arXiv subjects

Jian-Dong Zhang

Publications and source records attributed to Jian-Dong Zhang.

At least 19 recordsLinked to original sources

arXiv2024

Performance advantage of discriminating one-versus-two incoherent sources based on quantum hypothesis testing

Detecting the presence of multiple incoherent sources is a fundamental and challenging task for quantum imaging, especially within sub-Rayleigh region. In this paper, the discrimination of one-versus-two point-like incoherent sources in symmetric and asymmetric scenarios is studied. We calculate the quantum lower bounds on error probabilities of making a decision after one-shot and multi-shot tests. The results are compared with the error probability of prior-based direct guess, and the minimal number of tests required to make a decision outperforming direct guess is discussed. We also show the asymptotic quantum lower bound for a large number of tests. For practical purposes, we propose a specific strategy along with decision rule of which can work without any prior knowledge. With respect to each of two scenarios, the error probability can approach the quantum lower bound in one-shot test as well as multi-shot test. In addition, the potential challenges and solutions in a realistic scenario are analyzed. Our results may contribute to real-world quantum imaging such as microscopy and astronomy.

quant-ph↗

arXiv2024

Precision bounds for quantum phase estimation using two-mode squeezed Gaussian states

Quantum phase estimation based on Gaussian states plays a crucial role in many application fields. In this paper, we study the precision bound for the scheme using two-mode squeezed Gaussian states. The quantum Fisher information is calculated and its maximization is used to determine the optimal parameters. We find that two single-mode squeezed vacuum states are the optimal inputs and the corresponding precision bound is superior to the Heisenberg limit by a factor of 2. For practical purposes, we consider the effects originating from photon loss. The precision bound can still outperform the shot-noise limit when the lossy rate is below 0.4. Our work may demonstrate a significant and promising step towards practical quantum metrology.

quant-ph↗

arXiv2024

Performance advantage of quantum hypothesis testing for partially coherent optical sources

Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely incoherent. In this paper, this problem is generalized to the scenario with partially coherent sources and any prior probabilities. We compare the error probability limit given by the quantum Helstrom bound with the error probability given by direct decision based on the prior probability. On this basis, the quantum-optimal detection advantage and detection-useless region are analyzed. For practical purposes, we propose a specific detection strategy using binary spatial-mode demultiplexing, which can be used in the scenarios without any prior information. This strategy shows superior detection performance and the results hold prospects for achieving super-resolved microscopic and astronomical imaging.

quant-ph↗

arXiv2024

Superresolution imaging of two incoherent optical sources with unequal brightnesses

Resolving the separation between two incoherent optical sources with high precision is of great significance for fluorescence imaging and astronomical observations. In this paper, we focus on a more general scenario where two sources have unequal brightnesses. We give the ultimate precision limit with respect to separation by using the quantum Fisher information. Through the calculation of the classical Fisher information, we analyze and compare several specific measurement schemes including direct measurement, Gaussian mode measurement and zero-photon measurement. The results indicate that Gaussian mode measurement is the nearly optimal for a small separation. Our work provides a positive complement to the aspect of superresolution imaging of incoherent sources.

quant-ph↗

arXiv2024

Two-parameter estimation with single squeezed-light interferometer via double homodyne detection

The simultaneous two-parameter estimation problem in single squeezed-light Mach-Zehnder interferometer with double-port homodyne detection is investigated in this work. The analytical form of the two-parameter quantum Cramer-Bao bound defined by the quantum Fisher information matrix is presented, which shows the ultimate limit of the phase sensitivity will be further approved by the squeezed vacuum state. It can not only surpass the shot-noise limit, but also can even surpass the Heisenberg limit when half of the input intensity of the interferometer is provided by the coherent state and half by the squeezed light. For the double-port homodyne detection, the classical Fisher information matrix is also obtained. Our results show that although the classical Cramer-Rao bound does not saturate the quantum one, it can still asymptotically approach the quantum Cramer -Bao bound when the intensity of the coherent state is large enough. Our results also indicate that the squeezed vacuum state indeed can further improve the phase sensitivity. In addition, when half of the input intensity of the interferometer is provided by the coherent state and half by the squeezed light, the phase sensitivity obtained by the double-port homodyne detection can surpass the Heisenberg limit for a small range of the estimated phase.

quant-ph↗

arXiv2022

A Higher Probability of Detecting Lensed Supermassive Black Hole Binaries by LISA

Gravitational lensing of gravitational waves (GWs) is a powerful probe of the matter distribution in the universe. Here we revisit the wave-optics effects induced by dark matter (DM) halos on the GW signals of merging massive black hole binaries (MBHBs), and we study the possibility of discerning these effects using the Laser Interferometer Space Antenna (LISA). In particular, we include the halos in the low-mass range of $\rm 10^5-10^8\, M_\odot$ since they are the most numerous according to the cold DM model. We simulate the lensed signals corresponding to a wide range of impact parameters, and we find distinguishable deviation from the standard best-fit GW templates even when the impact parameter is as large $y\simeq50$. Consequently, we estimate that over $(0.1-1.6)\%$ of the MBHBs in the mass range of $\rm 10^{5.0}-10^{6.5}\, M_\odot$ and the redshift range of $4-10$ should show detectable wave-optics effects. This probability is one order of magnitude higher than that derived in previous works. The uncertainty comes mainly from the mass function of the DM halos. Not detecting any signal during the LISA mission would imply that DM halos with $\rm 10^5-10^8\, M_\odot$ are less numerous than what the cold DM model predicts.

