We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of $1/c^2$ terms representing (transverse) current-current interaction. For its derivation we use the classical formulation of Landau-Lifshitz, however consequently in the Coulomb gauge. Our Hamiltonian does not coincide with the Darwin Hamiltonian and we emphasize the mathematical inconsistency in its derivation. We show, that the quantized version of our Hamiltonian is equivalent to the non-relativistic QED considering only states without photons and retaining only terms of order $1/c^2$. The importance of this extended Hamiltonian lies in the possibility to distinguish external from internal magnetic fields. This aspect may be relevant for theories of the Meissner effect.

Electron-positron pair production from vacuum in external electric fields with space and time dependencies is studied numerically using real time Dirac-Heisenberg-Wigner formalism. The influence of spatial focusing scale of the electric field on momentum distribution and the total yield of the particles is examined by considering standing wave mode of the electric field with different temporal configurations. With the decrease of spatial extent of the external field, signatures of the temporal field are weaken in the momentum spectrum. Moreover, in the extremely small spatial extent, novel features emerge due to the combined effects of both temporal and spatial variations. We also find that for dynamically assisted particle production, while the total particle yield drops significantly in small spatial extents, the assistance mechanism tends to increase in these highly inhomogeneous regimes, where the slow and fast pulses are affected differently by the overall spatial inhomogeneity.

This paper is a programmatic article presenting an outline of a new view of the foundations of quantum mechanics and quantum field theory. In short, the proposed foundations are given by the following statements:

* Coherent quantum physics is physics in terms of a coherent space consisting of a line bundle over a classical phase space and an appropriate coherent product.

* The kinematical structure of quantum physics and the meaning of the fundamental quantum observables are given by the symmetries of this coherent space, their infinitesimal generators, and associated operators on the quantum space of the coherent space.

* The connection of quantum physics to experiment is given through the thermal interpretation. The dynamics of quantum physics is given (for isolated systems) by the Ehrenfest equations for q-expectations.

This paper continues the discussion of the thermal interpretation of quantum physics. While Part II and Part III of this series of papers explained and justified the reasons for the departure from tradition, the present Part IV summarizes the main features and adds intuitive explanations and new technical developments.

It is shown how the spectral features of quantum systems and an approximate classical dynamics arise under appropriate conditions.

Evidence is given for how, in the thermal interpretation, the measurement of a qubit by a pointer q-expectation may result in a binary detection event with probabilities given by the diagonal entries of the reduced density matrix of the prepared qubit.

Differences in the conventions about measurement errors in the thermal interpretation and in traditional interpretations are discussed in detail.

Several standard experiments, the double slit, Stern--Gerlach, and particle decay are described from the perspective of the thermal interpretation.

We introduce a framework for graphical security proofs in device-independent quantum cryptography using the methods of categorical quantum mechanics. We are optimistic that this approach will make some of the highly complex proofs in quantum cryptography more accessible, facilitate the discovery of new proofs, and enable automated proof verification. As an example of our framework, we reprove a previous result from device-independent quantum cryptography: any linear randomness expansion protocol can be converted into an unbounded randomness expansion protocol. We give a graphical proof of this result, and implement part of it in the Globular proof assistant.

Contextuality is an indicator of non-classicality, and a resource for various quantum procedures. In this paper, we use contextuality to evaluate the variational quantum eigensolver (VQE), one of the most promising tools for near-term quantum simulation. We present an efficiently computable test to determine whether or not the objective function for a VQE procedure is contextual. We apply this test to evaluate the contextuality of experimental implementations of VQE, and determine that several, but not all, fail this test of quantumness.

Quantum resource theories have been widely studied to systematically characterize the non-classicality of quantum systems. Most resource theories focus on quantum states and study the interconversion between different states. Although quantum channels are generally used as the tool for resource manipulation, such a manipulation ability can be naturally regarded as a generalized quantum resource, leading to an open research direction in the resource theories of quantum channels. Various resource-theoretic properties of channels have been investigated, however, without treating channels themselves as operational resources that can also be manipulated and converted. In this Letter, we address this problem by first proposing a general resource framework for quantum channels and introducing resource monotones based on general distance quantifiers of channels. We study the interplay between channel and state resource theories by relating resource monotones of a quantum channel to its manipulation power of the state resource. Regarding channels as operational resources, we introduce asymptotic channel distillation and dilution, the most important tasks in an operational resource theory, and show how to bound the conversion rates with channel resource monotones. Finally, we apply our results to quantum coherence as an example and introduce the coherence of channels, which characterizes the coherence generation ability of channels. We consider asymptotic channel distillation and dilution with maximally incoherent operations and find the theory asymptotically irreversible, in contrast to the asymptotic reversibility of the coherence of states.

