This paper reviews the structure of standard quantum mechanics, introducing the basics of the von Neumann-Dirac axiomatic formulation as well as the well-known Copenhagen interpretation. We review also the major conceptual difficulties arising from this theory, first and foremost, the well-known measurement problem. The main aim of this essay is to show the possibility to solve the conundrums affecting quantum mechanics via the methodology provided by the primitive ontology approach. Using Bohmian mechanics as an example, the paper argues for a realist attitude towards quantum theory. In the second place, it discusses the Quinean criterion for ontology and its limits when it comes to quantum physics, arguing that the primitive ontology programme should be considered as an improvement on Quine's method in determining the ontological commitments of a theory.

Quantum mechanics, devoid of any additional assumption, does not give any theoretical constraint on the projection basis to be used for the measurement process. It is shown in this paper that it does neither allow any physical means for an experimenter to determine which measurement bases have been used by another experimenter. As a consequence, quantum mechanics allows a situation in which two experimenters witness incoherent stories without being able to detect such incoherence, even if they are allowed to communicate freely by exchanging iterative and bilateral messages.

The classical Lippmann-Schwinger equation plays an important role in the scattering theory (non-relativistic case, Schr\"odinger equation). In the present paper we consider the relativistic analogue of the Lippmann-Schwinger equation. We represent the corresponding equation in the integral form. Using this integral equation we investigate the stationary scattering problems (relativistic case, Dirac equation). We consider the dynamical scattering problems (relativistic case, Dirac equation) as well.

Based on the hypothesis that the thermodynamic arrow of time is an emergent phenomenon of quantum state complexity evolution, we further propose that the natural pace of time flow is proportional to the changing rate of quantum state complexity. we then testify how the pace of time flow changes under both special and general relativity based on the analogy between qubit quantum operations and Lorentz transformations. Our simulation results show a qualitative consistency between our hypothesis and the time dilation effect of relativity. We also checked the relationship between our idea on time with the thermal time hypothesis and we showed that our idea can be regarded as a natural generalization of the thermal time hypothesis.

We describe an approach to fix the gauge degrees of freedom in tensor networks, including those with closed loops, which allows a canonical form for arbitrary tensor networks to be realized. Additionally, a measure for the internal correlations present in a tensor network is proposed, which quantifies the extent of resonances around closed loops in the network. Finally we describe an algorithm for the optimal truncation of an internal index from a tensor network, based upon proper removal of the redundant internal correlations. These results, which offer a unified theoretical framework for the manipulation of tensor networks with closed loops, can be applied to improve existing tensor network methods for the study of many-body systems and may also constitute key algorithmic components of sophisticated new tensor methods.

We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schr\"odinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.

We introduce two information-theoretical invariants for the projective unitary group acting on a finite-dimensional complex Hilbert space: PVM- and POVM-dynamical (quantum) entropies. They quantify the randomness of the successive quantum measurement results in the case where the evolution of the system between each two consecutive measurements is described by a given unitary operator. We study the class of chaotic unitaries, i.e., the ones of maximal entropy or, equivalently, such that they can be represented by suitably rescaled complex Hadamard matrices in some orthonormal bases. We provide necessary conditions for a unitary operator to be chaotic, which become also sufficient for qubits and qutrits. These conditions are expressed in terms of the relation between the trace and the determinant of the operator. We also compute the volume of the set of chaotic unitaries in dimensions two and three, and the average PVM-dynamical entropy over the unitary group in dimension two. We prove that this mean value behaves as the logarithm of the dimension of the Hilbert space, which implies that the probability that the dynamical entropy of a unitary is almost as large as possible approaches unity as the dimension tends to infinity.