astro-ph.CO↗

arXiv2021

Quantum-enhanced SU(1,1) interferometry via a Fock state

In this paper, we derive a general expression of the quantum Fisher information of an SU(1,1) interferometer with an arbitrary state and a Fock state as inputs by the phase-averaging method. Our results show that the same quantum Fisher information can be obtained regardless of the specific form of the arbitrary state. Then, we analytically prove that the parity measurement can saturate the quantum Cramer-Rao bound when the estimated phase sits at the optimal working point. For practical reasons, we investigate the phase sensitivity when the arbitrary state is a coherent or thermal state. We further show that a Fock state can indeed enhance the phase sensitivity within a constraint on the total mean photon number inside the interferometer.

quant-ph↗

arXiv2020

Phase sensitivity approaching quantum Cramer-Rao bound in a modified SU(1,1) interferometer

SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, the SU(1,1) interferometer cannot make full use of photons carrying phase information as the second nonlinear element annihilates some of the photons inside. Here, we focus on improving phase sensitivity and propose a new protocol based on a modified SU(1,1) interferometer, where the second nonlinear element is replaced by a beam splitter. We utilize two coherent states as inputs and implement balanced homodyne measurement at the output. Our analysis suggests that the protocol we propose can achieve sub-shot-noise-limited phase sensitivity and is robust against photon loss and background noise. Our work is important for practical quantum metrology using SU(1,1) interferometers.

quant-ph↗

arXiv2020

Classical Inputs and Measurements Enable Phase Sensitivity beyond the Shot-Noise Limit

Coherent-state-based phase estimation is a fruitful testbed for the field of precision measurements since coherent states are robust to decoherence when compared with exotic quantum states. The seminal work done by Caves (https://doi.org/10.1103/PhysRevD.23.1693 , Phys. Rev. D 23, 1693 (1981)) stated that the phase sensitivity of a U(2) interferometer fed with a coherent state is limited by the shot-noise limit (SNL). In this Letter, we demonstrate that this bound is not conclusive sensitivity limit and can be broken when the measurement includes an external phase reference. The SNL can be surpassed by a factor of $\sqrt{2}$ and the validity is supported through the calculation of quantum Fisher information. Additionally, we discuss other single-mode Gaussian inputs of which sensitivities are beyond the SNL. Our work shows potential applications for many metological scenarios, particularly when the measured samples immersed in great lossy environments or can withstand bright illumination.

quant-ph↗

arXiv2019

Single-shot Precise Ranging using Twisted Light

Over the past decade, optical orbital angular momentum (OAM) modes were shown to offer advantages in optical information acquisition. Here, we introduce a new scheme for optical ranging in which depth is estimated through the angular rotation of petal-like patterns produced by superposition of OAM modes. Uncertainty of depth estimation in our strategy depends on how fast the petal-like pattern rotates and how precisely the rotation angle can be estimated. The impact of these two factors on ranging accuracy are analyzed in presence of noise. We show that focusing the probe beam provides a quadratic enhancement on ranging accuracy because rotation speed of the beam is inversely proportional to the square of beam radius. Uncertainty of depth estimation is also proportional to uncertainty of rotation estimation, which can be optimized by picking proper OAM superposition. Finally, we unveil the possibility of optical ranging for scattering surface with uncertainties of few micrometers under noise. Unlike existing methods which rely on continuous detection for a period of time to achieve such ranging accuracy, our scheme needs only single-shot measurement.

physics.optics↗

arXiv2019

Control of Structured Light Enables Nearly Perfect Noise-filtering

The performance of laser-based active sensing has been severely limited by two types of noise: electrical noise, stemming from elements; optical noise, laser jamming from an eavesdropper and background from environment. Conventional methods to filter optical noise take advantage of the differences between signal and noise in time, wavelength, and polarization. However, they may be limited when the noise and signal share the same information on these degrees of freedoms (DoFs). In order to overcome this drawback, we experimentally demonstrate a groundbreaking noise-filtering method by controlling orbital angular momentum (OAM) to distinguish signal from noise. We provide a proof-of-principle experiment and discuss the dependence of azimuthal index of OAM and detection aperture on signal-to-noise ratio (SNR). Our results suggest that using OAM against noise is an efficient method, offering a new route to optical sensing immersed in high-level noise.

physics.optics↗

arXiv2019

Conclusive nonlinear phase sensitivity limit for a Mach-Zehnder interferometer with single-mode non-vacuum inputs

