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.     

Measurement Uncertainty and Its Connection to Quantum Coherence in an Inertial Unruh–DeWitt Detector

The dynamic characteristics of measured uncertainty and quantum coherence are explored for an inertial Unruh–DeWitt detector model in an expanding de Sitter space. Using the entropic uncertainty relation, the uncertainty of interest is correlated with the evolving time t, the energy level spacing δ, and the Hubble parameter H. The investigation shows that, for short time, a strong energy level spacing and small Hubble parameter can result in a relatively small uncertainty. The evolution of quantum coherence versus the evolving time and Hubble parameter, which varies almost inversely to that of the uncertainty, is then discussed, and the relationship between uncertainty and the coherence is explicitly derived. With respect to the l₁ norm of coherence, it is found that the environment for the quantum system considered possesses a strong non-Markovian property. The dynamic behavior of coherence non-monotonously decreases with the growth of evolving time. The dynamic features of uncertainty and coherence in the expanding space with those in flat space are also compared. Furthermore, quantum weak measurement is utilized to effectively reduce the magnitude of uncertainty, which offers realistic and important support for quantum precision measurements during the undertaking of quantum tasks.     

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.     

Entropic uncertainty relation in de Sitter space

The uncertainty principle restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables of a quantum particle. However, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). By the open quantum system approach, we explore how the nature of de Sitter space affects the EUR. When the quantum memory A$A$ freely falls in the de Sitter space, we demonstrate that the entropic uncertainty acquires an increase resulting from a thermal bath with the Gibbons–Hawking temperature. And for the static case, we find that the temperature coming from both the intrinsic thermal nature of the de Sitter space and the Unruh effect associated with the proper acceleration of A$A$ also brings effect on entropic uncertainty, and the higher the temperature, the greater the uncertainty and the quicker the uncertainty reaches the maximal value. And finally the possible mechanism behind this phenomenon is also explored.     

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.     

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.

     

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.     

Entropic Uncertainty in Neutrino and Meson Systems

The dynamics of quantum‐memory‐assisted entropic uncertainty for the closed neutrino system in the context of two flavor oscillations and the meson system within the framework of open quantum system are investigated. It is found that the entropic uncertainty exists in close relation with the quantum correlation, and growing quantum correlation can decrease the uncertainty. The oscillatory behaviors of entropic uncertainty in neutrino system brought about by neutrino oscillating property are different from the decaying behaviors of entropic uncertainty in meson system induced by the meson decaying nature. In addition, the entropic uncertainty is always equal to its lower bound in the two subatomic systems. This study would throw light on the particle behavior characteristics of high energy physics, and may be useful to the tasks of quantum information‐processing implemented with subatomic system since the uncertainty principle plays vital role in quantum information science and technology.     

On Entropic Uncertainty Relations for Measurements of Energy and Its “Complement”

Heisenberg's uncertainty principle in application to energy and time is a powerful heuristics. This statement plays an important role in foundations of quantum theory and statistical physics. If some state exists for a finite interval of time, then it cannot have a completely definite value of energy. It is well known that the case of energy and time principally differs from more familiar examples of two non‐commuting observables. Since quantum theory was originated, many approaches to energy–time uncertainties have been proposed. Entropic way to formulate the uncertainty principle is currently the subject of active researches. Using the Pegg concept of complementarity of the Hamiltonian, uncertainty relations of the “energy–time” type are obtained in terms of Rényi and Tsallis entropies. Although this concept is somehow restricted in scope, derived relations can be applied to systems typically used in quantum information processing. Both the state‐dependent and state‐independent formulations are of interest. Some of the derived state‐independent bounds are similar to the results obtained within a more general approach on the basis of sandwiched relative entropies. The developed method allows us to address the case of detection inefficiencies.     

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.     

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.     

Coherent fluorescence emission by using hybrid photonic–plasmonic crystals

The spatial and temporal coherence of the fluorescence emission controlled by a quasi‐two‐dimensional hybrid photonic–plasmonic crystal structure covered with a thin fluorescent‐molecular‐doped dielectric film is investigated experimentally. A simple theoretical model to describe how a confined quasi‐two‐dimensional optical mode may induce coherent fluorescence emission is also presented. Concerning the spatial coherence, it is experimentally observed that the coherence area in the plane of the light source is in excess of 49 μm², which results in enhanced directional fluorescence emission. Concerning temporal coherence, the obtained coherence time is 4 times longer than that of the normal fluorescence emission in vacuum. Moreover, a Young's double‐slit interference experiment is performed to directly confirm the spatially coherent emission. This smoking gun proof of spatial coherence is reported here for the first time for the optical‐mode‐modified emission.     

Unilateral Coherence and Coherence Distribution in Curved Spacetime

We study unilateral coherence and coherence distribution in the background of a Schwarzschild black hole. We find that, comparing to the flat spacetime, two types of unilateral coherence corresponding to the measurements on system A and system B, respectively, are asymmetric for any Hawking temperature, and the accessible coherence of system B is bigger than the accessible coherence of system A in curved spacetime. We also find that the local coherence of system B reduces with the increase of Hawking temperature, while the local coherence of system A remains unchanged. Unlike behavior of quantum entanglement in curved spacetime, the remaining coherence (correlated coherence) increases with the increase of finitevalued Hawking temperature.

