arXiv subjects

Waldemar Kłobus

Publications and source records attributed to Waldemar Kłobus.

18 recordsLinked to original sources

arXiv2026

Inter-qubit correlation dynamics driven by mutual interactions

A particularly useful tool for characterizing multi-qubit systems is the correlation tensor, providing an experimentally friendly and theoretically concise representation of quantum states. In this work, we analyze the evolution of the correlation tensor elements of quantum systems composed of $\frac12$-spins, generated by mutual interactions and the influence of the external field. We focus on two-body interactions in the form of anisotropic Heisenberg as well as antisymmetric exchange interaction models. The evolution of the system is visualized in the form of a trajectory in a suitable correlation space, which, depending on the system's frequencies, exhibits periodic or nonperiodic behavior. In the case of two $\frac12$-spins we study the stationary correlations for several classes of Hamiltonians, which allows a full characterization of the families of density matrices invariant under the evolution generated by the Hamiltonians. We discuss some common properties shared by the 2- and 3-qubit systems and show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.

quant-ph↗

arXiv2024

Exploring Many-body Interactions Through Quantum Fisher Information

The investigation of many-body interactions holds significant importance in both quantum foundations and information. Hamiltonians coupling multiple particles at once, beyond others, can lead to a faster entanglement generation, multiqubit gate implementation and improved error correction. As an increasing number of quantum platforms enable the realization of such physical settings, it becomes interesting to study the verification of many-body interaction resources. In this work, we explore the possibility of higher-order couplings detection through the quantum Fisher information. For a family of symmetric and translationally invariant $k$-body Ising-like Hamiltonians, we derive the bounds on the quantum Fisher information in product states. Due to its ordering with respect to the order of interaction, we demonstrate the possibility of detecting many-body couplings for a given Hamiltonian from the discussed family by observing violations of an appropriate bound. As a possible extension to these observations, we further analyse an example concerning the three-body interaction detection in the XY model.

quant-ph↗

arXiv2023

The fastest generation of multipartite entanglement with natural interactions

Natural interactions among multiple quantum objects are fundamentally composed of two-body terms only. In contradistinction, single global unitaries that generate highly entangled states typically arise from Hamiltonians that couple multiple individual subsystems simultaneously. Here, we study the time to produce strongly nonclassical multipartite correlations with a single unitary generated by the natural interactions. We restrict the symmetry of two-body interactions to match the symmetry of the target states and focus on the fastest generation of multipartite entangled Greenberger-Horne-Zeilinger (GHZ), W, Dicke and absolutely maximally entangled (AME) states for up to seven qubits. These results are obtained by constraining the energy in the system and accordingly can be seen as state-dependent quantum speed limits for symmetry-adjusted natural interactions. They give rise to a counter-intuitive effect where the creation of particular entangled states with an increasing number of particles does not require more time. The methods used rely on extensive numerical simulations and analytical estimations.

quant-ph↗

arXiv2023

Salient signatures of entanglement in the surrounding environment

We develop a model in which presence of entanglement in a quantum system can be confirmed through coarse observations of the environment surrounding the system. This counter-intuitive effect becomes possible when interaction between the system and its environment is proportional to an observable being an entanglement witness. While presenting intuitive examples we show that: i) a cloud of an ideal gas, when subject to a linear potential coupled with the entanglement witness, accelerates in the direction dictated by the sign of the witness; ii) when the environment is a radiation field, the direction of dielectric polarization depends on the presence of entanglement; iii) quadratures of electromagnetic field in a cavity coupled with two qubits (or a four-level atom) are displaced in the same manner.

