We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits achievable gain precision by entanglement. show that using tools from error correction this limitation can be overcome. This is demonstrated two scenarios, including a many-body Hamiltonian with single-qubit dephasing or depolarizing single-body transversal noise. In both cases, we Heisenberg scaling, hence quadratic improvement over classical case, retained. Moreover, for case frequency...

We establish general limits on how precise a parameter, e.g. frequency or the strength of magnetic field, can be estimated with aid full and fast quantum control. consider uncorrelated noisy evolutions N qubits show that control allows to fully restore Heisenberg scaling (~1/N^2) for all rank-one Pauli noise except dephasing. For other types asymptotic enhancement is unavoidably limited constant-factor improvement over standard limit (~1/N) even when allowing power The latter holds both in...

We address the issue of precisely estimating small parameters encoded in a general linear transformation modes bosonic quantum field. Such Bogoliubov transformations frequently appear context optics. provide set instructions for computing Fisher information arbitrary pure initial states. show that maximally achievable precision estimation is inversely proportional to squared average particle number and such Heisenberg scaling requires nonclassical but not necessarily entangled Our method...

Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilising entanglement and nonclassicality. However, the hurdle of actually implementing necessary quantum probe states measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that wide range tasks in metrology, 2D cluster (a particular family useful measurement-based computation) can serve as flexible resources allow one...

We consider the usage of dynamical decoupling in quantum metrology, where joint evolution system plus environment is described by a Hamiltonian. show that ultra-fast unitary control operations acting locally only on qubits, noise can be eliminated while desired reduced at most constant factor, leading to Heisenberg scaling. identify all kinds such an approach applicable. Only generated Hamiltonian estimated itself cannot altered. However, even for parallel noise, one achieve improved scaling...

Coherent superposition is a key feature of quantum mechanics that underlies the advantage technologies over their classical counterparts. Recently, coherence has been recast as resource theory in an attempt to identify and quantify it operationally well-defined manner. Here we study how present state can be used implement channel via incoherent operations and, turn, assess its degree coherence. We introduce robustness channel---which reduces homonymous measure for states when computed on...

We study the estimation of overlap between two unknown pure quantum states a finite-dimensional system, given $M$ and $N$ copies each type. This is fundamental primitive in information processing that commonly accomplished from outcomes swap tests, joint measurement on one copy type whose outcome probability linear function squared overlap. show more precise estimate can be obtained by allowing for general collective measurements all copies. derive statistics optimal compute mean square...

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of hypothesis testing. In particular our goal is to discriminate between two arbitrary states with a prescribed error threshold, $\epsilon$, when copies can be required demand. obtain ultimate lower bounds average number needed accomplish task. give block-sampling strategy that allows achieve bound for some classes states. The optimal both symmetric as well asymmetric setting sense it...

We consider fundamental limits on the detectable size of macroscopic quantum superpositions. argue that a full mechanical treatment system plus measurement device is required, and (classical) reference frame for phase or direction needs to be established certify state. When taking such classical into account, we show reliably distinguish superposition state from an incoherent mixture requires quadratically bigger than Whereas moderate sizes as generated in previous experiments this not...

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to profile of light as any misalignment modes effectively restores for small source separations. We study how much can one mitigate such an effect at level measurement which,...

We investigate different quantum parameter estimation scenarios in the presence of noise, and identify optimal probe states. For frequency local Hamiltonians with dephasing we determine states for up to 70 qubits, their key properties. find that so-called one-axis twisted spin-squeezed are only almost optimal, need not be spin-squeezed. kinds noise models, whether noiseless case remain superior product also noise. certain spatially temporally correlated no longer allow one reach standard...

We consider quantum metrology for unitary evolutions generated by parameter-dependent Hamiltonians. focus on the Ising Hamiltonian that describes dynamics of a one-dimensional chain spins with nearest-neighbour interactions and in presence global, transverse, magnetic field. analytically solve problem show precision which one can estimate field (interaction strength) given knows interaction strength (magnetic field) scales at Heisenberg limit, be achieved linear superposition vacuum N free...

