The uncertainty and quantum correlation of measurement in double quantum-dot systems

In this work, we study the entropic uncertainty and quantum discord in two double-quantum-dot (DQD) system coupled via a transmission line resonator (TLR). Explicitly, the dynamics of the systemic quantum correlation and measured uncertainty are analysed with respect to a general X-type state as the initial state. Interestingly, it is found that the different parameters, including the eigenvalue α of the coherent state, detuning amount δ, frequency ω and the coupling constant g, have subtle effects on the dynamics of the entropic uncertainty, such as the oscillation period of the uncertainty. It is clear to reveal that the quantum discord and the lower bound of the entropic uncertainty are anti-correlated when the initial state of the system is the Werner-type state, while quantum discord and the lower bound of the entropic uncertainty are not anti-correlated when the initial state of the system is the Bell-diagonal state. Thereby, we claim that the current investigation would provide an insight into the entropic uncertainty and quantum correlation in DQDs system, and are basically of importance to quantum precision measurement in practical quantum information processing.     

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle—serving as a quantum memory reservoir—undergoes free fall in the vicinity of the event horizon of the Schwarzschild space‐time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non‐tracing‐preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space‐time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.     

Controlling the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environments

The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that the uncertainty principle can be tightened by quantum discord and classical correlation in the presence of quantum memory.We investigate the control of the entropic uncertainty and quantum discord in two two-level systems by an ancilla in dissipative environment.Our results show that the entropic uncertainty of an observed system can be reduced and the quantum discord between the observed system and the quantum memory system can be enhanced in the steady state of the system by adding an dissipative ancilla.Particularly,via preparing the state of the system to the highest excited state with hight fidelity,the entropic uncertainty can be reduced markedly and the quantum discord can be enhanced obviously.We explain these results using the definition of state fidelity.Furthermore,we present an effective strategy to further reduce the the entropic uncertainty and to enhance the the quantum discord via quantum-jump-based feedback control.Therefore,our results may be of importance in the context of quantum information technologies.     

Dynamical Measurement's Uncertainty in the Curved Space‐Time

The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle–Horowitz–Strominger dilation space‐time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation‐parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti‐correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi‐component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space‐time.     

Entanglement and discord assisted entropic uncertainty relations under decoherence

The uncertainty principle is a crucial aspect of quantum mechanics.It has been shown that quantum entanglement as well as more general notions of correlations,such as quantum discord,can relax or tighten the entropic uncertainty relation in the presence of an ancillary system.We explored the behaviour of entropic uncertainty relations for system of two qubits—one of which subjects to several forms of independent quantum noise,in both Markovian and non-Markovian regimes.The uncertainties and their lower bounds,identified by the entropic uncertainty relations,increase under independent local unital Markovian noisy channels,but they may decrease under non-unital channels.The behaviour of the uncertainties(and lower bounds)exhibit periodical oscillations due to correlation dynamics under independent non-Markovian reservoirs.In addition,we compare different entropic uncertainty relations in several special cases and find that discord-tightened entropic uncertainty relations offer in general a better estimate of the uncertainties in play.     

Quantum correlation and entropic uncertainty in a quantum-dot system

We explore the dynamical behaviors of the measurement uncertainty and quantum correlation for a vertical quantum-dot system in the presence of magnetic field, including electron-electron interaction and Coulomb-blocked systems. Stemming from the quantum-memory-assisted entropic uncertainty relation, the uncertainty of interest is associated with temperature and parameters related to the magnetic field. Interestingly, the temperature has two kinds of influences on the variation of measurement uncertainty with respect to the magnetic-field-related parameters. We also discuss the relation between the lower bound of Berta et al. and the quantum discord. It is found that there is a natural competition between the quantum discord and the entropy min_Πi^BS_Πi^B(ρ_A|B). Finally, we bring in two improved bounds to offer a more precise limit to the entropic uncertainty.     

Tighter Bound of Entropic Uncertainty under the Unruh Effect

The uncertainty principle limits the ability to simultaneously predict measurement outcomes for two non-commuting observables of a quantum particle. However, the uncertainty can be violated by considering a particle as a quantum memory correlated with the primary particle. By modeling an Unruh–Dewitt detector coupled to a massless scalar field, it is explored how the Unruh effect affects the entropic uncertainty and the tighter lower bound for a pair of entangled detectors is probed when one of them is accelerated. It is found that Unruh thermal noise really gives rise to an increase of entropic uncertainty for the given conditions since the correlation between quantum memory and the measured system is decreased. It is shown that the bound of the entropic uncertainty relations, in the presence of memory, can be formulated by introducing the Holevo quantity and mutual information. It is also noticed that Adabi's lower bound is tighter than that of Berta, and just the optimal bound under the Unruh effect. Moreover, it is shown that Berta's lower bound is unrelated to the choice of complementary observables, while the optimal Adabi's lower bound is dependent on the measurement choice. It is worth mentioning that the investigations may offer a better understanding of the entropic uncertainty in a relativistic motion.     

Quantum‐Memory‐Assisted Entropic Uncertainty Relations

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy‐based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum‐memory‐assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.     

Controlling of entropic uncertainty in open quantum system via proper placement of quantum register

We investigate the dynamical behaviors of quantum-memory-assisted entropic uncertainty and its lower bound in the amplitude-damping channel. The influences of different placement positions of the quantum register on the dynamics of quantum coherence, quantum entanglement, and quantum discord are analyzed in detail. The numerical simulation results show that the quantum register should be placed in the channel of the non-Markovian effect. This option is beneficial to reduce the entropic uncertainty and its lower bound. We also find that this choice does not change the evolution of the quantum coherence and quantum entanglement, but changes the dynamical process of the quantum discord of the system.These results show that quantum coherence, quantum entanglement, and quantum discord are different quantum resources with unique characteristics and properties, and quantum discord can play a key role in reducing the uncertainty of quantum systems.     

