L. F. Santos, C. O. Escobar
We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the Navier-Stokes equation. This sort of analogy may be useful in the development of both areas.
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We collect and describe the observed geometrical and dynamical properties of turbulence in quantum fluids, particularly superfluid helium and atomic condensates for which more information about turbulence is available. Considering the spectral features, the temporal decay, and the comparison with relevant turbulent classical flows, we identify three main limiting types of quantum turbulence: Kolmogorov quantum turbulence, Vinen quantum turbulence, and strong quantum turbulence. This classification will be useful to analyse and interpret new results in these and other quantum fluids.
For some ideal quantum measurements, conservation laws would seem to be violated systematically. It is argued that the intrinsically non-"ideal" nature of quantum measurements rescues the conservation laws.
We raise fundamental questions about the very meaning of conservation laws in quantum mechanics and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended.
In the posting arXiv:2101.11052v2 an experimental protocol involving two spins is proposed, which should show violation of energy conservation in a quantum experiment. In the present comment an unjustified mathematical approximation leading to that conclusion is pointed out. A detailed analysis will restore energy conservation.
Superfluid Turbulence is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, inter penetrating turbulent fluids: the first is inviscid with quantised vorticity, the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those o ordinary turbulence. We present experimental, numerical and theoretical results which explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller sc…
Toward end-to-end quantum simulation of rapidly distorted turbulence
本文提出一种端到端量子算法，利用线性组合哈密顿量模拟快速扭曲湍流，展示了其在湍流统计量测量和湍流机制建模方面的有效性。
Experimental Demonstration of Turbulence-resistant Lidar via Quantum Entanglement
本研究通过纠缠光子对的双光子干涉实现了抗湍流量子激光雷达的原理性实验验证，该系统同时具备抗噪声能力，为湍流噪声环境下的高精度时频定位技术提供了新方向。
It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.
We explore the connections between the constraints on the precision of quantum logical operations that arise from a conservation law, and those arising from quantum field fluctuations. We show that the conservation-law based constraints apply in a number of situations of experimental interest, such as Raman excitations, and atoms in free space interacting with the multimode vacuum. We also show that for these systems, and for states with a sufficiently large photon number, the conservation-law based constraint represents an ultimate limit closely related to the fluctuations in the quantum fiel…
Conservation principles are essential to describe and quantify dynamical processes in all areas of physics. Classically, a conservation law holds because the description of reality can be considered independent of an observation (measurement). In quantum mechanics, however, invasive observations change quantities drastically, irrespective of any classical conservation law. One may hope to overcome this nonconservation by performing a weak, almost noninvasive measurement. Interestingly, we find that the nonconservation is manifest even in weakly measured correlations if some of the other observ…
We show that the no-deleting and no-cloning principles are implications of information conservation principle. This is unlike in classical physics, where cloning and deleting are possible, independently of information conservation. Connections with the second law of thermodynamics are also discusssed.
We show that conservation laws in quantum mechanics naturally lead to metric spaces for the set of related physical quantities. All such metric spaces have an "onion-shell" geometry. We demonstrate the power of this approach by considering many-body systems immersed in a magnetic field, with a finite ground state current. In the associated metric spaces we find regions of allowed and forbidden distances, a "band structure" in metric space directly arising from the conservation of the $z$ component of the angular momentum.
Quantum vortex structures and energy cascades are examined for two dimensional quantum turbulence (2D QT) at zero temperature. A special unitary evolution algorithm, the quantum lattice gas (QLG) algorithm, is employed to simulate the Bose-Einstein condensate (BEC) governed by the Gross-Pitaevskii (GP) equation. A parameter regime is uncovered in which, as in 3D QT, there is a short Poincaré recurrence time. It is demonstrated that such short recurrence times are destroyed as the nonlinear interaction is strengthened. The similar loss of Poincaré recurrence is also reported in 3D QT [1] Energy…
Being quantized, conserved Noether symmetry functions are represented by Hermitian operators in the space of solutions of the Schrodinger equation, and their mean values are conserved.
A scheme is described that allows Alice to communicate to Bob where on earth she is, even though she doesn't know herself. The situation described shows how the generalization of a recent result of Gisin and Popescu [quant-ph/9901072] could be useful.
We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a novel experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost imaging central image plane, we are able to dramatically increase the ghost image quality. When imaging a test pattern through turbulence, this method increased the imaged pattern visibility from V = 0.14 +/- 0.04 to V = 0.29 +/- 0.04.
Conservation laws are discussed in conjunction with quantum-mechanical indeterminacies of the corresponding observables. The considered examples show that the connections between energy and its indeterminacy may be quite intricate. The indeterminacies of the parts of a composite system may be correlated in such a way that the net value of the considered observable is definite. This may be the case with specific entangled superposition of eigenstates in a composite system. In some cases the fact of energy conservation cannot be convincingly established and generally the concept of conserving ob…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness $ε$ embedded in $R_3$. In such a system with a small thickness $ε$, the usual two-dimensional conservation law does not hold and we find an anomaly. The anomalous term is obtained by the expansion of $ε$. We find that this term has a Gaussian and mean curvature dependence and can be written as the total divergence of some geometr…
The evolution of the spatial degrees of freedom of a photon propagating through atmospheric turbulence is treated as a non-Markovian process. Here, we derive and solve the evolution equation for this process. The turbulent medium is modeled by a sequence of multiple phase screens for general turbulence conditions. The non-Markovian perspective leads to a second-order differential equation with respect to the propagation distance. The solution for this differential equation is obtained with the aid of a perturbative analysis, assuming the turbulence is relatively weak. We also provide another s…
In local quantum circuits with charge conservation, we initialize the system in random product states and study the dynamics of the Renyi entanglement entropy $R_α$. We rigorously prove that $R_α$ with Renyi index $α>1$ at time $t$ is $\le O(\sqrt{t\ln t})$ if the transport of charges is diffusive. Very recent numerical results of Rakovszky et al. show that this upper bound is saturated (up to the sub-logarithmic correction) in random local quantum circuits with charge conservation.
In this talk, we discuss real-time thermalization dynamics of $\mathbf{Z}_2$ Lattice Gauge Theory in 2+1 spacetime dimensions. While classical thermalization is commonly associated with chaotic behavior, turbulence and universality, the manifestation of these phenomena in quantum mechanical systems is not clear. However, when viewed through the lens of Entanglement Structure, we find that quantum thermalization proceeds in characteristic stages and reveals phenomena remarkably similar to their classical counterparts: chaos, turbulence and universality.
A principle of information conservation is shown in abstract terms to rule out probabilistic physical laws, necessitating the existence of state trajectories. It furthermore provides a geometric-thermodynamic mechanism for the appearance of probability distributions at the operational level, and thus may provide a dynamical explanation for Born's rule of quantum probabilities. This link between geometry and operational probabilities is argued to be a promising angle from which to study the potential for "hidden information" in quantum systems, and guide efforts in quantum foundations more gene…
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