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arXiv:1403.0313 · Europhysics Letters (EPL)

Fine-grained uncertainty relations under relativistic motion

Jun Feng, Yao-Zhong Zhang, M. D. Gould, Heng Fan

Published Jul 30, 2018• 9 citations
arXivHTMLPDF

Abstract

Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this letter, we explore this uncertainty relation in a relativistic regime. For an observer undergoing a uniform acceleration who is immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and the choice of Unruh modes. We find that the measurements in mutually unbiased bases, sharing the same uncertainty bound in the inertial frame, could be distinguished from each other for a noninertial observer. In an alternative scenario, for the observer restricted in a single rigid cavity, we show that the uncertainty bound exhibits a periodic evolution with respect to the duration of acceleration. With properly chosen cavity parameters, the uncertainty bounds could be protected. Moreover, we find that the uncertainty bound can be degraded for specific quantum measurements to violate the bound exhibited in the nonrelativistic limit, which can be attributed to the entanglement generation between cavity modes during a particular epoch. Several implications of our results are discussed.

DOI
10.1209/0295-5075/122/60001

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Among various uncertainty relations, the profound fine-grained uncertainty relation is used to distinguish the uncertainty inherent in obtaining any combination of outcomes for different measurements. In this letter, we explore this uncertainty relation in a relativistic regime. For an observer undergoing a uniform acceleration who is immersed in an Unruh thermal bath, we show that the uncertainty bound is dependent on the acceleration parameter and the choice of Unruh modes. We find that the measurements in mutually unbiased bases, sharing the same uncertainty bound in the inertial frame, could be distinguished from each other for a noninertial observer. In an alternative scenario, for the observer restricted in a single rigid cavity, we show that the uncertainty bound exhibits a periodic evolution with respect to the duration of acceleration. With properly chosen cavity parameters, the uncertainty bounds could be protected. Moreover, we find that the uncertainty bound can be degraded for specific quantum measurements to violate the bound exhibited in the nonrelativistic limit, which can be attributed to the entanglement generation between cavity modes during a particular epoch. Several implications of our results are discussed.
The fine-grained uncertainty relation (FUR) is investigated for accelerating open quantum system, which manifests the celebrated Unruh effect, a crucial piece of the jigsaw for combining relativity and quantum physics. For a single detector, we show that the inevitable Unruh decoherence can induce a smaller FUR uncertainty bound, which indicates an additional measurement uncertainty may exist. For an open system combined with two detectors, via a nonlocal retrieval game, the related FUR uncertainty bound is determined by the non-classical correlation of the system. By estimating the maximal violation of Bell inequality for an accelerating system, we show that the FUR uncertainty bound can be protected from Unruh decoherence, due to quantum correlation generated through Markovian dynamics.
Abstract The uncertainty principle offers a bound to show accuracy of the simultaneous measurement outcome for two incompatible observables. In this letter, we investigate quantum-memory-assisted entropic uncertainty relation (QMA–EUR) when the particle to be measured stays at an open system, and another particle is treated as quantum memory under a noninertial frame. In such a scenario, the collective influence of the unital and nonunital noise environment, and of the relativistic motion of the system, on the QMA–EUR is examined. By numerical analysis, we conclude that, firstly, the noises and the Unruh effect can both increase the uncertainty, due to the decoherence of the bipartite system induced by the noise or Unruh effect; secondly, the uncertainty is more affected by the noises than by the Unruh effect from the acceleration; thirdly, unital noises can reduce the uncertainty in long-time regime. We give a possible physical interpretation for those results: that the information of interest is redistributed among the bipartite, the noisy environment and the physically inaccessible region in the noninertial frame. Therefore, we claim that our observations provide an insight into dynamics of the entropic uncertainty in a noninertial frame, and might be important to quantum precision measurement under relativistic motion.
Quantum uncertainty is deeply linked to quantum correlations and relativistic motion. The entropic uncertainty relation with quantum memory offers a powerful way to study how shared entanglement affects measurement precision. However, under acceleration, the Unruh effect can degrade quantum correlations, raising questions about the reliability of QMA-EUR in such settings. Here, we investigate the QMA-EUR for two uniformly accelerating Unruh-DeWitt detectors coupled to a massless scalar field. Using the Kossakowski-Lindblad master equation, we calculate the entropic uncertainty, its lower bound, and the tightness of the relation under different Unruh temperatures. We find that acceleration does not always increase the lower bound on the uncertainty relation. Depending on the initial correlations between the detectors, it may either increase or decrease. This behavior results from the interplay between quantum discord and minimal missing information. Interestingly, a higher quantum discord does not necessarily lead to lower uncertainty.
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 study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that, for two observers undergoing finite acceleration, the entanglement vanishes between the lowest-frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement into multipartite quantum correlations among accessible and inaccessible modes from a noninertial perspective. We show that classical correlations are also lost from the perspective of two accelerated observers but conserved if one of the observers remains inertial.
We investigate the fine-grained uncertainty relations for qubit systems by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in ddd-dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.