Abstract The uncertainty principle sets a fundamental bound on the precision of measurement outcomes of two incompatible observables, which can be reduced in the presence of quantum memory. In this work, we investigate the dynamics of entropic uncertainty bound (EUB) for a bipartite system, where only the quantum memory is exposed to a nonequilibrium dephasing environment with an Ohmic-class spectrum, which is compared with the thermal equilibrium case. The nonequilibrium feature is defined by a nonstationary random function which can be controlled by engineering the relative initial phases of the bath modes. We show that this model renders a promising avenue for significantly suppressing the maximum steady-state value of the EUB for all the Ohmic spectral densities. Furthermore, we unveil the role of the reservoir’s Ohmic spectrum and the interplay between quantum discord and minimal conditional entropy of the measured particle in reducing the EUB. Additionally, we examine the state preparation and measurement choice condition in the engineered nonequilibrium environment case. The condition persists, and the nonequilibrium feature serves as a promising tool to impose a stronger limit on entropic uncertainty, enabling more accurate measurement outcomes under decoherence.
Abstract The uncertainty principle sets a fundamental bound on the precision of measurement outcomes of two incompatible observables, which can be reduced in the presence of quantum memory. In this work, we investigate the dynamics of entropic uncertainty bound (EUB) for a bipartite system, where only the quantum memory is exposed to a nonequilibrium dephasing environment with an Ohmic-class spectrum, which is compared with the thermal equilibrium case. The nonequilibrium feature is defined by a nonstationary random function which can be controlled by engineering the relative initial phases of the bath modes. We show that this model renders a promising avenue for significantly suppressing the maximum steady-state value of the EUB for all the Ohmic spectral densities. Furthermore, we unveil the role of the reservoir’s Ohmic spectrum and the interplay between quantum discord and minimal conditional entropy of the measured particle in reducing the EUB. Additionally, we examine the state preparation and measurement choice condition in the engineered nonequilibrium environment case. The condition persists, and the nonequilibrium feature serves as a promising tool to impose a stronger limit on entropic uncertainty, enabling more accurate measurement outcomes under decoherence.
The entropic uncertainty relation imposes a limit on the accuracy of measurement outcomes of two conjugate observables, which can be reduced in the presence of quantum memory. We theoretically study the dynamical behaviors of the quantum-memory-assisted entropic uncertainty relation for a bipartite system under local nonequilibrium dephasing environments and a common nonequilibrium dephasing environment. Particularly, we study the influence of the competition between nonequilibrium and non-Markovianity in controlling the entropic uncertainty bound (EUB) in weak- and strong-coupling regimes. We find that the nonequilibrium nature renders a promising protocol to efficiently harness the EUB in both regimes without requiring any operations on the main system. Further, we reveal that the EUB can be significantly reduced in a common bath case compared to the case of local baths. Moreover, we elucidate the primary factor responsible for governing the dynamical behaviors of EUB by examining the interplay between quantum discord and the minimal missing information about the particle to be measured. In addition, we investigate the state preparation and measurement choice (SPMC) condition in both environmental setups with weak- and strong-coupling regimes. Remarkably, we show that the SPMC condition does not hold in the common environment scenario.
The entropic uncertainty principle imposes a limit on how precisely two incompatible observables can be measured, which can be reduced when quantum memory is involved. We theoretically investigate the dynamics of the quantum-memory-assisted entropic uncertainty relation when either quantum memory alone or both the measured particle and the quantum memory interact with a squeezed-vacuum bath through energy-preserving interactions. We show that in both scenarios, the squeezing phase of the reservoir decreases the entropic uncertainty (EU), whereas the squeezing strength increases the EU. In addition, we find that EU can be significantly reduced when both the measured particle and quantum memory are subjected to a common squeezed-vacuum bath. Furthermore, we explore the key factors controlling the behavior of EU by exploring the competition between quantum discord and minimal missing information. Moreover, we examine the tightness of the entropic uncertainty bound (EUB) in both system-environment setups and observe that the EUB is less tight when both the measured particle and quantum memory are coupled to a common squeezed-vacuum bath.
