Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For time-dependent Hamiltonians, however, due to the complexity dynamics, little known about quantum metrology. Here we investigate Hamiltonians bridge this gap. We obtain optimal Fisher information parameters in and show proper Hamiltonian control is generally necessary optimize information. derive control, which adaptive, measurement scheme attain In minimal example qubit rotating magnetic...

Quantum metrology enhances the sensitivity of parameter estimation using distinctive resources quantum mechanics such as entanglement. It has been shown that precision estimating an overall multiplicative factor a Hamiltonian can be increased to exceed classical limit, yet little is known about general parameter. In this paper, we study problem in detail. We find scaling with number systems always optimized Heisenberg while time quite different from factor. derive generator local translation...

Postselected weak measurement is a useful protocol for amplifying physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While now clear that retaining failed postselections can yield more Fisher information than discarding them, the of postselection itself still remains to be clarified. In this Letter, we address problem by studying two widely used estimation strategies: averaging results, and maximum likelihood estimation,...

We develop a variational principle to determine the quantum controls and initial state that optimizes Fisher information, quantity characterizing precision in metrology. When set of available is limited, exact optimal are, general, dependent on probe time, feature missing unrestricted case. Yet, for time-independent Hamiltonians with restricted controls, problem can be approximately reduced unconstrained case via Floquet engineering. In particular, we find magnetometry spin chain containing...

We study quantum measurement with preselection and postselection, derive the precise expressions of results without any restriction on coupling strength between system measuring device. For a qubit system, we maximum pointer shifts by choosing appropriate initial finial states. A significant amplification effect is obtained when interaction device very weak, typical ideal are strong. The improvement signal-to-noise ratio (SNR) enhancement sensitivity (MS) weak measurements studied. Without...

Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in small parameter, which has also enabled simple method precise parameter estimation. However, producing large value requires low postselection probability an ancilla degree freedom, limits utility technique. We propose improvement this that uses entanglement increase efficiency. show by entangling and postselecting $n$ ancillas, can be increased factor while keeping fixed (compared...

We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. derive a matrix bound of classical Fisher information due each measurement operator. The saturation all these bounds results in Helstrom Cram\'er-Rao bound. Remarkably, is equivalent scalar respect any given positive definite weight matrix. Necessary sufficient conditions are obtained for optimal measurements that give rise associated state. To...

In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass Heisenberg scaling. Here, we consider interaction strength in linear systems with long-range and using Kitaev chains as a case study, establish transition from super-Heisenberg scaling Fisher information by varying range. We further show that control improve prefactor information. Our results explore advantage optimal metrology.

One of the fundamental questions in quantum information theory is to find how many measurement bases are required obtain full a state. While minimum four typically determine an arbitrary pure state, we prove that for any states generated by finite-depth Clifford + T circuits, just two sufficient. More generally, informationally complete determining algebraic whose state-vector elements represented computational basis numbers. Since state can be asymptotically approximated sequence with...

Given $n$ linearly independent pure states and their prior probabilities, we study the problem of optimum unambiguous discrimination these states. We derive properties solution equations that must be satisfied by measurement strategy which achieves maximum average success probability, also give detailed steps to obtain strategy. The general method results are illustrated both numerically geometrically. a simple analytical formula probability for given set states, it can used simplify...

In almost all quantum applications, one of the key steps is to verify that fidelity prepared state meets expectations. this Letter, we propose a new approach solving problem using machine-learning techniques. Compared other estimation methods, our method applicable arbitrary states, number required measurement settings small, and does not increase with size system. For example, for general five-qubit state, only four are predict its $\ifmmode\pm\else\textpm\fi{}1%$ precision in...

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive maximum likelihood estimation in general to first-order approximation a small deviation probability distribution and study robustness standard measurement postselected against errors. show that, with large value, when probe undergoes decoherence can be significantly lower than that measurement. This indicates another advantage weak-value amplification improving performance...

We investigate the fundamental limits in precision allowed by quantum mechanics from Landau-Zener transitions, concerning Hamiltonian parameters. While transition probabilities depend sensitively on system parameters, much more may be obtained using acquired phase, quantified Fisher information. This information scales with a power of elapsed time for case, whereas it is independent if alone are used. add coherent control to and increase permitted maximum this time-dependent system. The case...

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

The quantum Zeno effect is a distinctive phenomenon in mechanics, describing the nontrivial of frequent projective measurements on hindering evolution system. However, when subjected to environmental noise, system may dissipate, and no longer works. This research starts from physical mechanism for decay presence noise investigates coherent controls mitigating decrease survival probability that stays initial state induced by noise. We derive rate with without general, show frequency large but...

The Heisenberg scaling is an ultimate precision limit of parameter estimation allowed by the principles quantum mechanics, with no counterpart in classical realm, and has been a long-pursued goal metrology. It known that interactions between probes can help reach without entanglement. In this paper, we show additional dimensions ancillary system may also increase to surpass standard attain entanglement, if measurement scheme properly designed. Fisher information exhibits periodic patterns...

Due to the existence of quantum correlations between photon pairs, their average position can be determined more precisely than individual each photon. This effect is exploited enhance precision and resolution measuring optical displacements.

Postselected weak measurement has aroused broad interest for its distinctive ability to amplify small physical quantities. However, the low postselection efficiency obtain a large value been big obstacle application in practice since it may waste resources, and reduce precision. An improved protocol was proposed Pang et al., Phys. Rev. Lett. 113, 030401 (2014) make postselected dramatically more efficient by using entanglement. Such can increase Fisher information of approximately saturate...

Postselected weak measurement has been widely used in experiments to observe effects various physical systems. However, it is still unclear how large the amplification ability of a can be and what determines limit this ability, which fundamental understanding applying measurements. The limitation conventional weak-value formalism for problem divergence values when pre- postselections are nearly orthogonal. In paper, we study by variational approach general Hamiltonian...

A quantum computer encodes information in states and runs algorithms to surpass the classical counterparts by exploiting superposition correlation. Grover's search algorithm is a typical that proves superiority of computing over computing. It has quadratic reduction query complexity database known be optimal when no priori about elements provided. In this work we consider probabilistic Grover allowing nonzero probability failure for with general distribution minimize number oracle calls...

The Markovianity of quantum dynamics is an important property open systems determined by various ingredients the system and bath. Apart from system-bath interaction, initial state bath, etc., dimension bath plays a critical role in determining dynamics, as strict decay correlations requires infinite for In this work, we investigate finite considering simple but nontrivial model which central spin isotropically coupled to number spins, show how transits non-Markovian Markovian spins...

In this article, we study the problem of comparing mixed quantum states: given $n$ unknown states, can one determine whether they are identical or not with an unambiguous measurement? We first universal comparison and prove that task is generally impossible to accomplish. Then, focus on states arbitrarily chosen from a set $k$ states. The condition for existence measurement operator which produce conclusive result when actually same different studied independently. derive necessary...