We address quantum decision theory as a convenient framework to analyze process discrimination and estimation in qubit systems. In particular we discuss the following problems: i) how to discriminate whether or not a given unitary perturbation has been applied to a qubit system; ii) how to determine the amplitude of the minimum detectable perturbation. In order to solve the first problem, we exploit the so-called Bayes strategy, and look for the optimal measurement to discriminate, with minimum error probability, whether or not the unitary transformation has been applied to a given signal. Concerning the second problem, the strategy of Neyman and Pearson is used to determine the ultimate bound posed by quantum mechanics to the minimum detectable amplitude of the qubit transformation. We consider both pure and mixed initial preparations of the qubit, and solve the corresponding binary decision problems. We also analyze the use of entangled qubits in the estimation protocol and found that entanglement, in general, improves stability rather than precision. Finally, we take into account the possible occurrence of different kinds of background noise and evaluate the corresponding effects on the discrimination strategies.

The relativistic Lagrangian (L) justifies the importance of Reparametrization-Invariant (RI) Systems and especially the first-order homogeneous L in the velocities. The usual gravitational interaction term along with the finite propagational speed justifies the Minkowski space-time. The argument presented implies only one time-like coordinate. By using the freedom of parametrization for a process, it is argued that the corresponding causal structure results in the observed common Arrow of Time and nonnegative masses of the particles. RI Systems are studied from the point of view of the Lagrangian and extended Hamiltonian (H) formalism by using an Extended Poisson Bracket (EPB) that is generally covariant. The EPB is defined over the phase-space-time in a way consistent with the canonical quantization formalism (CQF). The corresponding extended H defines the classical phase space-time of the system as null-space constraint and guarantees that the classical H corresponds to the energy of the particle in the coordinate time parametrization. When the system is quantized by following the CQF and the corresponding Hilbert space is defined as null-space of the extended quantum H then the Schr\"odinger's equation emerges and the principle of superposition of quantum states is justified. A connection is demonstrated between the positivity of the energy (E>0) and the normalizability of the wave function by using the extended H that is relevant for the proper time parametrization. It is demonstrated that the choice of the extended H is closely related to the meaning of the process parameter $\lambda$. The two familiar roles that $\lambda$ can take upon, the coordinate time and the proper time, are illustrated using the simplest one-dimensional reparametrization invariant systems. In general, $\lambda$ can also be the proper length along the path of a particle for appropriately chosen generator.

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.

Production and verification of multipartite quantum state are an essential step in 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.

Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two main postulates: 1. the theory should be logically consistent; 2. inferences in the theory should be computable in polynomial time. The first postulate is what we require to each well-founded mathematical theory. The computation postulate defines the physical component of the theory. We show that the computation postulate is the only true divide between QT, seen as a generalised theory of probability, and classical probability. All quantum paradoxes, and entanglement in particular, arise from the clash of trying to reconcile a computationally intractable, somewhat idealised, theory (classical physics) with a computationally tractable theory (QT) or, in other words, from regarding physics as fundamental rather than computation.

Qubits used in quantum computing tend to suffer from errors, either from the qubit interacting with the environment, or from imperfect control when quantum logic gates are applied. Fault-tolerant construction based on quantum error correcting codes (QECC) can be used to recover from such errors. Effective implementation of QECC requires a high fidelity readout of the ancilla qubits from which the error syndrome can be determined, without affecting the data qubits in which relevant quantum information is stored for processing. Here, we present a detection scheme for \yb trapped ion qubits, where we use superconducting nanowire single photon detectors and utilize photon time-of-arrival statistics to improve the fidelity and speed. Qubit shuttling allows for creating a separate detection region where an ancilla qubit can be measured without disrupting a data qubit. We achieve an average qubit state detection time of 11$\mu$s with a fidelity of $99.931(6)\%$. The error due to the detection crosstalk, defined as the probability that the coherence of the data qubit is lost due to the process of detecting an ancilla qubit, is reduced to $\sim2\times10^{-5}$ by creating a separation of 370$\mu$m between them.

