arXiv subjects

Zdeněk Hradil

Publications and source records attributed to Zdeněk Hradil.

11 recordsLinked to original sources

arXiv2026

Fundamental and operational limitations of Fisher-information-based quantum metrology

Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, such an interpreta- tion is only justified within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting, estimator construction, prior information, and finite data effects. Here we develop an operational, end-to-end framework for quantum sensing under finite resources and identify general principles required for meaningful performance assess- ment. A central conceptual point is that the relevant unit of estimation is not a single detection event, but the complete data set required to construct a consistent estimator. Rather than relying on abstract statistical formalism, we analyze a set of paradigmatic and experimentally relevant ex- amples that expose common pitfalls in widely discussed quantum sensing strategies. These include quantum interferometry, sensing with squeezed states, and criticality-inspired protocols. Our results clarify when large Fisher information or nonclassical resources translate into genuine metrological advantage, and when they do not. They further provide a practical methodology for designing and evaluating quantum sensing protocols under realistic experimental constraints.

quant-ph↗

arXiv2026

Quantum-limited detection of arrival time and carrier frequency of time-dependent signals

Precise measurements of both the arrival time and carrier frequency of light pulses are essential for time-frequency-encoded quantum technologies. Quantum mechanics, however, imposes fundamental limits on the simultaneous determination of these quantities. In this work, we derive and experimentally verify the quantum uncertainty bounds governing joint time-frequency measurements. We show that when detection is restricted to finite time windows, the problem is naturally described by a quantum rotor, rendering the commonly used Heisenberg uncertainty relation inapplicable. We further propose an optimal detection scheme that saturates these fundamental limits. By sampling the Q-function, we demonstrate the reconstruction of the Wigner function beyond the harmonic oscillator. Using an experimental implementation based on a quantum pulse gate, we confirm that the proposed scheme approaches the ultimate quantum limit for simultaneous time-frequency measurements. These results provide a new framework for joint time-frequency detection with direct implications for precision measurements and quantum information processing.

quant-ph↗

arXiv2024

Pulse characterization at the single-photon level through chronocyclic $Q$-function measurements

The characterization of the complex spectral amplitude that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterisation techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic $Q-$function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate, which directly yield the chronocyclic $Q-$function. We evaluate the data with maximum likelihood estimation, which is the established technique for quantum state tomography. This yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any \textit{a priori} information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial also for classical pulse characterization problems.

quant-ph↗

arXiv2024

Unifying uncertainties for rotor-like quantum systems

The quantum rotor represents, after the harmonic oscillator, the next obvious quantum system to study the complementary pair of variables: the angular momentum and the unitary shift operator in angular momentum. Proper quantification of uncertainties and the incompatibility of these two operators are thus essential for applications of rotor-like quantum systems. While angular momentum uncertainty is characterized by variance, several uncertainty measures have been proposed for the shift operator, with dispersion the simplest example. We establish a hierarchy of those measures and corresponding uncertainty relations which are all perfectly or almost perfectly saturated by a tomographically complete set of von Mises states. Building on the interpretation of dispersion as the moment of inertia of the unit ring we then show that the other measures also possess the same mechanical interpretation. This unifying perspective allows us to express all measures as a particular instance of a single generic angular uncertainty measure. The importance of these measures is then highlighted by applying the simplest two of them to derive optimal simultaneous measurements of the angular momentum and the shift operator. Finally, we argue that the model of quantum rotor extends beyond its mechanical meaning with promising applications in the fields of singular optics, super-conductive circuits with a Josephson junction or optimal pulse shaping in the time-frequency domain. Our findings lay the groundwork for quantum-information and metrological applications of the quantum rotor and point to its interdisciplinary nature.

quant-ph↗

arXiv2022

Angle and angular momentum -- new twist for an old pair

Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum and exponential angular variable, and the structure of canonically conjugate position and momentum. This includes the notion of optimal simultaneous measurement of the angular momentum and angular variable, the identification of Einstein-Podolsky-Rosen-like variables and states, and finally a phase-space representation of quantum states. Our construction is based on close interconnection of the three concepts and may serve as a template for the treatment of other observables. This theory also provides a new testbed for implementation of quantum technologies combining discrete and continuous quantum variables.

quant-ph↗

arXiv2021

Exploring the ultimate limits: Super-resolution enhanced by partial coherence

The resolution of separation of two elementary signals forming a partially coherent superposition, defined by quantum Fisher information and normalised with respect to detection probabilities, is always limited by the resolution of incoherent mixtures. However, when the partially coherent superpositions are prepared in a controlled way the precision can be enhanced by up to several orders of magnitude above this limit. Coherence also allows the sorting of information about various parameters into distinct channels as demonstrated by parameter of separation linked with the anti-phase superposition and the centroid position linked with the in-phase superposition.

quant-ph↗

arXiv2020

Achieving the ultimate quantum timing resolution

Accurate time-delay measurement is at the core of many modern technologies. Here, we present a temporal-mode demultiplexing scheme that achieves the ultimate quantum precision for the simultaneous estimation of the temporal centroid, the time offset, and the relative intensities of an incoherent mixture of ultrashort pulses at the single-photon level. We experimentally resolve temporal separations ten times smaller than the pulse duration, as well as imbalanced intensities differing by a factor of $10^{2}$. This represents an improvement of more than an order of magnitude over the best standard methods based on intensity detection.

quant-ph↗

arXiv2019

Quantum Fisher Information with Coherence

In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.

quant-ph↗

arXiv2018

Quantum-limited time-frequency estimation through mode-selective photon measurement

By projecting onto complex optical mode profiles, it is possible to estimate arbitrarily small separations between objects with quantum-limited precision, free of uncertainty arising from overlapping intensity profiles. Here we extend these techniques to the time-frequency domain using mode-selective sum-frequency generation with shaped ultrafast pulses. We experimentally resolve temporal and spectral separations between incoherent mixtures of single-photon level signals ten times smaller than their optical bandwidths with a ten-fold improvement in precision over the intensity-only Cramér-Rao bound.

quant-ph↗

arXiv2017

Unraveling beam self-healing

We show that, contrary to popular belief, non only diffraction-free beams may reconstruct themselves after hitting an opaque obstacle but also, for example, Gaussian beams. We unravel the mathematics and the physics underlying the self-reconstruction mechanism and we provide for a novel definition for the minimum reconstruction distance beyond geometric optics, which is in principle applicable to any optical beam that admits an angular spectrum representation. Moreover, we propose to quantify the self-reconstruction ability of a beam via a newly established degree of self-healing. This is defined via a comparison between the amplitudes, as opposite to intensities, of the original beam and the obstructed one. Such comparison is experimentally accomplished by tailoring an innovative experimental technique based upon Shack-Hartmann wave front reconstruction. We believe that these results can open new avenues in this field.

physics.optics↗

arXiv1995

Entropy of phase measurement: Quantum phase via quadrature measurement

The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum state. As an explicit example the multiple measurement of quadrature operator is interpreted as quantum phase detection achieving the ultimate resolution predicted by the Fisher information.

quant-ph↗