We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of the formation criteria for boundary modes in terms of local Green functions, we outline a generic perspective on the appearance of such modes. In the process, we explain the skin effect in both topological and non-topological systems, evaluate bulk-boundary correspondence in the presence of non-Hermiticity, and generate a dispersion relation for the associated edge modes. This is accomplished via a doubled Green's function approach, inspired by the doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work therefore constitutes a useful and general tool, as well as, a unifying perspective for this rapidly evolving field.

Utilization of the spatial degree of freedom vastly enhances informational capacity of light at the cost of stringent requirements on the processing devices. Multi-mode quantum memories constitute a viable candidate for quantum and classical information processing; however, full utilization of the assets of high-dimensionality requires a flexible processing technique. We employ a spatially varying ac-Stark effect to perform arbitrary 1D phase modulation of a coherent spin-wave state stored in a wavevector-multiplexed quantum memory. A far-field and an interferometric near-field characterizations of the introduced phase profiles are presented. Additionally, coherence between temporally separated partial readouts of a single coherent spin-wave state is demonstrated, offering possible applications in adaptive measurements via conditional spin-wave modulation.

We design a quasi-one dimensional spin chain with engineered coupling strengths such that the natural dynamics of the spin chain evolves a single excitation localized at the left hand site to any specified single particle state on the whole chain. Our treatment is an exact solution to a problem which has already been addressed in approximate ways. As two important examples, we study the $W$ states and Gaussian states with arbitrary width.

We present the complete solution of the problem of determination of trace-norm geometric discord for arbitrary two-qubit state. Final answer is achieved due to effective reduction of the problem to the study of critical points of certain mapping depending on projectors. Our results are illustrated on various, also new, families of two-qubit states and compared to already known special solutions.

We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is illustrated with the basic example of the one-dimensional motion of a free particle in an interval and yields a fuzzy boundary, a position-dependent mass, and an extra potential on the quantum level. The consistency of our quantization is discussed by analyzing the semi-classical phase space portrait of the derived quantum dynamics, which is obtained as a regularization of its original classical counterpart.

The Index Erasure problem asks a quantum computer to prepare a uniform superposition over the image of an injective function given by an oracle. We prove a tight $\Omega(\sqrt{n})$ lower bound on the quantum query complexity of the non-coherent case of the problem, where, in addition to preparing the required superposition, the algorithm is allowed to leave the ancillary memory in an arbitrary function-dependent state. This resolves an open question of Ambainis, Magnin, Roetteler, and Roland (CCC 2011), who gave a tight bound for the coherent case, the case where the ancillary memory must return to its initial state.

The proof is based on evaluating certain Krein parameters of a symmetric association scheme defined over partial permutations. The study of this association scheme may be of independent interest.

Single photon emitters (SPEs) are critical building blocks needed for quantum science and technology. For practical applications, large-scale room-temperature solid-state platforms are required. Color centers in layered hexagonal boron nitride (hBN) have recently been found to be ultra-bright and stable SPEs at room temperature. Yet, to scale up solid-state quantum information processing, large tuning range of single photon energy is demanded for wavelength division multiplexing quantum key distribution, where indistinguishability is not required, and for indistinguishable single-photon production from multi-emitters. Stark effect can tune the single photon energy by an electric field, which however, has been achieved only at cryogenic temperature so far. Here we report the first room-temperature Stark effect of SPEs by exploiting hBN color centers. Surprisingly, we observe a giant Stark shift of single photon more than 30 meV, about one order of magnitude greater than previously reported in color center emitters. Moreover, for the first time, the orientation of the electric permanent dipole moment in the solid-state SPE is determined via angle-resolved Stark effect, revealing the intrinsic broken symmetries at such a color center. The remarkable Stark shift discovered here and the significant advance in understanding its atomic structure pave a way towards the scalable solid-state on-chip quantum communication and computation at room temperature.

