The uncertainty principle bounds our ability to simultaneously predict two incompatible observables of a quantum particle. Assisted by a quantum memory to store the particle, this uncertainty could be reduced and quantified by a new Entropic Uncertainty Relation (EUR). In this Letter, we explore how the relativistic motion of the system would affect the EUR in two sample scenarios. First, we show that the Unruh effect of an accelerating particle would surely increase the uncertainty if the system and particle entangled initially. On the other hand, the entanglement could be generated from nonuniform motion once the Unruh decoherence is prevented by utilizing the cavity. We show that, in a uncertainty game between an inertial cavity and a nonuniformly accelerated one, the uncertainty evolves periodically with respect to the duration of acceleration segment. Therefore, with properly chosen cavity parameters, the uncertainty bound could be protected. Implications of our results for gravitation are also discussed.Comment: 7 pages, 3 figure

We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit $-\log_2c$. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given.Comment: 11 pages, 2figures. Minor typos corrected, references and comment on the black hole firewall added. Matches the version to appear in Physics Letters

We investigate the quantum estimation on the Hubble parameter of an expanding de Sitter space by quantum metrological techniques. By exploring the dynamics of a freely falling Unruh-DeWitt detector, which interacts with a scalar field coupling to curvature, we calculate the Fisher information (FI) and quantum Fisher information (QFI) for the detector, which bound the highest precision of the estimation on Hubble parameter. In standard Bunch-Davies vacuum, we show that the maxima of FI/QFI are located for particular initial state of probe. Beside its dependence on the evolving time of detector and the energy spacing of atom ω, we show that the maxima of FI/QFI can be significantly enhanced once a proper coupling of scalar field to curvature is chosen. For instance, we show numerically that the estimation in the scenario with minimally/nearly minimally coupling scalar field can always outperform that with conformally coupling scalar field, corresponding to a higher FI/QFI in estimation. Moreover, we find that for general α−vacua of de Sitter space, a further improvement of estimation can be achieved, attributed to the squeezed nature of α−vacua that heavily constrains the measurement uncertainty. Some implications of our results are also discussed.

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Our result shows that, contrary to the eight-vertex model without a reflection end, the partition function can be expressed as a single determinant.

An analysis of Hawking radiation about apparent horizon in a FRW universe is performed by using the method developed in the paper (Banerjee, Majhi in JHEP 06:095 2008), in which the Hawking radiation of a black hole is treated as the quantum tunneling by Hamilton-Jacobi method beyond semiclassical approximation and then all the higher order quantum corrections can be given out. In our analysis, the Kodama vector instead of the Killing vector to define the energy of the particle plays a key role. We present our analysis under the Friedmann-Robertson-Walker like coordinate system and the much-like to Painlevé coordinate system respectively. The result show that the formulized procedure can be extended to fully analyse the Hawking radiation of a dynamical system.

We investigate the quantum teleportation between a conformal detector Alice and an inertial detector Bob in de Sitter space in two schemes, (i) one uses free scalar modes and (ii) one utilizes cavity to store qubit. We show that the fidelity of the teleportation is degraded for Bob in both cases. While the fidelity-loss is due to the Gibbons-Hawking effect associated with his cosmological horizon in the scheme (i), the entanglement decreases in the scheme (ii) because the ability to entangle the cavities is reduced by the spacetime curvature. With a cutoff at Planck-scale, comparing with the standard Bunch-Davies choice, we also show that the possible Planckian physics cause extra modifications to the fidelity of the teleportation protocol in both schemes.Comment: 6 pages, 2 figures, typos corrected. To appear in Phys. Lett.

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix for the open XXZ spin chain with non-diagonal boundary terms, we obtain the determinant representations of the scalar products of Bethe states of the model.

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