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how 'badly' can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

Traditional optical imaging faces an unavoidable trade-off between resolution and depth of field (DOF). To increase resolution, high numerical apertures (NA) are needed, but the associated large angular uncertainty results in a limited range of depths that can be put in sharp focus. Plenoptic imaging was introduced a few years ago to remedy this trade off. To this aim, plenoptic imaging reconstructs the path of light rays from the lens to the sensor. However, the improvement offered by standard plenoptic imaging is practical and not fundamental: the increased DOF leads to a proportional reduction of the resolution well above the diffraction limit imposed by the lens NA. In this paper, we demonstrate that correlation measurements enable pushing plenoptic imaging to its fundamental limits of both resolution and DOF. Namely, we demonstrate to maintain the imaging resolution at the diffraction limit while increasing the depth of field by a factor of 7. Our results represent the theoretical and experimental basis for the effective development of the promising applications of plenoptic imaging.

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016)] of strictly constructing continuous Wigner functions for qubit or spin systems. We find that the Wigner function of all pure states of a qubit has negative regions and the negativity completely vanishes when the purity of an arbitrary mixed state is less than $\frac{2}{3}$. We experimentally demonstrate these findings using a single cesium atom confined in an optical dipole trap, which undergoes a nearly pure dephasing process. Our method can be applied straightforwardly to multi-atom systems for measuring the Wigner function of their collective spin state.

At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterised by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterisation of the dynamics of quantum systems, including the measurement process.

The interaction of competing agents is described by the classical game theory. It is now well known that this can be extended to the quantum domain, where agents obey the rules of quantum mechanics. This is of emerging interest for exploring quantum foundations, quantum protocols, quantum auctions, quantum cryptography, and the dynamics of quantum cryptocurrency, for example. In this paper, we investigate two-player games in which a strategy pair can exist as a Nash equilibrium when the games obey the rules of quantum mechanics. Using a generalized Einstein-Podolsky-Rosen (EPR) setting for two-player quantum games, and considering a particular strategy pair, we identify sets of games for which the pair can exist as a Nash equilibrium only when Bell's inequality is violated. We thus determine specific games for which the Nash inequality becomes equivalent to Bell's inequality for the considered strategy pair.

The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of coherence is directly related to the maximum overlap with maximally coherent states under a particular class of operations, which provides an operational interpretation of max-relative entropy of coherence. Moreover, we show that, for any coherent state, there are examples of subchannel discrimination problems such that this coherent state allows for a higher probability of successfully discriminating subchannels than that of all incoherent states. This advantage of coherent states in subchannel discrimination can be exactly characterized by the max-relative entropy of coherence. By introducing suitable smooth max-relative entropy of coherence, we prove that the smooth max-relative entropy of coherence provides a lower bound of one-shot coherence cost, and the max-relative entropy of coherence is equivalent to the relative entropy of coherence in asymptotic limit. Similar to max-relative entropy of coherence, min-relative entropy of coherence has also been investigated. We show that the min-relative entropy of coherence provides an upper bound of one-shot coherence distillation, and in asymptotic limit the min-relative entropy of coherence is equivalent to the relative entropy of coherence.

The study of quantum thermal machines, and more generally of open quantum systems, often relies on master equations. Two approaches are mainly followed. On the one hand, there is the widely used, but often criticized, local approach, where machine sub-systems locally couple to thermal baths. On the other hand, in the more established global approach, thermal baths couple to global degrees of freedom of the machine. There has been debate as to which of these two conceptually different approaches should be used in situations out of thermal equilibrium. Here we compare the local and global approaches against an exact solution for a particular class of thermal machines. We consider thermodynamically relevant observables, such as heat currents, as well as the quantum state of the machine. Our results show that the use of a local master equation is generally well justified. In particular, for weak inter-system coupling, the local approach agrees with the exact solution, whereas the global approach fails for non-equilibrium situations. For intermediate coupling, the local and the global approach both agree with the exact solution and for strong coupling, the global approach is preferable. These results are backed by detailed derivations of the regimes of validity for the respective approaches.

We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum many-body spin dynamics, using different decomposition of the Hamiltonian. The effectiveness of the methods is tested for many-body spin systems up to 40 spins.

