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Annalen der Physik

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

Ying‐Yue Yang, Liu Ye, Dong Wang

Published Jul 1, 2020• 12 citations
Publisher

Abstract

Abstract 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.

DOI
10.1002/andp.202000062

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Abstract 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.
Abstract 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.
Abstract 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.
We investigate the interplay between quantum thermodynamics, quantum correlations, and quantum coherence within the framework of the Unruh-DeWitt (UdW) detector model. By analyzing both the steady and dynamical states of various quantum resources (including steerability, entanglement, quantum discord, and coherence), we study how these resources evolve under Markovian and non-Markovian environments. Furthermore, we investigate the impact of both the Unruh temperature and the energy levels on three key quantum phenomena: thermodynamic evolution, quantum correlations, and quantum coherence, considering different initial state preparations. The hierarchical structure relating quantum correlations and quantum coherence is determined. We further examine the thermodynamic performance of a quantum heat engine, highlighting the influence of memory effects and classical correlations on heat exchange, work extraction, and efficiency. Our results reveal that non-Markovian dynamics can enhance the preservation of quantum correlations and improve the engine's efficiency compared to purely Markovian regime. These findings provide insights into the role of quantum correlations and quantum coherence in quantum thermodynamic processes and open avenues for optimizing quantum devices operating in relativistic or open-system settings.
Abstract Quantum objects are susceptible to noise from their surrounding environments, interaction with which inevitably gives rise to quantum decoherence or dissipation effects. In this work, we examine how different types of local noise under an open system affect entropic uncertainty relations for two incompatible measurements. Explicitly, we observe the dynamics of the entropic uncertainty in the presence of quantum memory under two canonical categories of noisy environments: unital (phase flip) and nonunital (amplitude damping). Our study shows that the measurement uncertainty exhibits a non-monotonic dynamical behavior—that is, the amount of the uncertainty will first inflate, and subsequently decrease, with the growth of decoherence strengths in the two channels. In contrast, the uncertainty decreases monotonically with the growth of the purity of the initial state shared in prior. In order to reduce the measurement uncertainty in noisy environments, we put forward a remarkably effective strategy to steer the magnitude of uncertainty by means of a local non-unitary operation (i.e. weak measurement) on the qubit of interest. It turns out that this non-unitary operation can greatly reduce the entropic uncertainty, upon tuning the operation strength. Our investigations might thereby offer an insight into the dynamics and steering of entropic uncertainty in open systems.
Abstract 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.
Abstract Quantum coherence, a fundamental aspect of quantum mechanics, plays a crucial role in various quantum information tasks. However, preserving coherence under extreme conditions, such as relativistic acceleration, poses significant challenges. In this paper, we investigate the influence of Unruh temperature and energy levels on the evolution of maximal steered coherence (MSC) for different initial states. Our results reveal that MSC is strongly dependent on Unruh temperature, exhibiting behaviors ranging from monotonic decline to non-monotonic recovery, depending on the initial state parameter Δ0\Delta _0Δ0​ Δ 0 . Notably, when Δ0=1\Delta _0=1Δ0​=1 Δ 0 = 1 , MSC is generated as Unruh temperature increases. Additionally, we observe that higher energy levels help preserve or enhance MSC in the presence of Unruh effects. These findings offer valuable insights into the intricate relationship between relativistic effects and quantum coherence, with potential applications in developing robust quantum technologies for non-inertial environments.