Entropic Uncertainty Relations Research Articles

Experimental demonstration of the equivalence of entropic uncertainty with wave-particle duality.

Wave-particle duality is one of the most notable and counterintuitive features of quantum mechanics, illustrating that two incompatible observables cannot be measured simultaneously with arbitrary precision. In this work, we experimentally demonstrate the equivalence of wave-particle duality and entropic uncertainty relations using orbital angular momentum (OAM) states of light. Our experiment uses an innovative and reconfigurable platform composed of few-mode optical fibers and photonic lanterns, showcasing the versatility of this technology for quantum information processing. Our results provide fundamental insights into the complementarity principle from an informational perspective, with implications for the broader field of quantum technologies.

Entropic Uncertainty Relations and Mutual Information Correlation Sums in Two-level Superposition States of Coupled Oscillators

The effects of quantum interferences and interaction strength on the entropic uncertainty relations, and on mutual information correlation sums, are examined in two-level superposition states of two coupled oscillators. The presence of quantum interferences results in a movement of the entropy sums toward the uncertainty relation bound, for both attractive and repulsive interaction potentials. On the other hand, these interferences suppress the statistical correlations in the presence of an attractive potential, while the correlations increase for a repulsive one. In general, stronger interactions between particles move the entropy sums away from bound, with the result that the systems possess larger statistical correlations. However, there are superposition and attractive interaction regimes, where the entropy sum of an interacting system can actually lie closer to the bound, in comparison to the corresponding non-interacting one. In these cases, the statistical correlations between particles is lesser for the interacting systems, as compared to the non-interacting ones. These effects are not observed when repulsive potentials are present. Here, the non-interacting systems lower-bound both the entropy sums and correlation measures. These results offer insights into the nature of superposition or quantum interference effects in interacting quantum systems, and the behavior in terms of the entropic uncertainty relations, statistical correlations and interaction strength. Resumen. Se examinan los efectos que las interferencias cuánticas y la magnitud de la interacción tienen sobre las relaciones de incertidumbre entrópicas, así como sobre las sumas correlaciones me didas a través de la información mutua, en estados de superposición de dos niveles de dos osciladores acoplados. La presencia de interferencias cuánticas da como resultado un movimiento de las sumas entrópicas hacia la cota de la relación de incertidumbre, tanto para potenciales de interacción atractivos como repulsivos. Por otra parte, en presencia de un potencial atractivo, estas interferencias suprimen las correlaciones estadísticas, mientras que las correlaciones aumentan en presencia de uno repulsivo. En general, con interacciones más fuertes entre partículas, las sumas de entrópicas se alejan de la cota, dando como resultado mayores correlaciones estadísticas en los sistemas. Sin embargo, existen regímenes de superposición e interacción atractiva, en los cuales la suma entrópica de un sistema interactuante puede estar más cerca de la cota, en comparación con el sistema no interactuante correspondiente. En estos casos, las correlaciones estadísticas entre partículas son menores para los sistemas interactúantes que para los no interactuantes. Estos efectos no se observan en los potenciales repulsivos. En este caso, los sistemas no interactuantes establecen límites inferiores tanto para las sumas entrópicas como para las medidas de correlación. Estos resultados dan información sobre la naturaleza de los efectos de superposición o interferencia cuántica en sistemas cuánticos interactuantes, y su comportamiento en términos de relaciones de incertidumbre entrópica, correlaciones estadísticas y fuerza de interacción.

Steered quantum coherence and entropic uncertainty relation in the cluster Ising model

Abstract In this paper, we investigate the cluster Ising model (CIM) via steered quantum coherence (SQC) and entropic uncertainty relation (EUR). We present the behavior of SQC quantified by the L1 norm, relative entropy and quantum Jensen–Shannon divergence. We also demonstrate the properties of EUR in the CIM. In addition, we provide a comparative analysis of these measures and present detailed numerical results.

Entropic uncertainty relations and quantum Fisher information of top quarks in a large hadron collider

Entropic uncertainty relations and quantum Fisher information of top quarks in a large hadron collider

Entropic uncertainty relations and entanglement detection from quantum designs

Abstract Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information theory. In this article, we investigate entropic uncertainty relations and entanglement detection with an emphasis on quantum measurements with design structures. On the one hand, we derive improved Rényi entropic uncertainty relations for design-structured measurements, exploiting the property that the sum of powered (e.g., squared) probabilities of obtaining different measurement outcomes is now invariant under unitary transformations of the measured system and can be easily computed. On the other hand, the above property essentially imposes a state-independent upper bound, which is achieved at all pure states, on one’s ability to predict local outcomes when performing a set of design-structured measurements on quantum systems. Realizing this, we also obtain criteria for detecting multi-partite entanglement with design-structured measurements.

