Related papers: Randomized measurements for multi-parameter quantu…
This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…
We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is…
Relativistic quantum metrology provides an optimal strategy for the estimation of parameters encoded in quantum fields in flat and curved spacetime. These parameters usually correspond to physical quantities of interest such as proper…
Distinguishing assigned quantum states with assigned probabilities via quantum measurements is a crucial problem for the transmission of classical information through quantum channels. Measurement operators maximizing the probability of…
Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…
We study informationally overcomplete measurements for quantum state estimation so as to clarify their tomographic significance as compared with minimal informationally complete measurements. We show that informationally overcomplete…
Quantum physics constrains the accuracy of joint measurements of incompatible observables. Here we test tight measurement-uncertainty relations using single photons. We implement two independent, idealized uncertainty-estimation methods,…
We find the optimal measurement for distinguishing between symmetric multi-mode phase-randomized coherent states. A motivation for this is that phase-randomized coherent states can be used for quantum communication, including quantum…
We study the problems of quantum tomography and shadow tomography using measurements performed on individual, identical copies of an unknown $d$-dimensional state. We first revisit a known lower bound due to Haah et al. (2017) on quantum…
We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather…
The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Among the surprising features of quantum measurements, the problem of distinguishing and antidistinguishing general quantum measurements is fundamentally appealing. Unlike classical systems, quantum theory offers entangled states and…
We consider the problem of quantum state certification, where we are given the description of a mixed state $\sigma \in \mathbb{C}^{d \times d}$, $n$ copies of a mixed state $\rho \in \mathbb{C}^{d \times d}$, and $\varepsilon > 0$, and we…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
The traditional framework of quantum metrology commonly assumes unlimited access to resources, overlooking resource constraints in realistic scenarios. As such, the optimal strategies therein can be infeasible in practice. Here, we…
Limitations in measurement instruments can hinder the implementation of some quantum algorithms. Understanding the suboptimality of such measurements with restrictions may then lead to more efficient measurement policies. In this paper, we…
One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the…