arXiv subjects

Jan Kołodyński

Publications and source records attributed to Jan Kołodyński.

13 recordsLinked to original sources

arXiv2026

Precision assessment in non-Hermitian systems: a comparative study of three formalisms

Quantifying measurement precision in quantum systems is vital for advancing quantum technologies such as sensing, communication, and computation. The quantum Fisher information (QFI) sets the ultimate precision bound in Hermitian systems; however, extending this concept to non-Hermitian systems, even those with real spectra, poses conceptual challenges due to their non-unitary dynamics. We compare three probability-conserving approaches for evaluating QFI in such systems: (i) simple normalization, (ii) metric formalism, and (iii) master-equation framework. Although all three ensure probability conservation, they differ in physical interpretation and in how they quantify estimation precision. Our study is particularly motivated by previous studies that have shown that the simple normalization method for non-Hermitian Hamiltonian generated dynamics may lead to misleading or even unphysical conclusions for certain quantum information theoretic tasks. We emphasize, in this article, that the metric formalism naturally enables the use of standard Hermitian metrology tools in cases where it provides a coherent and physically consistent framework for non-Hermitian systems.

quant-ph↗

arXiv2023

Upper bounds on key rates in device-independent quantum key distribution based on convex-combination attacks

The device-independent framework constitutes the most pragmatic approach to quantum protocols that does not put any trust in their implementations. It requires all claims, about e.g. security, to be made at the level of the final classical data in hands of the end-users. This imposes a great challenge for determining attainable key rates in device-independent quantum key distribution (DIQKD), but also opens the door for consideration of eavesdropping attacks that stem from the possibility of a given data being just generated by a malicious third-party. In this work, we explore this path and present the convex-combination attack as an efficient, easy-to-use technique for upper-bounding DIQKD key rates. It allows verifying the accuracy of lower bounds on key rates for state-of-the-art protocols, whether involving one-way or two-way communication. In particular, we demonstrate with its help that the currently predicted constraints on the robustness of DIQKD protocols to experimental imperfections, such as the finite visibility or detection efficiency, are already very close to the ultimate tolerable thresholds.

quant-ph↗

arXiv2023

Zero-field optical magnetometer based on spin-alignment

Optically-pumped magnetometers are an important instrument for imaging biological magnetic signals without the need for cryogenic cooling. These magnetometers are presently available in the commercial market and utilize the principles of atomic alignment or orientation, enabling remarkable sensitivity and precision in the measurement of magnetic fields. This research focuses on utilizing a spin-aligned atomic ensemble for magnetometry at zero-field. A novel approach is introduced, which involves evaluating how the linear polarization of light rotates as it passes through the atomic vapor to null the magnetic field. Analytical expressions are derived for the resulting spin alignment and photodetection signals. Experimental results are provided, demonstrating good agreement with the theoretical predictions. The sensitivity and bandwidth of the magnetometer are characterized based on the detected polarization rotation signal. Lastly, the practical utility of the magnetometer for medical applications is demonstrated by successfully detecting a synthetic cardiac signal.

physics.app-ph↗

arXiv2022

Exploiting non-linear effects in optomechanical sensors with continuous photon-counting

Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavity. By performing simulations and resorting to Bayesian inference, we demonstrate that the non-classical correlations of the detected photons may crucially enhance the sensor performance in real time. We believe that our work may stimulate a new direction in the design of such devices, while our methods apply also to other platforms exploiting non-linear light-matter interactions and photon detection.

quant-ph↗

arXiv2022

Quantum metrology with imperfect measurements

The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, the ideal sensitivity (e.g.~the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-$1/2$ probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision.

quant-ph↗

arXiv2022

Bayesian quantum thermometry based on thermodynamic length

In this work, we propose a theory of temperature estimation of quantum systems, which is applicable in the regime of non-negligible prior temperature uncertainty and limited measurement data. In this regime the problem of establishing a well-defined measure of estimation precision becomes non-trivial, and furthermore the construction of a suitable criterion for optimal measurement design must be re-examined to account for the prior uncertainty. We propose a fully Bayesian approach to temperature estimation based on the concept of thermodynamic length, which solves both these problems. As an illustration of this framework, we consider thermal spin-$1/2$ particles and investigate the fundamental difference between two cases; on the one hand, when the spins are probing the temperature of a heat reservoir and, on the other, when the spins themselves constitute the sample.

quant-ph↗

arXiv2022

Fundamental limits in Bayesian thermometry and attainability via adaptive strategies

We investigate the limits of thermometry using quantum probes at thermal equilibrium within the Bayesian approach. We consider the possibility of engineering interactions between the probes in order to enhance their sensitivity, as well as feedback during the measurement process, i.e., adaptive protocols. On the one hand, we obtain an ultimate bound on thermometry precision in the Bayesian setting, valid for arbitrary interactions and measurement schemes, which lower bounds the error with a quadratic (Heisenberg-like) scaling with the number of probes. We develop a simple adaptive strategy that can saturate this limit. On the other hand, we derive a no-go theorem for non-adaptive protocols that does not allow for better than linear (shot-noise-like) scaling even if one has unlimited control over the probes, namely access to arbitrary many-body interactions.

quant-ph↗

arXiv2021

Bell nonlocality is not sufficient for the security of standard device-independent quantum key distribution protocols

Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by post-processing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when implemented on any correlation obtained by measuring local projective measurements on certain entangled nonlocal states, namely on a range of entangled two-qubit Werner states. To prove this result, we introduce a technique for upper-bounding the asymptotic key rate of device-independent quantum key distribution protocols, based on a simple eavesdropping attack. Our results imply that either different reconciliation techniques are needed for device-independent quantum key distribution in the large-noise regime, or Bell nonlocality is not sufficient for this task.

quant-ph↗

arXiv2020

Sub-Rayleigh resolution of two incoherent sources by array homodyning

Conventional incoherent imaging based on measuring the spatial intensity distribution in the image plane faces the resolution hurdle described by the Rayleigh diffraction criterion. Here, we demonstrate theoretically using the concept of the Fisher information that quadrature statistics measured by means of array homodyne detection enables estimation of the distance between two incoherent point sources well below the Rayleigh limit for sufficiently high signal-to-noise ratio. This capability is attributed to the availability of spatial coherence information between individual detector pixels acquired using the coherent detection technique. A simple analytical approximation for the precision attainable in the sub-Rayleigh region is presented. Furthermore, an estimation algorithm is proposed and applied to Monte Carlo simulated data.

quant-ph↗

arXiv2020

Device-independent quantum key distribution with single-photon sources

Device-independent quantum key distribution protocols allow two honest users to establish a secret key with minimal levels of trust on the provider, as security is proven without any assumption on the inner working of the devices used for the distribution. Unfortunately, the implementation of these protocols is challenging, as it requires the observation of a large Bell-inequality violation between the two distant users. Here, we introduce novel photonic protocols for device-independent quantum key distribution exploiting single-photon sources and heralding-type architectures. The heralding process is designed so that transmission losses become irrelevant for security. We then show how the use of single-photon sources for entanglement distribution in these architectures, instead of standard entangled-pair generation schemes, provides significant improvements on the attainable key rates and distances over previous proposals. Given the current progress in single-photon sources, our work opens up a promising avenue for device-independent quantum key distribution implementations.

quant-ph↗

arXiv2018

Precision Limits in Quantum Metrology with Open Quantum Systems

The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a broad class of parameters, like atomic frequencies in spectroscopy or external magnetic field in magnetometry, can be overcome when using quantum probes. Environmental noise, however, generally alters the ultimate precision that can be achieved in the estimation of an unknown parameter. This tutorial reviews recent theoretical work aimed at obtaining general precision bounds in the presence of an environment. We adopt a complementary approach, where we first analyze the problem within the general framework of describing the quantum systems in terms of quantum dynamical maps and then relate this abstract formalism to a microscopic description of the system's dissipative time evolution. We will show that although some forms of noise do render quantum systems standard quantum limited, precision beyond classical bounds is still possible in the presence of different forms of local environmental fluctuations.

quant-ph↗

arXiv2018

Fundamental limits to frequency estimation: A comprehensive microscopic perspective

We consider a scenario in which qubit-like probes are used to sense an external field that linearly affects their energy splitting. Following the frequency estimation approach in which one optimizes the state and sensing time of the probes to maximize the sensitivity, we provide a systematic study of the attainable precision under the impact of noise originating from independent bosonic baths. We invoke an explicit microscopic derivation of the probe dynamics using the spin-boson model with weak coupling of arbitrary geometry and clarify how the secular approximation leads to a phase-covariant dynamics, where the noise terms commute with the field Hamiltonian, while the inclusion of non-secular terms breaks the phase-covariance. Moreover, unless one restricts to a particular (i.e., Ohmic) spectral density of the bath modes, the noise terms may contain relevant information about the frequency to be estimated. Thus, by considering general evolutions of a single probe, we study regimes in which these two effects have a non-negligible impact on the achievable precision. We then consider baths of Ohmic spectral density yet fully accounting for the lack of phase-covariance, in order to characterize the ultimate attainable scaling of precision when $N$ probes are used in parallel. Crucially, we show that beyond the semigroup (Lindbladian) regime the Zeno limit imposing the $1/N^{3/2}$ scaling of the mean squared error, derived assuming phase-covariance, generalises to any dynamics of the probes, unless the latter are coupled to the baths in the direction perfectly transversal to the encoding---when a novel scaling of $1/N^{7/4}$ arises. As our microscopic approach covers all classes of dissipative dynamics, from semigroup to non-Markovian ones (potentially non-phase-covariant), it provides an exhaustive picture, in which all the different asymptotic scalings of precision naturally emerge.

quant-ph↗

arXiv2017

Random bosonic states for robust quantum metrology

We study how useful random states are for quantum metrology, i.e., surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to super-classical scaling of precision even when allowing for local unitary optimization. Conversely, we show that random states from the symmetric subspace typically achieve the optimal Heisenberg scaling without the need for local unitary optimization. Surprisingly, the Heisenberg scaling is observed for states of arbitrarily low purity and preserved under finite particle losses. Moreover, we prove that for such states a standard photon-counting interferometric measurement suffices to typically achieve the Heisenberg scaling of precision for all possible values of the phase at the same time. Finally, we demonstrate that metrologically useful states can be prepared with short random optical circuits generated from three types of beam-splitters and a non-linear (Kerr-like) transformation.

quant-ph↗