Entropic Dynamics (ED) is a framework in which Quantum Mechanics is derived as an application of entropic methods of inference. In ED the dynamics of the probability distribution is driven by entropy subject to constraints that are codified into a quantity later identified as the phase of the wave function. The central challenge is to specify how those constraints are themselves updated. In this paper we review and extend the ED framework in several directions. A new version of ED is introduced in which particles follow smooth differentiable Brownian trajectories (as opposed to non-differentiable Brownian paths). To construct the ED we make use of the fact that the space of probabilities and phases has a natural symplectic structure (i.e., it is a phase space with Hamiltonian flows and Poisson brackets). Then, using an argument based on information geometry, a metric structure is introduced. It is shown that the ED that preserves the symplectic and metric structures -- which is a Hamilton-Killing flow in phase space -- is the linear Schrödinger equation. These developments allow us to discuss why wave functions are complex and the connections between the superposition principle, the single-valuedness of wave functions, and the quantization of electric charges. Finally, it is observed that Hilbert spaces are not necessary ingredients in this construction. They are a clever but merely optional trick that turns out to be convenient for practical calculations.
Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from informati…
Standard Quantum Mechanics, although successful in terms of calculating and predicting results, is inherently difficult to understand and can suffer from misinterpretation. Entropic Dynamics is an epistemic approach to quantum mechanics based on logical inference. It incorporates the probabilities that naturally arise in situations where there is missing information. The development of Entropic Dynamics involves describing a particle in terms of a probability density, and then following the time evolution of the probability density based on diffusion-like motion and maximization of entropy. He…
We consider a stochastic process which is (a) described by a continuous-time Markov chain on only short time-scales and (b) constrained to conserve a number of hidden quantities on long time-scales. We assume that the transition matrix of the Markov chain is given and the conserved quantities are known to exist, but not explicitly given. To study the stochastic dynamics we propose to use the principle of stationary entropy production. Then the problem can be transformed into a variational problem for a suitably defined action and with time-dependent Lagrange multipliers. We show that the stoch…
Entropic Dynamics is a framework in which dynamical laws such as those that arise in physics are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to constraints reflecting the information that is relevant to the problem at hand. In this work I review the derivation of quantum theory but the fact that Entropic Dynamics is based on inference methods that are of universal applicability suggests that it may be possible to adapt these methods to fields other than physics.
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entro…
Entropic Dynamics is a framework for deriving the laws of physics from entropic inference. In an (ED) of particles, the central assumption is that particles have definite yet unknown positions. By appealing to certain symmetries, one can derive a quantum mechanics of scalar particles and particles with spin, in which the trajectories of the particles are given by a stochastic equation. This is much like Nelson's stochastic mechanics which also assumes a fluctuating particle as the basis of the microstates. The uniqueness of ED as an entropic inference of particles allows one to continuously tr…
The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The approach succeeds because ED achieves a clear-cut separation between ontic and epistemic elements: positions are ontic while probabilities and wave functions are epistemic. Thus, ED is a viable realist psi-epistemic model. Such models are widely assumed to be ruled out by various no-go theorems. We show that ED evades those theorems by adopting a purely epis…
The Leggett-Garg inequalities probe the classical-quantum boundary by putting limits on the sum of pairwise correlation functions between classical measurement devices that consecutively measured the same quantum system. The apparent violation of these inequalities by standard quantum measurements has cast doubt on quantum mechanics' ability to consistently describe classical objects. Recent work has concluded that these inequalities cannot be violated by either strong or weak projective measurements [1]. Here I consider an entropic version of the Leggett-Garg inequalities that are different f…
Heisenberg's uncertainty principle is a fundamental element in quantum mechanics. It sets a bound on our ability to predict the measurement outcomes of two incompatible observables simultaneously. In quantum information theory, the uncertainty principle can be expressed using entropic measures. The entropic uncertainty relation can be improved by considering an additional particle as a memory particle. The presence of quantum correlation between the memory particle and the measured particle reduces the uncertainty. In a curved space-time, the presence of the Hawking radiation can reduce quantu…