The uncertainty principle limits the ability for observer to precisely measure two incompatible observables, and plays a crucial role in quantum precision measurement in the quantum information science. When quantum systems interact with their surroundings, they inevitably result in decoherence, which increases the uncertainty of the system. In the process of quantum information processing, the effective regulation of uncertainty becomes a key problem that needs to be solved. In this work, we investigate the quantum-memory-assisted entropic uncertainty relation of a two-qubit system under correlated channels with dephasing colored noise. We demonstrate that it is possible to control the entropic uncertainty, U, and its lower bound, Ub, by combining correlations between successive uses of channels and the non-Markovianity of the dynamical evolution. Firstly, the evolutionary characteristics of the trace distance are employed to distinguish between Markovianity and non-Markovianity of the channel. Subsequently, the system is selected to be either a maximally entangled state or separated state initially. By adjusting the strength η of the correlations, we find that with the increase of η, the entropic uncertainty and its lower bound decrease. Especially, if the channel is fully correlated (η = 1), the entropic uncertainty and its lower bound remain constant under the channel, indicating that decoherence is completely suppressed. A comparison of Markovian channel with non-Markovian channel reveals that the entropic uncertainty and its lower bound exhibit oscillatory behaviour under non-Markovian channels. The combination of correlations and non-Markovianity of the channel demonstrates that the entropic uncertainty and its lower bound can be reduced under fully correlated channels where the non-Markovianity has no effect. This is because fully correlated channels suppress decoherence to a greatest extent. Under partially correlated channels, the combination of correlations and non-Markovianity can more effectively reduce the entropic uncertainty and its lower bound. Under such channels, correlations of the channel reduce the entropic uncertainty and its lower bound during the whole evolution, while the non-Markovianity contributes to their oscillations and reduce them in some specific time. Furthermore, the results show that the entropic uncertainty and its lower bound reach steady values that depend only on the strength of the correlations after long-time evolution. In other words, the stronger the correlations, the lower the entropy uncertainty and its lower bound of steady states will be. Finally, we analyse the physical nature of the decrease of the entropic uncertainty and its lower bound, and it is found that the decrease of the entropic uncertainty and its lower bound originate from the increase of the quantum correlations in the system.
Abstract We study theoretically the dynamics of quantum and classical correlations in the two-qubit system, locally experiencing a one-sided engineered pure dephasing non-equilibrium environment with an Ohmic class spectrum. The environmental non-equilibrium nature is characterized by random perturbations with non-stationary statistics. Particularly, we investigate the influence of the non-equilibrium feature on the protection of these correlations and, more specifically, its effect on the non-trivial phenomenon of time-invariant discord. Remarkably, we show that in the presence of this engineered non-equilibrium environment, time-invariant discord with a significantly larger magnitude exists for all Ohmic spectral densities, i.e., sub-Ohmic, Ohmic, and super-Ohmic without zero-temperature restriction. Additionally, we also show that our engineered non-equilibrium model provides a promising tool for trapping entanglement in a steady-state with a higher magnitude. Moreover, our proposed model also renders new insights for controlling decoherence through engineering the relative initial phases of the bath modes without performing any artificial operations on the main quantum system.
Abstract The uncertainty principle is an inherent characteristic of quantum mechanics. This principle can be formulated in various forms. Fundamentally, this principle can be expressed in terms of the standard deviation of the measured observables. In quantum information theory, the preferred mathematical quantity to express the entropic uncertainty relation is Shannon’s entropy. In this work, we consider the generalized entropic uncertainty relation in which there is an additional particle as a quantum memory. Alice measures on her particle A and Bob, with memory particle B , predicts Alice’s measurement outcomes. It has a wide range of applications, for example, entanglement witnessing and quantum key distribution. We study the effects of the environment on the entropic uncertainty lower bound in the presence of weak measurement and measurement reversal. The dynamical model that is intended in this work is as follows: first the weak measurement is performed, second, the decoherence affects the system and finally the measurement reversal is performed on the quantum system. Here, we consider the generalized amplitude damping channel and depolarizing channel as environmental noises. We will show that in the presence of weak measurement and measurement reversal, despite the presence of environmental factors, the entropic uncertainty lower bound drops to an optimal minimum value. In fact, weak measurement and measurement reversal enhance the quantum correlation between the subsystems A and B , and thus the uncertainty of Bob regarding Alice’s measurement outcomes reduces. Based on the entropic uncertainty relation, one can also show that the weak measurement and measurement reversal can preserve the quantum secret key rate lower bound from decoherence.
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables cannot be predicted simultaneously. In quantum information theory, this principle can be expressed in terms of entropic measures. M. Berta et al. [Nat. Phys. 6, 659 (2010)] have indicated that uncertainty bound can be altered by considering a particle as a quantum memory correlating with the primary particle. In this article, we obtain a lower bound for entropic uncertainty in the presence of a quantum memory by adding an additional term depending on the Holevo quantity and mutual information. We conclude that our lower bound will be tightened with respect to that of Berta et al. when the accessible information about measurements outcomes is less than the mutual information about the joint state. Some examples have been investigated for which our lower bound is tighter than Berta et al.'s lower bound. Using our lower bound, a lower bound for the entanglement of formation of bipartite quantum states has been obtained, as well as an upper bound for the regularized distillable common randomness.