We report an experimental and theoretical study of spin-noise correlations in a $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ unpolarized alkali-metal vapor dominated by spin-exchange collisions. observe strong unequal-time interspecies account for these with first-principles model. Since the two atomic species have different spin precession frequencies, dual-species enables use additional handle, applied magnetic field, untangling various subtypes correlations. In particular,...

We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT superselection. construct and quantify such for spin-0, 1/2, 1, Majorana particles show that quantum information processing is possible even with Our method employs unitary representation inversion by considering the aggregate action rather than composition separate C, P, T operations, as some these operations involve problematic antiunitary representations.

We determine the quantum states and measurements that optimize accessible information in a reference frame alignment protocol associated with groups U(1), corresponding to phase reference, , cyclic group of M elements. Our result provides an operational interpretation G-asymmetry which is information-theoretic was thus far lacking. In particular, we show limit many copies bounded-size frame, approaches Holevo bound. This implies rate frames, measured by (linearized) per system, equal...

We show that one can deterministically generate out of $N$ copies an unknown unitary operation up to $N^2$ almost perfect copies. The result holds for all operations generated by a Hamiltonian with interaction strength. This generalizes similar in the context phase covariant cloning where, however, super-replication comes at price exponentially reduced probability success. also multiple be emulated acting on much smaller space, e.g., magnetic field single $n$-level system allows emulate...

According to the Schr\"odinger equation, a closed quantum system evolves continuously in time. If it is subject measurement however, its state changes randomly and discontinuously, which mathematically described by projection postulate. But how long does take for this discontinuous change occur? Based on simple estimates, whose validity rests solely fact that all fundamental forces nature are finite-ranged, we show implementation of requires minimum This time scales proportionally with...

We consider the problem of correctly identifying a malfunctioning quantum device that forms part network <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>N</a:mi></a:math> such devices, which can be considered as analog classical anomaly detection. In case where devices in question are sources assumed to prepare identical pure states, with faulty source producing different anomalous state, we show optimal probability successful identification requires global measurement. also put...

We consider quantum metrology with arbitrary prior knowledge of the parameter. demonstrate that a single sensing two-level system can act as virtual multilevel offers increased sensitivity in Bayesian single-shot scenario, and allows one to estimate (arbitrary) large parameter values by avoiding phase wraps. This is achieved making use additional degrees freedom or auxiliary systems not participating process. The joint manipulated intermediate control operations such way an effective...

Quantum coherence generated in a physical process can only be cast as potentially useful resource if its effects detected at later time. Recently, the notion of non-coherence-generating-and-detecting (NCGD) dynamics has been introduced and related to classicality statistics associated with sequential measurements different times. However, order for NCGD, propagators need satisfy given set conditions all triples consecutive We reduce this finite $d(d-1)$ conditions, where $d$ is dimension...

We show how quantum metrology protocols that seek to estimate the parameters of a Hamiltonian exhibits phase transition can be efficiently simulated on an exponentially smaller computer. Specifically, by exploiting fact ground state such changes drastically around its phase-transition point, we construct suitable observable from which one relevant with Heisenberg scaling precision. then how, for one-dimensional Ising transverse magnetic field acting $N$ spins, protocol computer while...

We consider the problem of correctly identifying a malfunctioning quantum device that forms part network $N$ such devices, which can be considered as analogue classical anomaly detection. In case where devices in question are sources assumed to prepare identical pure states, with faulty source producing different anomalous state, we show optimal probability successful identification requires global measurement. also put forth several local measurement strategies -- both adaptive and...

The impossibility of superluminal communication is a fundamental principle physics. Here we show that this underpins the performance several tasks in quantum information processing and metrology. In particular, derive tight no-signaling bounds for probabilistic cloning superreplication coincide with corresponding optimal achievable fidelities rates known. context metrology, Heisenberg limit from certain scenarios including reference frame alignment maximum likelihood state estimation. We...

Abstract Operating quantum sensors and computers would make data in the form of states available for purely processing, opening new avenues studying physical processes certifying technologies. In this Perspective, we review a line works dealing with measurements that reveal structural properties datasets given product states. These algorithms are universal, meaning their performances do not depend on reference frame which dataset is provided. Requiring universality property implies...