In the Entropic Dynamics (ED) approach the essence of quantum theory lies in its probabilistic nature while the Hilbert space structure plays a secondary and ultimately optional role. The dynamics of probability distributions is driven by the maximization of an entropy subject to constraints that carry the relevant physical information -- directionality, correlations, gauge interactions, etc. The challenge is to identify those constraints and to establish a criterion for how the constraints themselves are updated. In this paper the ED framework is extended to describe a spin-1/2 point particle. In ED spin is neither modelled as a rotating body, nor through the motion of a point particle; it is an epistemic property of the wave function. The constraint that reflects the peculiar rotational properties of spin is most effectively expressed in the language of geometric algebra. The updating of all constraints is carried out in a way that stresses the central importance of symmetry principles. First we identify the appropriate symplectic and metric structures in the phase space of probabilities, their conjugate momenta, and the spin variables. This construction yields a derivation of the Fubini-Study metric for a spin-1/2 particle which highlights its deep connection to information geometry. Then we construct an ED that preserves both the symplectic structure (a Hamiltonian flow) and the metric structure (a Killing flow). We show that generic Hamiltonian-Killing flows are linear in the wave function. Imposing further that the Hamiltonian be the generator of an entropic evolution in time leads to an entropic dynamics described by the Pauli equation. We conclude with a discussion of the new interpretation of the formalism which yields a physical picture that is significantly different from that provided by other interpretations.
The information-theoretic formulation of quantum measurement uncertainty relations (MURs), based on the notion of relative entropy between measurement probabilities, is extended to the set of all the spin components for a generic spin s. For an approximate measurement of a spin vector, which gives approximate joint measurements of the spin components, we define the device information loss as the maximum loss of information per observable occurring in approximating the ideal incompatible components with the joint measurement at hand. By optimizing on the measuring device, we define the notion o…
Macrorealism from entropic Leggett-Garg inequalities
我们制定熵Leggett-Garg不等式，其中放置的约束的时间相关性的观测的统计结果。如果宏观实在论成立，则信息论不等式成立。我们发现，量子转子的时间分离的自旋分量之间的相关性的量子统计模拟的自旋相关性在两个空间分离的自旋$s$粒子共享一个状态的零总自旋。这导致了熵Leggett-Garg不等式被旋转量子自旋$s$系统以类似于熵贝尔不等式的方式破坏（Phys. Rev. Lett. 61，662（1988））通过形成复合自旋单重态的一对自旋- $s$粒子来实现。
The uncertainty principle is one of the key concepts in quantum theory. This principle states that it is not possible to measure two incompatible observables simultaneously and accurately. In quantum information theory, the uncertainty principle is formulated using the concept of entropy. In this work we consider the entropic uncertainty relation in the presence of quantum memory. We study the dynamics of entropic uncertainty bound for a two-qubit quantum system coupled to a spin chain with Dzyaloshinskii-Moriya interaction and we investigate the effect of environmental parameters on the entro…
We consider information characteristics of single qudit state (spin j=9/2), such as von Neumann entropy, von Neumann mutual information. We review different mathematical properties of these information characteristics: subadditivity and strong subadditivity conditions, Araki-Lieb inequality. The inequalities are entropic inequalities for composite systems (bipartite, tripartite), but they can be written for noncomposite systems. Using the density matrix, describing the noncomposite qudit system state in explicit matrix form we proved new entropic inequalities for single qudit state (spin j=9/2…
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…
We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behav…
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…
Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements
量子测量中噪声和干扰的信息论定义在Phys. Rev. Lett. 112，050401（2014），并且获得了与状态无关的噪声-扰动不确定性关系。在这里，我们推导出一个紧密的噪声干扰的互补量子比特可观测量的不确定性关系，并进行了实验测试。对中子自旋为1/2的系统进行了连续的投影测量，并进行了减少干扰的校正。我们的实验结果饱和时，应用最佳的校正程序的量子比特的紧噪声干扰不确定性关系。
A tight information-theoretic measurement uncertainty relation is experimentally tested with neutron spin-1/2 qubits. The noise associated to the measurement of an observable is defined via conditional Shannon entropies and a tradeoff relation between the noises for two arbitrary spin observables is demonstrated. The optimal bound of this tradeoff is experimentally obtained for various non-commuting spin observables. For some of these observables this lower bound can be reached with projective measurements, but we observe that, in other cases, the tradeoff is only saturated by general quantum …
In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the trace-distance or Bures-distance revivals between distinct evolved system states have been shown to be subordinated to the establishment of system-environment correlations or changes in the environmental state. We show that this interpretation can be substantiated also for a class of entropic quantifiers. We exploit a suitably regularized version of Umegaki'…
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.