We study the spreading of initially-local operators under unitary time evolution in a 1d random quantum circuit model which is constrained to conserve a $U(1)$ charge and its dipole moment, motivated by the quantum dynamics of fracton phases. We discover that charge remains localized at its initial position, providing a crisp example of a non-ergodic dynamical phase of random circuit dynamics. This localization can be understood as a consequence of the return properties of low dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing. The charge dynamics is well-described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions in good agreement with numerics. Importantly, these equations also predict localization in 2d fractonic circuits. Immobile fractonic charge emits non-conserved operators, whose spreading is governed by exponents distinct to non-fractonic circuits. Fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement. The entanglement spectrum follows semi-Poisson statistics, similar to eigenstates of MBL systems. The non-ergodic phenomenology persists to initial conditions containing non-zero density of dipolar or fractonic charge. Our work implies that low-dimensional fracton systems preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories. It also implies that 1d and 2d fracton systems should realize true MBL under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translation invariant systems and in d>1 being evaded by the nature of the mechanism responsible for localization. We also suggest a possible route to new non-ergodic phases in high dimensions.

A theoretical model of endogenous fluctuations of the norm of the wave function, consistent with the standard quantum theory, is presented. These fluctuations are a subsystem of endogenous quantum fluctuations and describe one of the decoherence channels and the dynamics of the collapse of the quantum state.

Author(s): D. Vasylyev, W. Vogel, and F. Moll

The establishment of quantum communication links over a global scale is enabled by satellite nodes. We examine the influence of the Earth's atmosphere on the performance of quantum optical communication channels with emphasis on the downlink scenario. We derive the geometrical path length between a ...

[Phys. Rev. A 99, 053830] Published Tue May 21, 2019

Author(s): Hugo Defienne and Sylvain Gigan

We demonstrate experimental generation of spatially entangled photon pairs by spontaneous parametric down-conversion (SPDC) using a partial spatially coherent pump beam. By varying the spatial coherence of the pump, we show its influence on the down-converted photon's spatial correlations and on its...

[Phys. Rev. A 99, 053831] Published Tue May 21, 2019

Researchers observe a critical point—a feature indicative of a continuous phase transition—in the brain’s electrical activity as it switches from an asleep-like to an awake-like state.

[Physics] Published Tue May 21, 2019

Categories: Physics

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices that execute a simulation using less memory than possible by classical means. To realise this advantage it is essential that the memory register remains coherent, and coherently interacts with the processor, allowing the simulator to operate over many time steps. Here we report a multi-time-step experimental simulation of a stochastic process using less memory than the classical limit. A key feature of the photonic quantum information processor is that it creates a quantum superposition of all possible future trajectories that the system can evolve into. This superposition allows us to introduce, and demonstrate, the idea of comparing statistical futures of two classical processes via quantum interference. We demonstrate interference of two 16-dimensional quantum states, representing statistical futures of our process, with a visibility of 0.96 $\pm$ 0.02.

We introduce topological invariants for critical bosonic and fermionic chains. More generally, the symmetry properties of operators in the low-energy conformal field theory (CFT) provide discrete invariants, establishing the notion of symmetry-enriched quantum criticality. For nonlocal operators, these invariants are topological and imply the presence of localized edge modes. Depending on the symmetry, the finite-size splitting of this topological degeneracy can be exponential or algebraic in system size. An example of the former is given by tuning the spin-1 Heisenberg chain to an Ising phase. An example of the latter arises between the gapped Ising and cluster phases: this symmetry-enriched Ising CFT has an edge mode with finite-size splitting $\sim 1/L^{14}$. More generally, our formalism unifies various examples previously studied in the literature. Similar to gapped symmetry-protected topological phases, a given CFT can split into several distinct symmetry-enriched CFTs. This raises the question of classification, to which we give a partial answer---including a complete characterization of symmetry-enriched Ising CFTs.