a general time-dependent density-functional theory to study correlated electron, nuclear and photon interactions on the same quantized footing. In our work we demonstrate the arising one-to-one correspondence in quantum-electrodynamical density-functional theory, introduce Kohn-Sham systems, and discuss possible routes for approximations to the emerging exchange-correlation potentials. We complement our theoretical formulation with the first ab initio calculation of a correlated electron-nuclear-photon system. From the time-dependent dipole moment of a CO$_2$ molecule in an optical cavity, we construct the infrared spectra and time-dependent quantum-electrodynamical observables such as the electric displacement field, Rabi splitting between the upper and lower polaritonic branches and cavity-modulated molecular motion. This cavity-modulated molecular motion has the potential to alter and open new chemical reaction pathways as well as create new hybrid states of light and matter. Our work opens an important new avenue in introducing ab initio methods to the nascent field of collective strong vibrational light-matter interactions.

Gravitons are the quantum counterparts of gravitational waves in low-energy theories of gravity. Using Feynman rules one can compute scattering amplitudes describing the interaction between gravitons and other fields. Here, we consider the interaction between gravitons and photons. Using the quantum Boltzmann equation formalism, we derive fully general equations describing the radiation transfer of photon polarization, due to the forward scattering with gravitons. We show that the Q and U photon linear polarization modes couple with the V photon circular polarization mode, if gravitons have anisotropies in their power-spectrum statistics. As an example, we apply our results to the case of primordial gravitons, considering models of inflation where an anisotropic primordial graviton distribution is produced. Finally, we evaluate the effect on Cosmic Microwave Background (CMB) polarization, showing that in general the expected effects on the observable CMB frequencies are very small. However, our result is promising, since it could provide a novel tool for detecting anisotropic backgrounds of gravitational waves, as well as for getting further insight on the physics of gravitational waves.

Current work presents a new approach to quantum color codes on compact surfaces with genus $g \geq 2$ using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with a very good parameters and we present tables with several examples of these codes whose parameters had not been shown before. We also present a family of codes with minimum distance $d=4$ and the encoding rate asymptotically going to 1 while $n \rightarrow \infty$.

In this paper we explore the entanglement of two relativistic spin-$1/2$ particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations.

Broadcasting information anonymously becomes more difficult as surveillance technology improves, but remarkably, quantum protocols exist that enable provably traceless broadcasting. The difficulty is making scalable entangled resource states that are robust to errors. We propose an anonymous broadcasting protocol that uses a continuous-variable surface-code state that can be produced using current technology. High squeezing enables large transmission bandwidth and strong anonymity, and the topological nature of the state enables local error mitigation.

We prove that any one-dimensional (1D) quantum state with small quantum conditional mutual information in all certain tripartite splits of the system, which we call a quantum approximate Markov chain, can be well-approximated by a Gibbs state of a short-range quantum Hamiltonian. Conversely, we also derive an upper bound on the (quantum) conditional mutual information of Gibbs states of 1D short-range quantum Hamiltonians. We show that the conditional mutual information between two regions A and C conditioned on the middle region B decays exponentially with the square root of the length of B.

These two results constitute a variant of the Hammersley-Clifford theorem (which characterizes Markov networks, i.e. probability distributions which have vanishing conditional mutual information, as Gibbs states of classical short-range Hamiltonians) for 1D quantum systems. The result can be seen as a strengthening - for 1D systems - of the mutual information area law for thermal states. It directly implies an efficient preparation of any 1D Gibbs state at finite temperature by a constant-depth quantum circuit.

To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$. The former is called a signed particle and the latter a weighted particle. In this paper, we propose two efficient strategies to realize the signed-particle implementation. One is to interpret the multiplicative functional as the probability to generate pairs of particles instead of the incremental weight, and the other is to utilize a bootstrap filter to adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both strategies and the variance reduction property of the second approach. We provide an improvement of the first signed-particle implementation that partially alleviates the restriction on the time step and perform a thorough theoretical and numerical comparison among all the existing signed-particle implementations. Details on implementing the importance sampling according to the quasi-probability density and an efficient resampling or particle reduction are also provided.

We present a planar surface-code-based scheme for fault-tolerant quantum computation which eliminates the time overhead of single-qubit Clifford gates, and implements long-range multi-target CNOT gates with a time overhead that scales only logarithmically with the control-target separation. This is done by replacing hardware operations for single-qubit Clifford gates with a classical tracking protocol. Inter-qubit communication is added via a modified lattice surgery protocol that employs twist defects of the surface code. The long-range multi-target CNOT gates facilitate magic state distillation, which renders our scheme fault-tolerant and universal.

