In the paper, the question whether truth values can be assigned to the propositions about properties of a state of a physical system before the measurement is discussed. To answer this question, a notion that a propositionally noncontextual theory can provide a map linking each element of a bounded lattice to a truth value so as to explain the outcomes of experimental propositions associated with the state of the system is introduced. The paper demonstrates that no model based on the propositionally noncontextual theory can be consistent with the occurrence of a non-vanishing "two-path" quantum interference term and the quantum collapse postulate.

We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling (CDT) and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.

By using an analogy with axionic like systems, we study light propagation in periodic photonic topological insulator (PTI). The main result of this paper is an explicit expression for the PTI band structure. More specifically, it was found that for nonzero values of the topological phase difference $\gamma=\theta_2-\theta_1$ a finite gap $\delta \propto\gamma^2$ opens in the spectrum which is equivalent to appearance of nonzero effective photon mass $m^{*}(\delta)\propto \frac{\sqrt{\delta}}{\delta +2}$.

We study collapse of evaporating spherically-symmetric thin dust shells and dust balls assuming that quantum effects are encapsulated in a spherically-symmetric metric that satisfied mild regularity conditions. The evaporation may accelerate collapse, but for a generic metric the Schwarzschild radius is not crossed. Instead the shell (or the layer in the ball of dust) is always at a certain sub-Planckian distance from it.

We theoretically investigate the quantum scattering of a single-photon pulse interacting with an ensemble of $\Lambda$-type three-level atoms coupled to a one-dimensional waveguide. With an effective non-Hermitian Hamiltonian, we study the collective interaction between the atoms mediated by the waveguide mode. In our scheme, the atoms are randomly placed in the lattice along the axis of the one-dimensional waveguide, which closely corresponds to the practical condition that the atomic positions can not be controlled precisely in experiment. Many interesting optical properties occur in our waveguide-atom system, such as electromagnetically induced transparency (EIT) and optical depth. Moreover, we observe that strong photon-photon correlation with quantum beats can be generated in the off-resonant case, which provides an effective candidate for producing non-classical light in experiment. With remarkable progress in waveguide-emitter system, our scheme may be feasible in the near future.

We provide a general construction of convex roof measures of coherence. This construction is based on arbitrary coherence measures of pure states in the framework of resource theory of coherence. Convex roof measures of coherence bound from above all possible coherence measures, given specific valid quantifications of pure states.

Generating and detection coherent high-frequency heat-carrying phonons has been a great topic of interest in recent years. While there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect these phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the last century and a similar theory for phonon detection is necessary. Here, we re-examine the optical sideband fluorescence technique that has been used detect high frequency phonons in materials with optically active defects. We apply the quantum theory of photodetection to the sideband technique and propose signatures in sideband photon-counting statistics and second-order correlation measurement of sideband signals that indicates the degree of phonon coherence. Our theory can be implemented in recently performed experiments to bridge the gap of determining phonon coherence to be on par with that of photons.

We present a thorough investigation of the phenomena of frozen and time-invariant quantum discord for two-qubit systems independently interacting with local reservoirs. Our work takes into account several significant effects present in decoherence models, which have not been yet explored in the context of time-invariant quantum discord, but which in fact must be typically considered in almost all realistic models. Firstly, we study the combined influence of dephasing, dissipation and heating reservoirs at finite temperature. Contrarily to previous claims in the literature, we show the existence of time-invariant discord at high temperature limit in the weak coupling regime, and also examine the effect of thermal photons on the dynamical behaviour of frozen discord. Secondly, we explore the consequences of having initial correlations between the dephasing reservoirs. We demonstrate in detail how the time-invariant discord is modified depending on the relevant system parameters such as the strength of the initial amount of entanglement between the reservoirs.

The main distinction between open and closed quantum systems is the intricate incoherent dynamics of the former, which is generically attributed to an ongoing correlation between the system and its environment. However, incoherent dynamics can also arise as a result of classical averaging over an ensemble of autonomous Hamiltonian evolutions, as it arises, e.g., in disordered quantum systems. Here, we discover a deeper correspondence between Hamiltonian ensembles and open quantum systems. We identify sufficient conditions under which a general system-environment Hamiltonian can be translated into a Hamiltonian ensemble on the system side. Moreover, we show how to construct an appropriate Hamiltonian ensemble to simulate the dynamics of the spin-boson model with arbitrary spectral density, even though the model Hamiltonian does not enjoy the ensemble form. The presence of an external driving, on the other hand, can destroy the validity of the Hamiltonian ensemble representation. This leads us to proposing a new way to witness the "nonclassicality" of open system evolutions.

The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time.