Entropic uncertainty relations and quantum coherence in the two-dimensional XXZ spin model with Dzyaloshinskii–Moriya interaction

Quantum renormalization group (QRG) is a tractable method for studying the criticalities of one-dimensional (1D) and two-dimensional (2D) many-body systems. By employing the QRG method, we first derive the effective Hamiltonian and QRG equations of a 2D XXZ model with Dzyaloshinskii–Moriya (DM) interaction analytically. The linear-entropy-based uncertainty, the quantum discord (QD), and the multipartite quantum coherence based on the square root of the quantum Jensen–Shannon divergence of the 2D XXZ model are then studied as the indicators of quantum phase transitions (QPTs). The nonanalytic and scaling behaviors of the uncertainty, QD and quantum coherence are also analyzed through numerical calculations. Moreover, we investigate the effect of the easy-axis anisotropy parameter and DM interaction on the QPT. We find that the uncertainty, QD, and quantum coherence can all be utilized to detect QPTs. Our findings could shed new light on the observable of the QPT of the many-body system with the uncertainty and quantum coherence, and enrich the application of QRG method to Heisenberg spin models.

Entropic distinguishability of quantum fields in phase space

We present a general way of quantifying the entropic uncertainty of quantum field configurations in phase space in terms of entropic distinguishability with respect to the vacuum. Our approach is based on the functional Husimi Q-distribution and a suitably chosen relative entropy, which we show to be non-trivially bounded from above by the uncertainty principle. The resulting relative entropic uncertainty relation is as general as the concept of coherent states and thus holds for quantum fields of bosonic and fermionic type. Its simple form enables diverse applications, among which we present a complete characterization of the uncertainty surplus of arbitrary states in terms of the total particle number for a scalar field and the fermionic description of the Ising model. Moreover, we provide a quantitative interpretation of the role of the uncertainty principle for quantum phase transitions.

Entropic uncertainty relations in Schwarzschild space-time

The uncertainty principle is deemed as one of cornerstones in quantum mechanics, and exploring its lower limit of uncertainty will be helpful to understand the principle's nature. In this study, we propose a generalized entropic uncertainty relation for arbitrary multiple-observable in multipartite system, and further derive a tighter lower bound by considering Holevo quality and mutual information. Importantly, we detailedly discuss the proposed uncertainty relations and quantum coherence in the context of Schwarzschild space-time. It is interesting to find that Hawking radiation will damage the coherence of the physically accessible region and increase the uncertainty. Furthermore, we argue that the properties of the uncertainty in Schwarzschild space-time can be explained from the systems' purity and the information redistribution of the different regions. Therefore, it is believed that our findings provide the generalized entropic uncertainty relations in multipartite systems, which may facilitate us deeper understanding of quantumness and information paradox of the black holes.

Proving the Security of Mediated Semi‐Quantum Key Distribution Using Entropic Uncertainty Relation

AbstractIn recent years, mediated semi‐quantum key distribution (MSQKD) has become a hot topic in quantum cryptography. In this study, the original MSQKD protocol is revisited and a new scheme for proving security based on information theory is developed. At first, a new bound on the key rate of the protocol is derived using an entropic uncertainty relation, thus proving the unconditional security of the protocol. In addition, in the asymptotic scenario, a higher noise tolerance that improves the previous results is found. The legitimate communicating parties have to abort the protocol when they observe the error rate is larger than the noise tolerance. Furthermore, the security of a single‐state MSQKD protocol and a single‐state semi‐quantum key distribution (SQKD) protocol is proven using a similar scheme.

Maximally Entangled Squeezed Spin Coherent States and Entropic Uncertainty Relation

Maximally Entangled Squeezed Spin Coherent States and Entropic Uncertainty Relation

The entropic uncertainty preservation in non-Markovian environment via classical driving fields

Uncertainty relations in terms of entropies were initially proposed to deal with conceptual shortcomings in the original formulation of the uncertainty principle and, hence, play an important role in quantum foundations. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is the Shannon’s entropy. In this work, we investigate the effect of a classical driving field on entropic uncertainty lower bound (EULB). In this regard, we consider a particle as the quantum memory correlated with a measured particle, where during the interaction with the environment, the quantum memory is driven by the external classical field. Our result reveals that in the presence of the classical driving fields, the EULB is reduced and consequently, the measurement accuracy is increased.

Evaluating extractable work of quantum batteries via entropic uncertainty relations.