quant-ph↗

arXiv2021

Transition from order to chaos in reduced quantum dynamics

We study a damped kicked top dynamics of a large number of qubits ($N \rightarrow \infty$) and focus on an evolution of a reduced single-qubit subsystem. Each subsystem is subjected to the amplitude damping channel controlled by the damping constant $r\in [0,1]$, which plays the role of the single control parameter. In the parameter range for which the classical dynamics is chaotic, while varying $r$ we find the universal period-doubling behavior characteristic to one-dimensional maps: period-two dynamics starts at $r_1 \approx 0.3181$, while the next bifurcation occurs at $ r_2 \approx 0.5387$. In parallel with period-four oscillations observed for $r \leq r_3 \approx 0.5672$, we identify a secondary bifurcation diagram around $r\approx 0.544$, responsible for a small-scale chaotic dynamics inside the attractor. The doubling of the principal bifurcation tree continues until $r \leq r_{\infty} \sim 0.578$, which marks the onset of the full scale chaos interrupted by the windows of the oscillatory dynamics corresponding to the Sharkovsky order.

quant-ph↗

arXiv2020

Multipartite Entanglement Analysis From Random Correlations

Quantum entanglement is usually revealed via a well aligned, carefully chosen set of measurements. Yet, under a number of experimental conditions, for example in communication within multiparty quantum networks, noise along the channels or fluctuating orientations of reference frames may ruin the quality of the distributed states. Here we show that even for strong fluctuations one can still gain detailed information about the state and its entanglement using random measurements. Correlations between all or subsets of the measurement outcomes and especially their distributions provide information about the entanglement structure of a state and also enable to witness genuine multipartite entanglement. As long as the rate of entanglement generation is sufficiently high, this method overcomes any type and strength of localized unitary noise.

quant-ph↗

arXiv2018

The Conditional Uncertainty Principle

We develop a general operational framework that formalizes the concept of conditional uncertainty in a measure-independent fashion. Our formalism is built upon a mathematical relation which we call conditional majorization. We define conditional majorization and, for the case of classical memory, we provide its thorough characterization in terms of monotones, i.e., functions that preserve the partial order under conditional majorization. We demonstrate the application of this framework by deriving two types of memory-assisted uncertainty relations: (1) a monotone-based conditional uncertainty relation, (2) a universal measure-independent conditional uncertainty relation, both of which set a lower bound on the minimal uncertainty that Bob has about Alice's pair of incompatible measurements, conditioned on arbitrary measurement that Bob makes on his own system. We next compare the obtained relations with their existing entropic counterparts and find that they are at least independent.

quant-ph↗

arXiv2017

No-signaling versus quantum constraints for spatio-temporal correlations caused by weak measurement

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of non-locality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by non-locality and no-signaling.

quant-ph↗

arXiv2017

Measurement uncertainty from no-signaling and non-locality

quant-ph↗

arXiv2015

Communication strength of correlations violating monogamy relations

In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this aim, we first provide a framework associating them with classical channels whose capacities are then used to quantify the usefulness of these correlations in sending information. Finally, we determine the minimal amount of information that can be sent using signaling correlations violating the monogamy relation associated to the chained Bell inequalities.

quant-ph↗

arXiv2015

Axiomatic approach to contextuality and nonlocality

We present a unified axiomatic approach to contextuality and non-locality based on the fact that both are resource theories. In those theories the main objects are consistent boxes, which can be transformed by certain operations to achieve certain tasks. The amount of resource is quantified by appropriate measures of the resource. Following recent paper [J.I. de Vicente, J. Phys. A: Math. Theor. {\bf 47}, 424017 (2014)], and recent development of abstract approach to resource theories, such as entanglement theory, we propose axioms and welcome properties for operations and measures of resources. As one of the axioms of the measure we propose the asymptotic continuity: the measure should not differ on boxes that are close to each other by more than the distance with a factor depending logarithmically on the dimension of the boxes. We prove that relative entropy of contextuality is asymptotically continuous. Considering another concept from entanglement theory---the convex roof of a measure---we prove that for some non-local and contextual polytopes, the relative entropy of a resource is upper bounded up to a constant factor by the cost of the resource. Finally, we prove that providing a measure $X$ of resource does not increase under allowed class of operations, such as e.g. wirings, the maximal distillable resource which can be obtained by these operations is bounded from above by the value of $X$ up to a constant factor. We show explicitly which axioms are used in the proofs of presented results, so that analogous results may remain true in other resource theories with analogous axioms. We also make use of the known distillation protocol of bipartite nonlocality to show how contextual resources can be distilled.