We demonstrate a two-photon interference experiment for phase coherent biphoton frequency combs (BFCs), created through spectral amplitude filtering of biphotons with a continuous broadband spectrum. By using an electro-optic phase modulator, we project the BFC lines into sidebands that overlap in frequency. The resulting high-visibility interference patterns provide an approach to verify frequency-bin entanglement even with slow single-photon detectors; we show interference patterns with visibilities that surpass the classical threshold for qubit and qutrit states. Additionally, we show that with entangled qutrits, two-photon interference occurs even with projections onto different final frequency states. Finally, we show the versatility of this scheme for weak-light measurements by performing a series of two-dimensional experiments at different signal-idler frequency offsets to measure the dispersion of a single-mode fiber.

The characteristics of BQC is that it enables a client with less quantum abilities to delegate her quantum computation to a server with strong quantum computablities while keeping the client's privacy. In this article, we study single client-server BQC based on measurement which is verifiable. In detail, the verifiability is that the client Alice can obtain the correct measurement results if the server Bob is honest, while Bob does not get nothing of Alice's secret information if he is malicious. We construct a latticed state, composed of six-qubit cluster states and eight-qubit entangled states, to realize Alice's quantum computing. In this proposed protocol, the cilent Alice prepares and sends initial single-qubit states to Bob, where the initial states include useful qubits and trap qubits. And then Bob performs controlled-Z gate to produce the entanglement and returns them to Alice. Alice will send trap qubits and useful qubits to Bob randomly and Bob returns all measurement results to her. Alice makes a comparison for trap qubits between true results and Bob's results to check the honesty of Bob. In a word, the trap qubtis have two purposes: 1) confusing Bob to keep the blindness; 2)verifying the honesty of Bob and correctness of Bob's quantum computing. There has an important feature that Alice does not need to encrypt the computing angles by $r\pi$ (r$\in\{0,1\}$), meanwhile the blindness and correctness can also be ensured. That is, Alice's computing results don't need to flipped since Bob is not impossible know anything about the quantum computation. Our work gives a better understanding for verifiable BQC based on measurement.

It is well established that quantum criticality is one of the most intriguing phenomena which signals the presence of new states of matter. Without prior knowledge of the local order parameter, the quantum information metric (or fidelity susceptibility) can indicate the presence of a phase transition as well as it measures distance between quantum states. In this work, we calculate distance between quantum states which is equal to the fidelity susceptibility in quantum model for a time-dependent system describing a two-level atom coupled to a time-driven external field. As inspired by the Landau-Lifshitz quantum model, we find in the present work information metric induced by fidelity susceptibility. We for the first time derive a higher-order rank-3 tensor as third-order fidelity susceptibility. Having computed quantum noise function in this simple time-dependent model we show that the noise function eternally lasts long in our model.

Development of scalable quantum photonic technologies requires on-chip integration of components such as photonic crystal cavities and waveguides with nonclassical light sources. Recently, hexagonal boron nitride (hBN) has emerged as a promising platform for nanophotonics, following reports of hyperbolic phonon-polaritons and optically stable, ultra-bright quantum emitters. However, exploitation of hBN in scalable, on-chip nanophotonic circuits, quantum information processing and cavity quantum electrodynamics (QED) experiments requires robust techniques for the fabrication of monolithic optical resonators. In this letter, we design and engineer high quality photonic crystal cavities from hBN. We employ two approaches based on a focused ion beam method and a minimally-invasive electron beam induced etching (EBIE) technique to fabricate suspended two dimensional (2D) and one dimensional (1D) cavities with quality (Q) factors in excess of 2,000. Subsequently, we show deterministic, iterative tuning of individual cavities by direct-write, single-step EBIE without significant degradation of the Q-factor. The demonstration of tunable, high Q cavities made from hBN is an unprecedented advance in nanophotonics based on van der Waals materials. Our results and hBN processing methods open up promising new avenues for solid-state systems with applications in integrated quantum photonics, polaritonics and cavity QED experiments.