For multipartite entangled states, entanglement monogamy is an important property. We investigate the monogamy relations for multiqubit generalized W-class states. We present new analytical monogamy inequalities satisfied by the $x$-th power of the dual of convex-roof extended negativity, namely CRENOA, for $x\geq2$ and $x\leq0$. As for The squared R\'{e}nyi-$\alpha$ entanglement (SR$\alpha$E) with $\alpha$ in the region $[(\sqrt 7 - 1)/2,(\sqrt {13} - 1)/2]$, we show the upper bound of SR$\alpha$E.

We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite dimensional General Probabilistic Theory. The conditions are on the geometry of the state space, they require existence of two pairs of parallel exposed faces with additional condition on their intersections. We introduce the notion of discrimination measurement and show that the conditions for a pair of two-outcome measurements to be maximally incompatible are equivalent to requiring that a (potential, yet non-existing) joint measurement of the maximally incompatible measurements would have to discriminate affinely dependent points. We present several examples to demonstrate our results.

We study the quantum stability of the dynamics of ions in a Paul trap. We revisit the results of Wang et al. [Phys. Rev. A 52, 1419 (1995)], which showed that quantum trajectories did not have the same region of stability as their classical counterpart, contrary to what is obtained from a Floquet analysis of the motion in the periodic trapping field. Using numerical simulations of the full wave-packet dynamics, we confirm that the classical trapping criterion are fully applicable to quantum motion, when considering both the expectation value of the position of the wave packet and its width.

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the proper category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtrations decomposed into the (entangled) orbits generated by actions/representations of internal hidden symmetries. In such a way, we open a possibility for the exact description and reinterpretation of a lot of quantum phenomena.

Ambiguous measurements do not reveal complete information about the system under test. Their quantum-mechanical counterparts are semi-weak (or in the limit, weak-) measurements and here we discuss their role in tests of the Leggett-Garg inequalities. We show that, whilst ambiguous measurements allow one to forgo the usual non-invasive measureability assumption, to derive an LGI that may be violated, we are forced to introduce another assumption that equates the invasive influence of ambiguous and unambiguous detectors. We then derive signalling conditions that should be fulfilled for the plausibility of the Leggett-Garg test and propose an experiment on a three-level system with a direct quantum-optics realisation that satisfies all signalling constraints and violates a Leggett-garg inequality.

We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like equations. The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behavior on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).

Quantum samplers are believed capable of sampling efficiently from distributions that are classically hard to sample from. We consider a sampler inspired by the Ising model. It is nonadaptive and therefore experimentally amenable. Under a plausible average-case hardness conjecture, classical sampling upto additive errors from this model is known to be hard. We present a trap-based verification scheme for quantum supremacy that only requires the verifier to prepare single-qubit states. The verification is done on the same model as the original sampler, a square lattice, with only a constant factor overhead. We next revamp our verification scheme to operate in the presence of noise by emulating a fault-tolerant procedure without correcting on-line for the errors, thus keeping the model non-adaptive, but verifying supremacy fault-tolerantly. We show that classically sampling upto additive errors is likely hard in our revamped scheme. Our results are applicable to more general sampling problems such as the Instantaneous Quantum Polynomial-time (IQP) computation model. It should also assist near-term attempts at experimentally demonstrating quantum supremacy and guide long-term ones.

In the task of assisted coherence distillation via the set of operations X, where X is either local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), or separable quantum incoherent operations (SQI), two parties, namely Alice and Bob, share many copies of a bipartite joint state. The aim of the process is to generate the maximal possible coherence on the subsystem of Bob. In this paper, we investigate the assisted coherence distillation of some special mixed states, the states with vanished basis-dependent discord and Werner states. We show that all the four sets of operations are equivalent for assisted coherence distillation, whenever Alice and Bob share one of those mixed quantum states. Moreover, we prove that the assisted coherence distillation of the former can reach the upper bound, namely QI relative entropy, while that of the latter can not. Meanwhile, we also present a sufficient condition such that the assistance of Alice via the set of operations X can not help Bob improve his distillable coherence, and this condition is that the state shared by Alice and Bob has vanished basis-dependent discord.

The phase dependence of the cavity quantum dynamics in a driven equidistant three-level ladder-type system found in a quantum well structure with perpendicular transition dipoles is investigated in the good cavity limit. The pumping laser phases are directly transferred to the superposed amplitudes of the cavity-quantum-well interaction. Their phase difference may be tuned in order to obtain destructive quantum interferences. Therefore, the cavity field vanishes although the emitter continues to be pumped.

In previous work, we used non-standard analysis to introduce a new dagger compact category Star Hilb suitable for categorical quantum mechanics (CQM) in arbitrary separable Hilbert spaces. In this work we further extend our construction, and we present a number of novel applications to iconic examples from textbook quantum mechanics. Specifically, we cover in detail the cases of particles in boxes with periodic boundary conditions, particles on lattices and particles in unbounded real spaces. Not quite satisfied with this, we show how certain non-separable Hilbert spaces can be modelled in our extended framework, and we explicitly treat the case of quantum fields on infinite lattices and unbounded real spaces. In other words, we boldly go where no CQM has gone before.