Many works have stated that nonlinear interactions can improve phase sensitivity beyond the Heisenberg limit scaling of $1/N$ with $N$ being the mean photon number. This raises some open questions---among them the conclusive sensitivity limits with respect to single-mode inputs. Namely, when one of two inputs is vacuum, is there a shot-noise-style sensitivity bound on a nonlinear Mach-Zehnder interferometer? Within the reach of second-order nonlinear phase shifts, we make an attempt to provide an answer to this question. Based upon phase-averaging approach, this puzzle is partially resolved with careful calculations of the quantum Fisher information regarding three kinds of common inputs: Gaussian states, squeezed number states, and Schrödinger cat states. The results suggest that shot-noise-style sensitivity limit is no longer available, and the ideal candidate is squeezed vacuum.

quant-ph↗

arXiv2019

A nearly optimal and robust protocol for nonlinear phase estimation using coherent states

We propose a protocol for the second-order nonlinear phase estimation with a coherent state as input and balanced homodyne detection as measurement strategy. The sensitivity is sub-Heisenberg limit, which scales as $N^{-3/2}$ for $N$ photons on average. By ruling out hidden resources in quantum Fisher information, the fundamental sensitivity limit is recalculated and compared to the optimal sensitivity of our protocol. In addition, we investigate the effect of photon loss on sensitivity, and discuss the robustness of measurement strategy. The results indicate that our protocol is nearly optimal and robust.

quant-ph↗

arXiv2019

Angular-spectrum-based analysis on the self-healing effect of Laguerre-Gaussian beams after an obstacle

Self-healing, as an exotic effect, has showed many potential applications. In this paper, we focus on the self-healing effect of Laguerre-Gaussian beams after an obstacle. By taking advantage of angular spectrum theory, we study self-healing limit of the beam against on-axis obstacle. The dependence of self-healing capability on the radius of obstacle is analyzed. Additionally, we briefly discuss the self-healing limit of the beam in an off-axis scenario. Our results indicate that field amplitude of the beam will be healed well when the obstacle is approximately on-axis without oversized radius, perhaps providing advantages for optical communication, imaging, and remote sensing systems.

physics.optics↗

arXiv2018

Sub-Heisenberg-limited nonlinear phase estimation: Parity measurement approaches the quantum Cramér-Rao bound

Quantum-enhanced phase estimation paves the way to ultra-precision sensing and is of great realistic significance. In this paper we investigate theoretically the estimation of a second-order nonlinear phase shift using a coherent state and parity measurement. A numerical expression is derived, the resolution and the sensitivity of parity signal are contrasted to linear phase estimation protocol, and the signal visibility is analyzed. Additionally, by virtue of phase-averaging approach to eliminate any hidden resources, we make an attempt at unveiling the low-down on the fundamental sensitivity limit from the quantum Fisher information. Finally, the effects of several realistic scenarios on the resolution and the sensitivity are studied, including photon loss, imperfect detector, and those which are a combination thereof.

quant-ph↗

arXiv2018

Deterministic super-resolved estimation towards angular displacements based upon a Sagnac interferometer and parity measurement

Super-resolved angular displacement estimation is of crucial significances for quantum information process and optical lithography. Here we report on and experimentally demonstrate a protocol for angular displacement estimation based on a coherent state containing orbital angular momentum. In the lossless scenario, with using parity measurement, this protocol can theoretically achieve 4$\ell$-fold super-resolution with quantum number $\ell$, and shot-noise-limited sensitivity saturating the quantum Cramér-Rao bound. Several realistic factors and their effects are considered, including nonideal state preparation, photon loss, and imperfect detector. Finally, given mean photon number $\bar N=2.297$ and $\ell=1$, we show an angular displacement super-resolution effect with a factor of 7.88, and the sensitivity approaching shot-noise limit is reachable.

quant-ph↗

arXiv2018

Optimal binary strategy for angular displacement estimation based upon fidelity appraisal

We report on an optimal binary strategy for angular displacement estimation. The measuring system is a modified Mach-Zehnder interferometer fed by a coherent state carrying orbital angular momentum, and two Dove prisms are embedded in two paths. In terms of the fidelity appraisal, parity detection and Z detection are discussed, and the optimal estimation strategy is presented. We additionally study the effects of several realistic scenarios on the fidelity, including transmission loss, detection efficiency, dark counts, and those which are a combination thereof. Finally, we exhibit a proof of principle experiment and perform Bayesian estimation on data processing. The experimental results imply resolved enhancement by a factor of 1.86 suggesting super-resolving signal. Meanwhile, on the trial greater than 500, we show that the angular displacement can be precisely estimated via acquired outcome information.

quant-ph↗

arXiv2018

Angular displacement estimation of Heisenberg scaling: Tunable squeezed Bell state via the enhancement of spin and orbital angular momenta

We demonstrate an angular momentum-enhanced protocol that permits an angular displacement estimation by using tunable squeezed Bell state and parity detection. We consider the resolution and the sensitivity, super-resolution is presented along with Heisenberg scaling sensitivity for arbitrary tunable factor, the tunable factor which can optimize the sensitivity is also discussed. Additionally, we analyze the advantages of using angular momentum via considering and comparing simulation results. Under the situation of the optimal tunable factor, the Heisenberg-limited sensitivity and $2\left(\ell+1\right)$-fold super-resolution peak with quantum number $\ell$ are achieved.

quant-ph↗