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Conventional wisdom dictates that to image the position of fluorescent atoms or molecules, one should stimulate as much emission and collect as many photons as possible. That is, in this classical case, it has always been assumed that the…
We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition, for capturing the physics of how incoming photons interact with finite-sized dispersive media, which is not describable by the…
For a particle moving on a half-line or in an interval the operator $\hat p = - i \partial_x$ is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on $\hat p$ fails. Based upon a…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Canonical quantization (CQ) is built around $[Q,P]=i\hbar1\!\!1$, while affine quantization (AQ) is built around $[Q,D]=i\hbar\,Q$, where $D\equiv(PQ+QP)/2$. The basic CQ operators must fit $-\infty< P, Q <\infty$, while the basic AQ…
An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…
A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. This paper shows that quantum entanglement and squeezing can be employed to…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
Quantum-enhanced measurements use quantum mechanical effects in order to enhance the sensitivity of the measurement of classical quantities, such as the length of an optical cavity. The major goal is to beat the standard quantum limit…
Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements.…
Canonical quantization of the photon -- a free massless vector field -- is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting…
We propose a numerical homogenization method for scalar linear partial differential equations with rough coefficients, that integrates classical coarse-scale solvers with quantum subroutines for fine-scale corrections. Inspired by the…
Quantum entanglement is known as a unique quantum feature that cannot be obtained by classical physics. Over the last several decades, however, such an understanding on quantum entanglement might have confined us in a limited world of weird…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional…
Shared entanglement can significantly amplify classical correlations between systems interacting over a limited quantum channel. A natural avenue is to use entanglement of the same dimension as the channel because this allows for unitary…
We develop a systematic classical framework to accommodate canonical quantization of geometric and matter perturbations on a quantum homogeneous isotropic flat spacetime. The existing approach of standard cosmological perturbations is…
The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the…
Combinatorial optimization problems have wide-ranging applications in industry and academia. Quantum computers may help solve them by sampling from carefully prepared Ansatz quantum circuits. However, current quantum computers are limited…
Quantum sensing can enhance imaging performance by reducing measurement noise below the classical limit, thereby improving the signal-to-noise ratio (SNR) of acquired data. In conventional quantum imaging schemes, squeezing is applied…