arXiv subjects

Shengshi Pang

Publications and source records attributed to Shengshi Pang.

At least 37 records · Page 2Linked to original sources

arXiv2021

Direct Fidelity Estimation of Quantum States using Machine Learning

In almost all quantum applications, one of the key steps is to verify that the fidelity of the prepared quantum state meets expectations. In this Letter, we propose a new approach solving this problem using machine-learning techniques. Compared to other fidelity estimation methods, our method is applicable to arbitrary quantum states, the number of required measurement settings is small, and this number does not increase with the size of the system. For example, for a general five-qubit quantum state, only four measurement settings are required to predict its fidelity with $\pm1\%$ precision in a nonadversarial scenario. This machine-learning-based approach for estimating quantum state fidelity has the potential to be widely used in the field of quantum information.

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arXiv2019

Optimal measurements for quantum multiparameter estimation with general states

We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement operator. The saturation of all these bounds results in the saturation of the matrix Helstrom Cramér-Rao bound. Remarkably, the saturation of the matrix bound is equivalent to the saturation of the scalar bound with respect to any given positive definite weight matrix. Necessary and sufficient conditions are obtained for the optimal measurements that give rise to the Helstrom Cramér-Rao bound associated with a general quantum state. To saturate the Helstrom bound with separable measurements or collective measurement entangling only a small number of identical states, we find it is necessary for the symmetric logarithmic derivatives to commute on the support of the state. As an important application of our results, we construct several local optimal measurements for the problem of estimating the three-dimensional separation of two incoherent optical point sources.

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arXiv2018

Quantum state tomography with time-continuous measurements: reconstruction with resource limitations

We propose and analyze quantum state estimation (tomography) using continuous quantum measurements with resource limitations, allowing the global state of many qubits to be constructed from only measuring a few. We give a proof-of-principle investigation demonstrating successful tomographic reconstruction of an arbitrary initial quantum state for three different situations: single qubit, remote qubit, and two interacting qubits. The tomographic reconstruction utilizes only a continuous weak probe of a single qubit observable, a fixed coupling Hamiltonian, together with single-qubit controls. In the single qubit case, a combination of the continuous measurement of an observable and a Rabi oscillation is sufficient to find all three unknown qubit state components. For two interacting qubits, where only one observable of the first qubit is measured, the control Hamiltonian can be implemented to transfer all quantum information to the measured observable, via the qubit-qubit interaction and Rabi oscillation controls applied locally on each qubit. We discuss different sets of controls by analyzing the unitary dynamics and the Fisher information matrix of the estimation in the limit of weak measurement, and simulate tomographic results numerically. As a result, we obtained reconstructed state fidelities in excess of 0.98 with a few thousand measurement runs.

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arXiv2017

Abrupt transitions between Markovian and non-Markovian dynamics in open quantum systems

A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understanding that Markovian dynamics is an asymptotic behavior under the Born-Markov approximation. We also study the time correlation of the bath, and find that the decay rate of bath time correlation is of the same order as the system evolution speed. This suggests that quantum Markovian dynamics can exist beyond the usual short bath correlation limit.

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arXiv2017

Optimal adaptive control for quantum metrology with time-dependent Hamiltonians

Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of $T^{2}$ time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches $T^{4}$ in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case.

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arXiv2016

Quantum parameter estimation with the Landau-Zener transition

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While the Landau-Zener transition probabilities depend sensitively on the system parameters, much more precision may be obtained using the acquired phase, quantified by the quantum Fisher information. This information scales with a power of the elapsed time for the quantum case, whereas it is time-independent if the transition probabilities alone are used. We add coherent control to the system, and increase the permitted maximum precision in this time-dependent quantum system. The case of multiple passes before measurement, "Landau-Zener-Stueckelberg interferometry", is considered, and we demonstrate that proper quantum control can cause the quantum Fisher information about the oscillation frequency to scale as $T^4$, where $T$ is the elapsed time.

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arXiv2016

Protecting weak measurements against systematic errors

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak measurements against systematic errors. We show that, with a large weak value, the systematic error of a postselected weak measurement when the probe undergoes decoherence can be significantly lower than that of a standard weak measurement. This indicates the advantage of weak value amplification in improving the performance of parameter estimation. We illustrate the results by an exact numerical simulation of decoherence arising from a bosonic mode and compare it to the first-order analytical result we obtain.

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arXiv2016

Quantum metrology for a general Hamiltonian parameter

Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a Hamiltonian can be increased to exceed the classical limit, yet little is known about estimating a general Hamiltonian parameter. In this paper, we study this problem in detail. We find that the scaling of the estimation precision with the number of systems can always be optimized to the Heisenberg limit, while the time scaling can be quite different from that of estimating an overall multiplicative factor. We derive the generator of local parameter translation on the unitary evolution operator of the Hamiltonian, and use it to evaluate the estimation precision of the parameter and establish a general upper bound on the quantum Fisher information. The results indicate that the quantum Fisher information generally can be divided into two parts: one is quadratic in time, while the other oscillates with time. When the eigenvalues of the Hamiltonian do not depend on the parameter, the quadratic term vanishes, and the quantum Fisher information will be bounded in this case. To illustrate the results, we give an example of estimating a parameter of a magnetic field by measuring a spin-$\frac{1}{2}$ particle, and compare the results for estimating the amplitude and the direction of the magnetic field.