quant-ph↗

arXiv2015

Some exact results for the zero-bandwidth extended Hubbard model with intersite charge and magnetic interactions

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site $U$ interaction and intersite (ii) density-density interaction $W$ and (iii) Ising-like magnetic exchange interaction $J$ (between the nearest-neighbors). We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D-chain in two particular cases: (a) $W=0$ and $n=1$; (b) $U\rightarrow+\infty$ and $n=1/2$ ($W\neq 0$, $J\neq 0$). We obtain the exact formulas for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat ($c$), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of $c$ involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state.

cond-mat.str-el↗

arXiv2014

When Are Popescu-Rohrlich Boxes and Random Access Codes Equivalent?

We study a problem of interconvertibility of two supra-quantum resources: one is so called PR-box, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It has been known, that PR-box supplemented with one bit of communication can be used to simulate RAC. We ask the converse question: to what extent RAC can simulate PR-box? To this end we introduce racbox: a box such that supplemented with one bit of communication offers RAC. As said, PR-box can simulate racbox. The question we raise, is whether any racbox can simulate PR-box. We show that a non-signaling racbox indeed can simulate PR-box, hence those two resources are equivalent. We also provide an example of signalling racbox which cannot simulate PR-box. We give a resource inequality between racbox es and PR-boxes, and show that it is saturated.

quant-ph↗

arXiv2014

Entanglement witnessing and quantum cryptography with non-ideal ferromagnetic detectors

We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $η> 1/\sqrt{3} \approx 58 %$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $η> 1/\sqrt[4]{2}\approx 84%$. In addition, we discuss the impact of decoherence and noise on entanglement detection and apply the presented framework to a simple quantum cryptography protocol. Our results are directly applicable to a large variety of experiments.

cond-mat.mes-hall↗

arXiv2013

Conjectured strong complementary-correlations tradeoff

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from Maassen-Uffink uncertainty relation and is much stronger than Hall uncertainty relation derived from the latter. The second uncertainty relation bounds the sum of two mutual informations when each party measures one of two observables. We provide numerical evidence for validity of conjectured uncertainty relations and prove them for large classes of states and observables.

quant-ph↗

arXiv2012

Nonlocality activation in entanglement swapping chains

We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate CHSH inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. However, if this number is achieved then for some results of Bell measurements obtained in the protocol of entanglement swapping the output state violates CHSH inequality. Moreover, we show that for different states we have different critical numbers for which CHSH inequality is activated.

quant-ph↗

arXiv2012

Magnetic orderings and phase separations in the zero-bandwidth limit of the extended Hubbard model with intersite magnetic interactions

A simple effective model for a description of magnetically ordered insulators is analysed. The tight binding Hamiltonian consists of the effective on-site interaction (U) and intersite magnetic exchange interactions (Jz, Jxy) between nearest-neighbours. The phase diagrams of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We show that, depending on the values of interaction parameters and the electron concentration, the system can exhibit not only homogeneous phases: (anti-)ferromagnetic (F) and nonordered (NO), but also phase separated states (PS: F-NO).

cond-mat.str-el↗

arXiv2011

Interplay between charge and magnetic orderings in the zero-bandwidth limit of the extended Hubbard model for strong on-site repulsion

A simple effective model of charge ordered and (or) magnetically ordered insulators is studied. The tight binding Hamiltonian analyzed consists of (i) the effective on-site interaction U, (ii) the intersite density-density interaction W and (iii) intersite magnetic exchange interaction Jz (or Jxy) between nearest-neighbors. The intersite interaction are treated within the mean-field approximation. One shows that the systems considered can exhibit very interesting multicritical behaviors, including among others bicritical, tricritical, tetracritical and critical end points. The analysis of the model has been performed for an arbitrary electron concentration as well as an arbitrary chemical potential in the limit of strong on-site repulsion. The phase diagrams obtained in such a case are shown to consist of at least 9 different states, including four homogenous phases: nonordered (NO), ferromagnetic (F), charge ordered (CO), ferrimagnetic (intermediate, I) and five types of phase separation: NO-NO, F-NO, F-F, CO-F, CO-I.

cond-mat.str-el↗