Reducing the Entropic Uncertainty via Non-Markovian Effect and Detuning in the Presence of Quantum Memory ∗

The influence of non-Markovian effect and detuning on the entropic uncertainty in the presence of quantum memory is studied by the time-convolutionless master-equation approach. The result shows that the entropic uncertainty in the presence of quantum memory is obviously dependent on both detuning and non-Markovian effect. The bigger the detuning is and the stronger the non-Markovian effect is, the smaller the entropic uncertainty is. Its physical explanation is that the known quantum information stored in the quantum memory can reduce or eliminate the entropic uncertainty about the measurement outcomes of another particle, which is entangled with the quantum memory.     

Complementary relation between quantum entanglement and entropic uncertainty

Quantum entanglement is regarded as one of the core concepts,which is used to describe the nonclassical correlation between subsystems,and entropic uncertainty relation plays a vital role in quantum precision measurement.It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states.An interesting question is naturally raised:is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement?Or if the relation can be applied to estimate the entanglement.In this work,we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation.The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system,and specifically the larger uncertainty will induce the weaker entanglement of the probed system,and vice versa.Besides,we use randomly generated states as illustrations to verify our results.Therefore,we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.     

Entropic Leggett–Garg inequality in neutrinos and <Emphasis Type="Italic">B</Emphasis>(<Emphasis Type="Italic">K</Emphasis>) meson systems

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral \(B_d\), \(B_s\) and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter \(\mathscr {D}^{[n]}\) closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in \(B_d\) and \(B_s\) systems.     

Information erasure in quantum systems

The physical cost of information erasure is considered within a new approach that regards erasure as loss of correlation between the state of an erasable quantum system and that of an enduring “referent” system holding classical information. A physical model of information erasure built on this referential picture is described in detail, and lower bounds on entropic and energetic costs are obtained from quantum dynamics and entropic inequalities alone.     

The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.      

Reduction of entropic uncertainty in entangled qubits system by local PT-symmetric operation

We investigate the quantum-memory-assisted entropic uncertainty for an entangled two-qubit system in a local quantum noise channel with PT-symmetric operation performing on one of the two particles. Our results show that the quantum-memory-assisted entropic uncertainty in the qubits system can be reduced effectively by the local PT-symmetric operation. Physical explanations for the behavior of the quantum-memory-assisted entropic uncertainty are given based on the property of entanglement of the qubits system and the non-locality induced by the re-normalization procedure for the non-Hermitian PT-symmetric operation.     

Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom-Cavity Couplings

Based on the time-convolutionless master-equation approach,the entropic uncertainty in the presence of quantum memory is investigated for a two-atom system in two dissipative cavities.We find that the entropic uncertainty can be controlled by the non-Markovian effect and the atom-cavity coupling.The results show that increasing the atom-cavity coupling can enlarge the oscillating frequencies of the entropic uncertainty and can decrease the minimal value of the entropic uncertainty.Enhancing the non-Markovian effect can reduce the minimal value of the entropic uncertainty.In particular,if the atom-cavity coupling or the non-Markovian effect is very strong,the entropic uncertainty will be very close to zero at certain time points,thus Bob can minimize his uncertainty about Alice's measurement outcomes.     

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP\mathcal{CP} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.     

The Entropic Uncertainty Relation for Two Qubits in the Cavity‐Based Architecture

Based on a simple cavity‐engineered architecture, the dynamics of quantum memory–assisted entropic uncertainty relation (QMA‐EUR) for two qubits initially prepared in a generic Werner state is investigated. The effects of cavity decay rate, qubit–cavity couplings, and cavity–cavity couplings on the uncertainty are explored. It is found that the damped oscillation of uncertainty can be induced by the increase of two types of coupling strengths mentioned above. It is demonstrated that the maximum value of uncertainty is closely related to the purity of the initial state. The uncertainty can be either increased or decreased, depending on the threshold value of coupling strength between the two cavities. Finally, in agreement with a recent observation, an asynchronous relation between uncertainty and mixedness is found during the initial time evolution.     

Controlling of the Entropic Uncertainty in Open Quantum System

We investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under two typical categories of noise: phase damping channel and depolarizing channel in detail. It shows that, owing to the dissipation, the entropic uncertainty monotonically increases and tends to a steady-state value with the increase of the decoherence in phase damping channel, and can always keep its lower bound during the evolution when the initial state is the maximum entangled state. The larger correlated dephasing rate is favorable for suppressing the amount of entropic uncertainty. In contrast, under the depolarizing channel with memory, the entropic uncertainty always fails to reach its lower bound. Besides, the entropic uncertainty and its lower bound firstly increase with time, then turn down and tend to a steady-state value. The larger correlated decay rate has no benefit to improve the accuracy of quantum measurement. Our investigations might offer an insight into the dynamics of the measurement uncertainty under decoherence, and be important to quantum precision measurement in open systems.

     

Entropic uncertainty relations for nonextensive quantum scattering

In this paper the angle-angular momentum entropic uncertainty relations are obtained for Tsallis-like entropies for nonextensive quantum scattering of spinless particles. The number-phase entropic uncertainty relations are also proved for nonextensive quantum scattering. Numerical results on the experimental tests of these entropic uncertainty relations, for the nonextensive (q≠1) statistics case are obtained by calculations of Tsallis-like scattering entropies from the 48 experimental sets of the pion-nucleus phase shifts.