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arXiv2016

Precision optical displacement measurements using biphotons

We propose and examine the use of biphoton pairs, such as those created in parametric down conversion or four-wave mixing, to enhance the precision and the resolution of measuring optical displacements by position-sensitive detection. We show that the precision of measuring a small optical beam displacement with this method can be significantly enhanced by the correlation between the two photons, given the same optical mode. The improvement is largest if the correlations between the photons are strong, and falls off as the biphoton correlation weakens. More surprisingly, we find that the smallest resolvable parameter of a simple split detector scales as the inverse of the number of biphotons for small biphoton number ("Heisenberg scaling"), because the Fisher information diverges as the parameter to be estimated decreases in value. One usually sees this scaling only for systems with many entangled degrees of freedom. We discuss the transition for the split-detection scheme to the standard quantum limit scaling for imperfect correlations as the biphoton number is increased. An analysis of an $N$-pixel detector is also given to investigate the benefit of using a higher resolution detector. The physical limit of these metrology schemes is determined by the uncertainty in the birth zone of the biphoton in the nonlinear crystal.

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arXiv2015

Improving the precision of weak measurements by postselection measurement

Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.

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arXiv2015

Suppressing technical noises in weak measurement by entanglement

Postselected weak measurement has aroused broad interest for its distinctive ability to amplify small physical quantities. However, the low postselection efficiency to obtain a large weak value has been a big obstacle to its application in practice, since it may waste resources, and reduce the measurement precision. An improved protocol was proposed in [Phys. Rev. Lett. 113, 030401 (2014)] to make the postselected weak measurement dramatically more efficient by using entanglement. Such a protocol can increase the Fisher information of the measurement to approximately saturate the well-known Heisenberg limit. In this paper, we review the entanglement-assisted protocol of postselected weak measurement in detail, and study its robustness against technical noises. We focus on readout errors. Readout errors can greatly degrade the performance of postselected weak measurement, especially when the readout error probability is comparable to the postselection probability. We show that entanglement can significantly reduce the two main detrimental effects of readout errors: inaccuracy in the measurement result, and the loss of Fisher information. We extend the protocol by introducing a majority vote scheme to postselection to further compensate for readout errors. With a proper threshold, almost no Fisher information will be lost. These results demonstrate the effectiveness of entanglement in protecting postselected weak measurement against readout errors.

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arXiv2014

Amplification limit of weak measurements: a variational approach

Post-selected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the limit of this ability, which is fundamental to understanding and applying weak measurements. The limitation of the conventional weak value formalism for this problem is the divergence of weak values when the pre- and post-selections are nearly orthogonal. In this paper, we study this problem by a variational approach for a general Hamiltonian $H_{\mathrm{int}}=gA\otimesΩδ(t-t_{0}),\, g\ll1$. We derive a general asymptotic solution, and show that the amplification limit is essentially independent of $g$, and determined only by the initial state of the detector and the number of distinct eigenvalues of $A$ or $Ω$. An example of spin-$\frac{1}{2}$ particles with a pair of Stern-Gerlach devices is given to illustrate the results. The limiting case of continuous variable systems is also investigated to demonstrate the influence of system dimension on the amplification limit.

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arXiv2014

Entanglement-assisted weak value amplification

Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting $n$ ancillas, the postselection probability can be increased by a factor of $n$ while keeping the weak value fixed (compared to $n$ uncorrelated attempts with one ancilla), which is the optimal scaling with $n$ that is expected from quantum metrology. Furthermore, we show the surprising result that the quantum Fisher information about the detected parameter can be almost entirely preserved in the postselected state, which allows the sensitive estimation to approximately saturate the optimal quantum Cramér-Rao bound. To illustrate this protocol we provide simple quantum circuits that can be implemented using current experimental realizations of three entangled qubits.

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arXiv2012

Unambiguous Examining the Orthogonality of Multiple Quantum States

In this article, we study an opposite problem of universal quantum state comparison, that is unambiguous determining whether multiple unknown quantum states from a Hilbert space are orthogonal or not. We show that no unambiguous quantum measurement can accomplish this task with a non-zero probability. Moreover, we extend the problem to a more general case, that is to compare how orthogonal multiple unknown quantum states are with a threshold, and it turns out that given any threshold this extended task is also impossible by any unambiguous quantum measurement except for a trivial case. It will be seen that the impossibility revealed in our problem is stronger than that in the universal quantum state comparison problem and distinct from those in the existing "no-go" theorems.

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arXiv2012

Weak measurement with orthogonal pre-selection and post-selection

Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the pre-selection and the post-selection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and post-selections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and post-selections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and post-selections tend to be orthogonal.

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arXiv2011

Nonexistence of a universal quantum machine to examine the precision of unknown quantum states

In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This impossibility is distinct from the existing impossibilities in that it is a "collective" impossibility on multiple quantum states while most other "no-go" theorems concern with only one single state each time, i.e., it is an impossibility on a non-local quantum operation. This novel impossibility may provide a new insight into the nature of quantum mechanics and it implies more limitations on quantum information tasks than the existing "no-go" theorems.

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arXiv2011

Quantum measurements with preselection and postselection

We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-tonoise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.

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arXiv2011

Non-existence of invariant EPR correlation for two qudits, d>2

The two qubit (spin 1/2) singlet state has invariant perfect EPR correlations: if two observers measure {\em any} identical observables the results are always perfectly (anti-)correlated. We show that no such correlations exists in $d\otimes d$ pure or mixed bipartite quantum states if $d\geq3$. This points that two qubit singlets are high-quality quantum information carriers in long distance transmission: their correlations are unaffected by identical random unitary transformations of both qubits. Pairs of entangled qu$d$its, $d>2$, do not have this property. Thus, qu$d$it properties should be rather exploited only in protocols in which transmission is not a long distance one.

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