In this study, we investigate the effectiveness of entropic uncertainty relations (EURs) in discerning the energy variation in quantum batteries (QBs) modelled by battery-charger field in the presence of bosonic and fermionic reservoirs. Our results suggest that the extractable works (exergy and ergotropy) have versatile characteristics in different scenarios, resulting in a complex relationship between tightness and extractable work. It is worth noting that the tightness of the lower bound of entropic uncertainty can be a good indicator for energy conversion efficiency in charging QBs. Furthermore, we disclose how the EUR including uncertainty and lower bound contributes to energy conversion efficiency in the QB system. It is believed that these findings will be beneficial for better understanding the role of quantum uncertainty in evaluating quantum battery performance.

Tight Bounds from Multiple‐Observable Entropic Uncertainty Relations

AbstractThe additivity properties for both bipartite and multipartite systems are investigated by using entropic uncertainty relations (EUR) defined in terms of the joint Shannon entropy of probabilities of local measurement outcomes. In particular, state‐independent and state‐dependent entropic inequalities are introduced. Interestingly, the violation of these inequalities is strictly connected with the presence of quantum correlations. It is shown that the additivity of EUR holds only for EUR that involve two observables, while this is not the case for inequalities that consider more than two observables or the addition of the von Neumann entropy of a subsystem. They are applied to bipartite systems and to several classes of states of a three‐qubit system.

Entropic uncertainty relations for measurements assigned to a projective two-design

The current study aims to examine uncertainty relations for quantum measurements assigned to a projective two-design. Complete sets of mutually unbiased bases and symmetric informationally complete measurements are important cases of such measurements. To characterize the amount of uncertainty, we use the Tsallis and Rényi entropies as well as the probabilities of separate outcomes. The obtained results are based on an estimation of the index of coincidence. They improve some uncertainty relations given in the literature.

Thermal entanglement versus quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg system with Herring–Flicker coupling under Dzyaloshinsky–Moriya interaction

Thermal entanglement versus quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg system with Herring–Flicker coupling under Dzyaloshinsky–Moriya interaction

The influence of a magnetic field on Shannon entropy and thermal properties in graphene

We conducted an investigation into the impact of an external magnetic field on graphene under two proposed conditions: a constant magnetic field (ω), and a field characterized by exponential decay (μ). The resulting eigenvalue solutions were utilized to analyze the Shannon entropy of low-lying states and thermodynamic properties. Regarding Shannon entropy, we observed that both conditions led to increased fermion localization in position space and delocalization in momentum space. Furthermore, we calculated the BBM entropic uncertainty relation and confirmed its validity in one dimension. As for the thermodynamic properties, we found that augmenting the influence of the magnetic fields altered their respective behaviors.

Coherence versus quantum-memory-assisted entropic uncertainty relation of double quantum dots with Rashba spin–orbit interaction

Coherence versus quantum-memory-assisted entropic uncertainty relation of double quantum dots with Rashba spin–orbit interaction

Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?

Does conditional entropy squeezing indicate normalized entropic uncertainty relation steering?

Entropic characterization of stabilizer states and magic states

Quantum states with minimum or maximum uncertainty are of special significance due to their extreme properties. Celebrated examples are coherent states induced from certain Lie groups and intelligent states for various uncertainty relations. In this work, by virtue of the Maassen-Uffink entropic uncertainty relation, we introduce an entropic quantifier of uncertainty and use it to characterize several important families of states in the stabilizer formalism of quantum computation. More specifically, we show that the stabilizer states and T-type magic states stand at the two extremes of the entropic quantifier of uncertainty: The former are precisely the minimum entropic uncertainty states, while the latter are precisely the maximum entropic uncertainty states. Moreover, interpolating between the above two extremes, the H-type magic states are the saddle points of the entropic quantifier of uncertainty. These entropic characterizations reveal some intrinsic features of stabilizer states, H- and T-type magic states, and cast novel light on the resource-theoretic viewpoint of regarding the stabilizer states as free states and the T-type magic states as the most precious source states in the stabilizer quantum theory.

Effects of detuning on entropic uncertainty bound and quantum correlations in dissipative environments

One of the fundamental arguments in quantum information theory is the uncertainty principle. According to this principle, two incompatible observables cannot be measured with high precision at the same time. In this work, we will use the entropic uncertainty relation in the presence of quantum memory. Considering a dissipative environment, the effects of the detuning between the transition frequency of a quantum memory and the center frequency of a cavity on entropic uncertainty bound and the quantum correlation between quantum memory and measured particle will be studied. It is shown that by increasing the detuning, quantum correlation is maintained. As a result, due to the inverse relationship between the uncertainty bound and quantum correlations, the measurement results are guessed more accurately.