Gravity does not naturally fit well with canonical quantization. Affine quantization is an alternative procedure that is similar to canonical quantization but may offer a positive result when canonical quantization fails to offer a positive result. Two simple examples given initially illustrate the power of affine quantization. These examples clearly point toward an affine quantization procedure that vastly simplifies a successful quantization of general relativity.

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater X$\alpha$ approximations.

To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to choose a finite set of single-particle wave functions and find all possible distributions of a given number of particles in these states. It is known, however, that this construction leads to very inaccurate results since it does not take into account different many-body states having the same energy on equal footing. Here we present a fast and surprisingly simple algorithm for generating the many-body Fock basis build from many-body Fock states having the lowest non-interacting energies. The algorithm is insensitive to details of the distribution of single-particle energies and it can be used for an arbitrary number of particles obeying bosonic or fermionic statistics. Moreover, it can be easily generalized to a larger number of components. Taking as a simple example the system of two ultra-cold bosons in an anharmonic trap, we show that exact calculations in the basis generated with the algorithm are substantially more accurate than calculations performed within the standard approach.

To obtain estimates of electronic energies, the Variational Quantum Eigensolver (VQE) technique performs separate measurements for multiple parts of the system Hamiltonian. Current quantum hardware is restricted to projective single-qubit measurements, and thus, only parts of the Hamiltonian which form mutually qubit-wise commuting groups can be measured simultaneously. The number of such groups in the electronic structure Hamiltonians grows as $N^4$, where $N$ is the number of qubits, and thus puts serious restrictions on the size of the systems that can be studied. Using a partitioning of the system Hamiltonian as a linear combination of unitary operators we found a circuit formulation of the VQE algorithm that allows one to measure a group of fully anti-commuting terms of the Hamiltonian in a single series of single-qubit measurements. Numerical comparison of the unitary partitioning to previously used grouping of Hamiltonian terms based on their qubit-wise commutativity shows an $N$-fold reduction in the number of measurable groups.

We show that dynamic quantum phase transitions (DQPT) in many situations involve renormalization group (RG) fixed points that are unphysical in the context of thermal phase transitions. In such cases, boundary conditions are shown to become relevant to the extent of even completely suppressing the bulk transitions. We establish these by performing exact RG analysis of the quantum Ising model on scale-invariant lattices of different dimensions, and by analyzing the zeros of the Loschmidt amplitude. Further corroboration of boundaries affecting the bulk transition comes from the three-state quantum Potts chain, for which we also show that the DQPT corresponds to a pair of period-2 fixed points.

One of the major concerns of Schr\"odinger, Lorentz, Einstein, and many others about the wave function is that it is defined on the $3\mathbf{N}$-dimensional configuration space, rather than on the $3$-dimensional physical space. This gives the impression that quantum mechanics cannot have a three-dimensional space or spacetime ontology, even in the absence of quantum measurements. In particular, this seems to affect interpretations which take the wave function as a physical entity, in particular the many worlds and the spontaneous collapse interpretations, and some versions of the pilot wave theory.

Here, a representation of the many-particle states is given, as multi-layered fields defined on the $3$-dimensional physical space. This representation is equivalent to the usual representation on the configuration space, but it makes it explicit that it is possible to interpret the wave functions as defined on the physical space. As long as only unitary evolution is involved, the interactions are local. I intended this representation to capture and formalize the non-explicit and informal intuition of many working quantum physicists, who, by considering the wave function sometimes to be defined on the configuration space, and sometimes on the physical space, may seem to researchers in the foundations of quantum theory as adopting an inconsistent view about its ontology. This representation does not aim to solve the measurement problem, and it allows for Schr\"odinger cats just like the usual one. But it may help various interpretations to solve these problems, through inclusion of the wave function as (part of) their primitive ontology.

In an appendix, it is shown how the multi-layered field representation can be extended to quantum field theory.

We present a general and systematic study of how a Bell experiment on the cosmic microwave background could be carried out. We introduce different classes of pseudo-spin operators and show that, if the system is placed in a two-mode squeezed state as inflation predicts, they all lead to a violation of the Bell inequality. However, we also discuss the obstacles that one faces in order to realize this program in practice and show that they are probably insurmountable. We suggest alternative methods that would reveal the quantum origin of cosmological structures without relying on Bell experiments.

Author(s): Rahul Trivedi, Kevin Fischer, Sattwik Deb Mishra, and Jelena Vučković

We present the point-coupling Hamiltonian as a model for frequency-independent linear optical devices acting on propagating optical modes described as a continua of harmonic oscillators. We formally integrate the Heisenberg equations of motion for this Hamiltonian, calculate its quantum scattering m...

