Related papers: A necessary and sufficient condition for minimum p…
In this paper we derived the precise formula in a sine function form of the norm of the amplitude in the desired state, and by means of he precise formula we presented the necessary and sufficient phase condition for any quantum algorithm…
We answer a number of open problems concerning phase retrieval and phase retrieval by projections. In particular, one main theorem classifies phase retrieval by projections via collections of sequences of vectors allowing norm retrieval.…
In a typical multi-standard military communication receiver, fast and reliable spectrum sensing unit is required to extract the information of multiple channels (frequency bands) present in a wideband input signal. In this paper, an energy…
In this work, we study the phase estimation problem. We show an alternative, simpler and self-contained proof of query lower bounds. Technically, compared to the previous proofs [NW99, Bes05], our proof is considerably elementary.…
We show that there are extremely simple signal detection schemes where the finiteness of energy resources places no limit to the resolution. On the contrary, larger resolution can be obtained with lower energy. To this end the generator of…
This paper investigates the stability of phase retrieval by analyzing the condition number of the nonlinear map $\Psi_{\boldsymbol{A}}(\boldsymbol{x}) = \bigl(\lvert \langle {\boldsymbol{a}}_j, \boldsymbol{x} \rangle \rvert^2 \bigr)_{1 \le…
An uncertainty relation for the number and phase of a single-mode field state is derived. It is then used to find a lower bound on the phase noise of a classical state. Any state that violates this condition is nonclassical. An example of…
The Kennedy-like receiver is a quasi-optimal receiver employed in binary phase-shift-keyed communication schemes with coherent states. It is based on the interference of the two signals encoding the message with a reference local oscillator…
The so-called Transport of Intensity Equation (TIE) phase retrieval technique is widely applied in light, x-ray and electron optics to reconstruct, e.g., refractive indices, electric and magnetic fields in solids. Here, we present a largely…
The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In…
In this article we describe the basic principles of Rydberg atom-based RF sensing and present the development of atomic pulsed RF detection and RF phase sensing establishing capabilities pertinent to applications in communications and…
We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral…
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…
We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under…
In this paper we present the necessary and sufficient conditions of separability for multipartite pure states. These conditions are very simple, and they don't require Schmidt decomposition or tracing out operations. We also give a…
Path-entangled multi-photon states allow optical phase-sensing beyond the shot-noise limit, provided that an efficient parity measurement can be implemented. Realising this experimentally is technologically demanding, as it requires…
Distinguishability takes a crucial rule in studying observability of hybrid system such as switched system. Recently, for two linear systems, Lou and Si gave a condition not only necessary but also sufficient to the distinguishability of…
A measurement scheme to perform a repeatable phase detection on a two-mode field is presented. The interaction with the probe state (the output state of a phase-insensitive high-gain amplifier) is described by a Hamiltonian which is…
Continuous measurements play a pivotal role in the study of dynamical open quantum systems. `Dyne' detections are among the most widespread and efficient measurement schemes, and give rise to quantum diffusion of the conditioned state. In…
Recent advances in convex optimization have led to new strides in the phase retrieval problem over finite-dimensional vector spaces. However, certain fundamental questions remain: What sorts of measurement vectors uniquely determine every…