We calculate quantum and classical Fisher informations for gravity sensors based on matterwave interference, and find that current Mach-Zehnder interferometry is not optimally extracting the full metrological potential of these sensors. We show that by making measurements that resolve either the momentum or the position we can considerably improve the sensitivity. We also provide a simple modification that is capable of more than doubling the sensitivity.

In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM functional theory. To avoid non-uniqueness issues we consider the case of fermionic and bosonic systems at elevated temperature and variable particle number, i.e, a grand-canonical ensemble. For the fermionic case the Fock space is finite dimensional due to the Pauli principle and we can provide a rigorous 1RDM functional theory relatively straightforwardly. For the bosonic case, where arbitrarily many particles can occupy a single state, the Fock space is infinite dimensional and mathematical subtleties (not every hermitian Hamiltonian is self-adjoint, expectation values can become infinite, and not every self-adjoint Hamiltonian has a Gibbs state) make it necessary to impose restrictions on the allowed Hamiltonians and external non-local potentials. For simple conditions on the interaction of the bosons a rigorous 1RDM functional theory can be established, where we exploit the fact that due to the finite one-particle space all 1RDMs are finite dimensional. We also discuss the problems arising of 1RDM functional theory as well as DFT formulated for an infinite-dimensional one-particle space.

We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

We consider a generic framework of optimization algorithms based on gradient descent. We develop a quantum algorithm that computes the gradient of a multi-variate real-valued function $f:\mathbb{R}^d\rightarrow \mathbb{R}$ by evaluating it at only a logarithmic number of points in superposition. Our algorithm is an improved version of Stephen Jordan's gradient computation algorithm, providing an approximation of the gradient $\nabla f$ with quadratically better dependence on the evaluation accuracy of $f$, for an important class of smooth functions. Furthermore, we show that most objective functions arising from quantum optimization procedures satisfy the necessary smoothness conditions, hence our algorithm provides a quadratic improvement in the complexity of computing their gradient. We also show that in a continuous phase-query model, our gradient computation algorithm has optimal query complexity up to poly-logarithmic factors, for a particular class of smooth functions. Moreover, we show that for low-degree multivariate polynomials our algorithm can provide exponential speedups compared to Jordan's algorithm in terms of the dimension $d$.

One of the technical challenges in applying our gradient computation procedure for quantum optimization problems is the need to convert between a probability oracle (which is common in quantum optimization procedures) and a phase oracle (which is common in quantum algorithms) of the objective function $f$. We provide efficient subroutines to perform this delicate interconversion between the two types of oracles incurring only a logarithmic overhead, which might be of independent interest. Finally, using these tools we improve the runtime of prior approaches for training quantum auto-encoders, variational quantum eigensolvers (VQE), and quantum approximate optimization algorithms (QAOA).

In the context of the readout scheme for gravitational-wave detectors, the "double balanced homodyne detection" proposed in [K.~Nakamura and M.-K.~Fujimoto, arXiv:1709.01697.] is discussed in detail. This double balanced homodyne detection enables us to measure the expectation values of the photon creation and annihilation operators. Although it has been said that the operator $\hat{b}_{\theta}:=\cos\theta\hat{b}_{1}+\sin\theta\hat{b}_{2}$ can be measured through the homodyne detection in literature, we first show that the expectation value of the operator $\hat{b}_{\theta}$ cannot be measured as the linear combination of the upper- and lower-sidebands from the output of the balanced homodyne detection. Here, the operators $\hat{b}_{1}$ and $\hat{b}_{2}$ are the amplitude and phase quadrature in the two-photon formulation, respectively. On the other hand, it is shown that the above double balanced homodyne detection enables us to measure the expectation value of the operator $\hat{b}_{\theta}$ if we can appropriately prepare the complex amplitude of the coherent state from the local oscillator. It is also shown that the interferometer set up of the eight-port homodyne detection realizes our idea of the double balanced homodyne detection. We also evaluate the noise-spectral density of the gravitational-wave detectors when our double balanced homodyne detection is applied as their readout scheme. Some requirements for the coherent state from the local oscillator to realize the double balanced homodyne detection are also discussed.

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels, we may express the quantum Cram\'er Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.