[Phys. Rev. A 100, 043827] Published Mon Oct 21, 2019

Author(s): Sergey V. Sazonov

On the basis of the approximate method of the averaged Lagrangian, the propagation modes of spatiotemporal solitons in a graded-index optical fiber with a Kerr nonlinearity and anisotropic transverse distribution of the linear refractive index are investigated. It is shown that within the framework ...

[Phys. Rev. A 100, 043828] Published Mon Oct 21, 2019

Author(s): Fei Song, Shunyu Yao, and Zhong Wang

One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely, that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians,...

[Phys. Rev. Lett. 123, 170401] Published Mon Oct 21, 2019

Quantum computers still need lots of development before they can compete with conventional computers in chemistry, drug development, and materials science, but they are making progress.

[Physics 12, 112] Published Mon Oct 21, 2019

Categories: Physics

Author(s): Davide Calonico

An all-optical clock scheme could improve time metrology standards, taking an important step toward the redefinition of the second.

[Physics 12, 114] Published Mon Oct 21, 2019

Categories: Physics

Author(s): Shayan-Shawn Majidy, Hemant Katiyar, Galit Anikeeva, Jonathan Halliwell, and Raymond Laflamme

Macroscopic realism (MR) is the view that a system may possess definite properties at any time independent of past or future measurements and may be tested experimentally using the Leggett-Garg inequalities (LGIs). In this work we advance the study of LGIs in two ways using experiments carried out o...

[Phys. Rev. A 100, 042325] Published Mon Oct 21, 2019

Author(s): Long Huang, Xiaohua Wu, and Tao Zhou

In quantum error correction, the description of the noise channel cannot be completely accurate and fluctuation always appears in the noise channel. It is found that when fluctuation of the physical noise channel is considered, the average effective channel is dependent only on the average of the ph...

[Phys. Rev. A 100, 042321] Published Mon Oct 21, 2019

Author(s): M. Carrera, T. Gorin, and C. Pineda

We study the open dynamics of a quantum two-level system coupled to an environment modeled by random matrices. Using the quantum channel formalism, we investigate different quantum Markovianity measures and criteria. A thorough analysis of the whole parameter space reveals a wide range of different ...

[Phys. Rev. A 100, 042322] Published Mon Oct 21, 2019

Author(s): Senrui Chen, Xingjian Zhang, You Zhou, and Qi Zhao

The resource theory of quantum coherence is an important topic in quantum information science. Standard coherence distillation and dilution problems have been thoroughly studied. In this paper, we introduce and study the problem of one-shot coherence distillation with catalysts. In order to distill ...

[Phys. Rev. A 100, 042323] Published Mon Oct 21, 2019

Author(s): Scott M. Cohen

Given a protocol P that implements multipartite quantum channel E by repeated rounds of local operations and classical communication (LOCC), we construct an alternate LOCC protocol for E in no more rounds than P and no more than a fixed, constant number of outcomes for each local measurement, the sa...

[Phys. Rev. A 100, 042324] Published Mon Oct 21, 2019

Complexity in quantum physics measures how difficult a state can be reached from a reference state and more precisely it is the number of fundamental unitary gates we have to operate to transform the reference state to the state we are considering. In the holographic context, based on several explicit calculations and arguments, it is conjectured that certain bulk volume calculates the boundary field theory subregion complexity. In this paper, we will show that the $T\bar{T}$ deformation shows a strong signal of the correctness of this complexity equals volume conjecture. A bonus is a way to look at the $T\bar{T}$ deformation, by its reversibility, as operating a unitary quantum circuit which prepares states in quantum field theory.

We describe a diagrammatic technique for non-Hermitian fermionic systems that is applicable in the steady state, and which allows addressing correlations effects by systematic expansion. Applying this method to exceptional points or rings, we find that nodal objects in non-Hermitian systems are generically displaced in momentum-space due to interactions. This in turn can be connected to the fact that exceptional points invariably break a class of orthonormal symmetries that are generally present for nodal points in Hermitian systems, and which protect the integrity of the node at low energy scales.

This work focuses on the response to an external field of a Brownian particle submerged in an Ohmic quantum thermal bath. The field only affects the dynamics of the central particle without affecting the thermal reservoir. The thermodynamic function to be analyzed is the average work due only to the external force. Being energy a non-local function of the protocol, a standard variational principle is used to derive it. It was found that the energy reaches a minimum imposing a restriction on the optimal protocol. This is found by applying the variational principle to the non-local work functional.It is also a minimum and only depends of the friction coefficient of the surrounding fluid.