     

An Informational Characterization of Schrödinger's Uncertainty Relations

Heisenberg's uncertainty relations employ commutators of observables to set fundamental limits on quantum measurement. The information concerning incompatibility (non-commutativity) of observables is well included but that concerning correlation is missing. Schrödinger's uncertainty relations remedy this defect by supplementing the correlation in terms of anti-commutators. However, both Heisenberg's uncertainty relations and Schrödinger's uncertainty relations are expressed in terms of variances, which are not good measures of uncertainty in general situations (e.g., when mixed states are involved). By virtue of the Wigner–Yanase skew information, we will establish an uncertainty relation along the spirit of Schrödinger from a statistical inference perspective and propose a conjecture. The result may be interpreted as a quantification of certain aspect of the celebrated Wigner–Araki–Yanase theorem for quantum measurement, which states that observables not commuting with a conserved quantity cannot be measured exactly.     

The generalized uncertainty principle in (A)dS space and the modification of Hawking temperature from the minimal length

Recently, the Heisenberg's uncertainty principle has been extended to incorporate the existence of a large (cut-off) length scale in de Sitter or anti-de Sitter space, and the Hawking temperatures of the Schwarzshild–(anti) de Sitter black holes have been reproduced by using the extended uncertainty principle. I generalize the extended uncertainty to the case with an absolute minimum length and compute its modification to the Hawking temperature. I obtain a general trend that the generalized uncertainty principle due to the absolute minimum length “always” increases the Hawking temperature, implying “faster” decay, which is in conformity with the result in the asymptotically flat space. I also revisit the black hole-string phase transition, in the context of the generalized uncertainty principle.     

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables. In terms of the coherence measure based on the Wigner-Yanase skew information, we establish several uncertainty relations for coherence with respect to von Neumann measurements, mutually unbiased bases(MUBs), and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively. Since coherence is intimately connected with quantum uncertainties, the obtained uncertainty relations are of intrinsically quantum nature, in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties). From a dual viewpoint, we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement. In particular, it is shown that if the density operators representing the quantum states do not commute, then there is no measurement(reference basis) such that the coherence of these states can be simultaneously small.     

The Effects of an Impurity in an Ising‐XXZ Diamond Chain on Thermal Entanglement,on Quantum Coherence,and on Quantum Teleportation

The effects of an impurity plaquette on the thermal quantum correlations measurement by the concurrence, on quantum coherence quantified by the recently proposed l₁‐norm of coherence and on quantum teleportation in a Ising‐ $XXZ$ diamond chain are discussed. Such an impurity is formed by the $XXZ$ interaction between the interstitial Heisenberg dimers and the nearest‐neighbor Ising coupling between the nodal and interstitial spins. All the interaction parameters are different from those of the rest of the chain. By tailoring them, quantum entanglement and quantum coherence can be controlled and tuned. Therefore, the quantum resources—thermal entanglement and quantum coherence—of the model exhibit a clear performance improvement in comparison to the original model without impurities. It is demonstrated that quantum teleportation can be tuned by its inclusion. Thermal teleportation is modified in a significant way as well, and a strong increase in the average fidelity is observed. The exact solution is furnished by the use of the transfer‐matrix method.     

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.     

Quantum-Memory-Assisted Entropic Uncertainty Relation and Quantum Coherence in Structured Reservoir

The uncertainty principle is regarded as one of basics in quantum mechanics, which sets up a strict lower bound to quantify the prediction on the outcome concerning a set of incompatible measurements. In this paper, we investigate the dynamic behaviors of quantum-memory-assisted entropic uncertainty relation (EUR), and quantum coherence in structured reservoir. The results shown that the EUR is smallest in the vanishing limit of noise regardless of the forms of the initial sate we considered, while the coherence keeps the maximal value. During the time-evolution process, the uncertainty bound is lifted and the coherence damps monotonously. Subsequently, the EUR converges to an asymptotic nonzero constant in the long-time limit, yet the coherence asymptotically decays to zero. Moreover, the initial state purity plays a deterministic role in the initial amounts of EUR and coherence, i.e. the larger purity the less EUR and larger coherence. As an application, we employ the EUR to witness the coherence, and prove that the corresponding witnessing efficiencies are only depended on the version of coherence, while are insensitive to the reservoir.

     

On the Origin of Entropic Gravity and Inertia

It was recently suggested that quantum field theory is not fundamental but emerges from the loss of phase space information about matter crossing causal horizons. Possible connections between this formalism and Verlinde’s entropic gravity and Jacobson’s thermodynamic gravity are proposed. The holographic screen in Verlinde’s formalism can be identified as local Rindler horizons and its entropy as that of the bulk fields beyond the horizons. This naturally resolves some issues on entropic gravity. The quantum fluctuation of the fields is the origin of the thermodynamic nature of entropic gravity. It is also suggested that inertia is related to dragging Rindler horizons.