The uncertainty principle is the most important feature of quantum mechanics, which can be called the heart of quantum mechanics. This principle sets a lower bound on the uncertainties of two incompatible measurement. In quantum information theory, this principle is expressed in terms of entropic measures. Entropic uncertainty bound can be altered by considering a particle as a quantum memory. In this work we investigate the entropic uncertainty relation under the relativistic motion. In relativistic uncertainty game Alice and Bob agree on two observables, $\hat{Q}$ and $\hat{R}$, Bob prepares…
Reality of quantum observables, a feature of long-standing interest within foundations of quantum mechanics, has recently been quantified and deeply studied by means of entropic measures [Phys. Rev. A 97, 022107 (2018)]. However, there is no state-independent "reality trade-off" between noncommuting observables, as in certain systems all observables are real [Europhys. Lett. 112, 40005 (2015)]. We show that the entropic uncertainty relation in the presence of quantum memory [Nature Phys. 6, 659 (2010)] perfectly supplements the discussed notion of reality, rendering trade-offs between reality …
We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2; C) time-dependent Hamiltonian operators used to describe distinct types of analog quantum search schemes. The Riemannian metrization on the manifold is specified by the Fisher information evaluated along the parametrized squared probability amplitudes obtained from analysis of the temporal quantum mechanical evolution of a spin-1/2 particle in an external time-dependent magnetic fiel…
The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kuchař, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which inst…
Entropic uncertainty and measurement reversibility
来自[Berta et al.，6，659（2010）]是与量子力学的两个显著特征相关的统一原理：由于测量不相容性引起的量子不确定性和纠缠。在这些关系中，量子不确定性采取准备不确定性的形式，其中应用两个不相容测量之一。特别是，EUR-QSI中的“不确定性见证”下限不是测量后状态的函数。来自[Coles et al.，物理修订信函108，210405（2012）]利用了量子力学假设的基本数学推论，该推论被称为在量子信道下量子相对熵的不增加。在这里，我们利用这个角度来建立一个紧缩的EUR-QSI增加了一个新的状态依赖项的下限，以及如何可以逆转的量子测量的行动。因此，该新项是测量后状态的直接函数，并且可以被认为是量化给定测量引起的干扰程度。因此，我们的结果定量地统一了量子力学的这一特征与上述其他特征。我们已经在IBM量子体验上对我们的理论预测进行了实验测试，并发现我们的预测与实验结果之间存在合理的一致性。
Recently, an inequality satisfied by non-contextual hidden-variable models and violated by quantum mechanics for all states of a four-level system has been derived based on information-theoretic distance approach to non-classical correlations. In this work, we experimentally demonstrate violation of this inequality with single photons. Our experiment offers a method to study a distinction between quantum and classical correlations from an information-theoretic perspective.
What does it mean for one quantum process to be more disordered than another? Here we provide a precise answer to this question in terms of a quantum-mechanical generalization of majorization. The framework admits a complete description in terms of single-shot entropies, and provides a range of significant applications. These include applications to the comparison of quantum statistical models and quantum channels, to the resource theory of asymmetry, and to quantum thermodynamics. In particular, within quantum thermodynamics, we apply our results to provide the first complete set of of necess…
Tighter entropic uncertainty relations in the presence of quantum memories for complete sets of mutually unbiased bases
Changsha University of Science and Technology（长沙理工大学）；Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Sicence and Technology（长沙理工大学数学建模与工程分析湖南省重点实验室）；Capital Normal University（首都师范大学）；Jining University（济宁学院）
In the Entropic Dynamics framework the dynamics is driven by maximizing entropy subject to appropriate constraints. In this work we bring Entropic Dynamics one step closer to full equivalence with quantum theory by identifying constraints that lead to wave functions that remain single-valued even for multi-valued phases by recognizing the intimate relation between quantum phases, gauge symmetry, and charge quantization.
We analyze and compare different measures for the degree of non-Markovianity in the dynamics of open quantum systems. These measures are based on the distinguishability of quantum states which is quantified, on the one hand, by the trace distance or, more generally, by the trace norm of the Helstrom matrix, and, on the other hand, by entropic quantifiers: the Jensen-Shannon divergence, the Holevo or the quantum skew divergence. We explicitly construct a qubit dynamics for which the trace norm based non-Markovianity measure is nonzero, while all the entropic measures turn out to be zero. This l…
Entropic Dynamics (ED) is an inference-based framework that seeks to construct dynamical theories of physics without assuming the conventional formalism --- the Hamiltonians, Poisson brackets, Hilbert spaces, etc. --- typically associated with physics. In this work we develop an ED of scalar fields that is both quantum and manifestly covariant. The framework for accomplishing this is inspired by the covariant methods of Dirac, Teitelboim, and Kuchar. In addition to the ostensible result of a covariant quantum ED, we also show how the covariance requirement of path independence proposed by Teit…