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.
Entropic uncertainty and entanglement are two distinct aspects of quantum mechanical procedures. To estimate entropic uncertainty relations, entropies are used: the greater the entropy bound, the less effective the quantum operations and entanglement are. In this regard, we analyze the entropic uncertainty, entropic uncertainty lower bound, and concurrence dynamics in two non-interacting qubits. The exposure of two qubits is studied in two different qubit-noise configurations, namely, common qubit-noise and independent qubit-noise interactions. To include the noisy effects of the local externa…
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…
Perimeter Institute for Theoretical Physics（佩里曼理论物理研究所）；Department of Mathematics and Statistics, Dalhousie University（达尔豪斯大学数学与统计系）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）
Spin-outcome correlations and memory-assisted entropic uncertainty in Bhabha scattering with an entangled spectator
State Key Laboratory of Opto-Electronic Information Acquisition and Protection Technology, School of Physics, Anhui University（安徽大学光电信息获取与保护技术国家重点实验室物理学院）
We introduce an entropic quantity for two-dimensional (2D) quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator algebra defined on an annular region, which encodes the superselection sectors of the model. The quantity is calculable from local properties, and it is invariant under any constant-depth local quantum circuit, and thus an indicator of gapped quantum spin-liquids. We explicitly calculate the quantity for Kitaev's quantum double models, and show that the val…
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…
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…
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-differentia…
Entropic Dynamics (ED) is a framework for constructing dynamical theories of inference using the tools of inductive reasoning. A central feature of the ED framework is the special focus placed on time. In previous work a global entropic time was used to derive a quantum theory of relativistic scalar fields. This theory, however, suffered from a lack of explicit or manifest Lorentz symmetry. In this paper we explore an alternative formulation in which the relativistic aspects of the theory are manifest. The approach we pursue here is inspired by the works of Dirac, Kuchar, and Teitelboim in the…
Entropic dynamics (ED) is a general framework for constructing indeterministic dynamical models based on entropic methods. ED has been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in a dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference the dynamics is dictated by information encode…
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…
In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical information. In previous work, a manifestly covariant ED of quantum scalar fields in a fixed background spacetime was developed. Manifest relativistic covariance was achieved by imposing constraints in the form of Poisson brackets and of intial conditions to be satisfied by a set of local Hamiltonian generators. Our approach succeeded in extending to the quant…
Entanglement dynamics and position-momentum entropic uncertainty relation of a $Λ$-type three-level atom interacting with a two-mode cavity field in the presence of nonlinearities
Heisenberg uncertainty principle describes a basic restriction on observer's ability of precisely predicting the measurement for a pair of non-commuting observables, and virtually is at the core of quantum mechanics. We herein aim to study entropic uncertainty relation under the background of the Schwarzschild black hole and its control. Explicitly, we develop dynamical features of the measuring uncertainty via entropy in a practical model where a stationary particle interacts with its surrounding environment while another particle --- serving as a quantum memory reservoir --- undergoes freefa…
We study a driven, spin-orbit coupled fermionic system in a lattice at the resonant regime where the drive frequency equals the Hubbard repulsion, for which non-trivial constrained dynamics emerge at fast timescales. An effective density-dependent tunneling model is derived, and examined in the sparse filling regime in 1D. The system exhibits entropic self-localization, where while even numbers of atoms propagate ballistically, odd numbers form localized bound states induced by an effective attraction from a higher configurational entropy. These phenomena occur in the strong coupling limit whe…