We analytically show that a new type of operator, atomic state amplification operator, can be defined that probabilistically amplifies a coherent atomic state without introducing noise to the state. We show that this is because of entanglement among atoms in an ensemble. Based on this result, we introduce and study a scheme to realize conditional noiseless amplification of coherent optical states. Our scheme requires small amount of resources compared to previous schemes for probabilistic optical state amplification. The scheme consists of an atomic ensemble of $\Lambda$-level interacting with two pumping lasers and a weak incident coherent state. The amplification is realized by implementing quantum light storage of the weak coherent state followed by detection of multiple Raman scattered photons conditionally projecting the coherent state into an amplified state upon retrieval.

In this work we study how the non-Markovian character of the dynamics can affect the thermodynamic performance of a quantum thermal engine, by analysing the maximum power output of Carnot and Otto cycles departing from the quasi-static and infinite-time-thermalization regime respectively. In our model, non-Markovianity is introduced by allowing some degrees of freedom of the reservoirs to be taken into account explicitly and share correlations with the engine by Hamiltonian coupling. It is found that the non-Markovian effects can fasten the control and improve the power output.

Squeezing of quantum fluctuation plays an important role in fundamental quantum physics and has marked influence on ultrasensitive detection. We propose a scheme to generate and enhance the squeezing of mechanical mode by exposing the optomechanical system to a non-Markovian environment. It is shown that the effective parametric resonance term of mechanical mode can be induced due to the interaction with cavity and non-Markovian reservoir, thus resulting in quadrature squeezing of the mechanical resonator. And jointing the two kinds of interactions can enhance the squeezing effect. Comparing with the usual Markovian regime, we can obtain stronger squeezing, and significantly the squeezing can approach a low asymptotic stable value.

We present the design, fabrication and characterization of LNOI fiber-to-chip inverse tapers for efficient edge coupling. The etching characteristics of various LNOI crystal cuts are investigated for the realization of butt-coupling devices. We experimentally demonstrate that the crystal cut limits the performance of mode matching tapers. We report a butt-coupling loss of 2.5 dB/facet and 6 dB/facet by implementing 200 nm tip mode matching tapers in $+Z$-cut LNOI and $X$-cut MgO:LNOI waveguides with low propagation loss. We anticipate that these results will provide insight into the nanostructuring of LNOI and into the further development of efficient butt-coupling in this platform.

We consider performance of a simple quantum convolutional code in a fault-tolerant regime using several syndrome measurement/decoding strategies and three different error models, including the circuit model.

We investigate the polygamy relations of multipartite quantum states. General polygamy inequalities are given in the $\alpha$th $(\alpha\geq 2)$ power of concurrence of assistance, $\beta$th $(\beta \geq1)$ power of entanglement of assistance, and the squared convex-roof extended negativity of assistance (SCRENoA).

Production and verification of multipartite quantum state is an essential step for quantum information processing. In this work, we propose an efficient method to decompose symmetric multipartite observables, which are invariant under permutations between parties, with only $(N+1)(N+2)/2$ local measurement settings, where $N$ is the number of qubits. We apply the decomposition technique to evaluate the fidelity between an unknown prepared state and any target permutation invariant state. In addition, for some typical permutation invariant states, such as the Dicke state with a constant number of excitations, $m$, we derive a tight linear bound on the number of local measurement settings, $m(2m+3)N+1$. Meanwhile, for the $GHZ$ state, the $W$ state, and the Dicke state, we prove a linear lower bound, $\Theta(N)$. Hence, for these particular states, our decomposition technique is optimal.

In a recent paper entitled "Winding around non-Hermitian singularities" by Zhong et al., published in Nat. Commun. 9, 4808 (2018), a formalism is proposed for calculating the permutations of eigenstates that arise upon encircling (multiple) exceptional points (EPs) in the complex parameter plane of an analytic non-Hermitian Hamiltonian. The authors suggest that upon encircling EPs one should track the eigenvalue branch cuts that are traversed, and multiply the associated permutation matrices accordingly. In this comment we point out a serious shortcoming of this approach, illustrated by an explicit example that yields the wrong result for a specific loop. A more general method that has been published earlier by us and that does not suffer from this problem, is based on using fundamental loops. We briefly explain the method and list its various advantages. In addition, we argue that this method can be verified in a three wave-guide system, which then also unambiguously establishes the noncommutativity associated with encircling multiple EPs.

Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and thermodynamically stable, results of a more careful study of the problem seemed to indicate that quantum time crystals could be realized only in systems out of equilibrium. Here we show that, in contrast to the general belief, thermodynamically stable macroscopic quantum time crystals can exist. The order parameter of this new state of matter is periodic in both real and imaginary time but its average over the phase of the oscillations equals zero. At the same time, correlation functions characterizing physical quantities oscillate periodically in time without any decay. An alternative interpretation of the results is based on a concept of an operator order parameter. Calculations are performed for a rather general microscopic model that may in particular be suitable for describing the pseudogap state in superconducting cuprates.

The computational treatment of many-electron systems capable of exchanging {electrons and nuclei} with the environment represents one of the outermost frontiers in simulation methodology. The exchanging process occurs in a large variety of natural and artificially induced phenomena which are of major relevance to several leading fields of academic research and modern technology. In this progress report I will present an overview of problems in current materials science and chemical physics where the corresponding computational approaches require the concept of an electronic system with open boundaries. Quantum and Quantum/Classical computational techniques treat the exchange of electrons with the environment at different computational efficiency, conceptual rigorousness and numerical accuracy. The overall emerging picture shows a rich availability of interesting ideas, some with a higher weight on the pragmatic side, others with higher weight on the conceptual side; possible combinations, in perspective, may push the field much beyond its current frontiers.

Randomness is of paramount importance to human activities, from election to drug design and to digital cryptography. The origin of randomness and its applications are under active investigations. The recent realizations of device-independent quantum random number generation provide intrinsically unpredictable random numbers without trusting the inner working of devices, where a great deal of input randomness was used to generate a small output randomness. Randomness expansion$-$generating a longer sequence of random numbers from a short one, is viable in quantum mechanics but not allowed classically since all classical algorithms are essentially deterministic. Quantum randomness expansion is not only a fundamental question in science but also of practical interest. Here we report the first experimental realization of device-independent quantum randomness expansion by employing the quantum probability estimation framework. We demonstrate to generate output randomness exceeding the input randomness unpredictably by 512 bits at a latency of less than 8 mins, and to achieve an asymptotic rate of $\approx0.08$ bit per trial, the largest for unpredictable random bits generation to date, with a failure probability $2^{-64}\approx5.4\times10^{-20}$. Device-independent quantum randomness expansion harvesting quantum advantage not only furthers our understanding of randomness but also is resource-efficient in the generation of quantum-certifiable random bits for practical applications.

In this paper, we discuss the possibility of unexplored behaviours for the entanglement entropy in extended quantum systems. Namely, we study the R\'enyi entanglement entropy for the ground state of long-range Kitaev chains with slow decaying couplings. We obtain that, under some circumstances, the entropy grows sublogarithmically with the length of the subsystem. Our result is based on the asymptotic behaviour of a new class of Toeplitz determinants whose symbol does not lie within the application domain of the Strong Szeg\H{o} Theorem or the Fisher-Hartwig conjecture.

The famous Fiat-Shamir transformation turns any public-coin three-round interactive proof, i.e., any so-called sigma-protocol, into a non-interactive proof in the random-oracle model. We study this transformation in the setting of a quantum adversary that in particular may query the random oracle in quantum superposition.

Our main result is a generic reduction that transforms any quantum dishonest prover attacking the Fiat-Shamir transformation in the quantum random-oracle model into a similarly successful quantum dishonest prover attacking the underlying sigma-protocol (in the standard model). Applied to the standard soundness and proof-of-knowledge definitions, our reduction implies that both these security properties, in both the computational and the statistical variant, are preserved under the Fiat-Shamir transformation even when allowing quantum attacks. Our result improves and completes the partial results that have been known so far, but it also proves wrong certain claims made in the literature.

In the context of post-quantum secure signature schemes, our results imply that for any sigma-protocol that is a proof-of-knowledge against quantum dishonest provers (and that satisfies some additional natural properties), the corresponding Fiat-Shamir signature scheme is secure in the quantum random-oracle model. For example, we can conclude that the non-optimized version of Fish, which is the bare Fiat-Shamir variant of the NIST candidate Picnic, is secure in the quantum random-oracle model.