Related papers: Trace identities and their semiclassical implicati…
Applying new computing paradigms like quantum computing to the field of machine learning has recently gained attention. However, as high-dimensional real-world applications are not yet feasible to be solved using purely quantum hardware,…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We derive a relationship between two different notions of fidelity (entanglement fidelity and average fidelity) for a completely depolarizing quantum channel. This relationship gives rise to a quantum analog of the MacWilliams identities in…
Non-classical correlations can be regarded as resources for quantum information processing. However, the classification problem of non-classical correlations for quantum states remains a challenge, even for finite-size systems. Although…
We show that in principle, $N$-partite unitary transformations can be perfectly discriminated under local measurement and classical communication (LOCC) despite of their nonlocal properties. Based on this result, some related topics,…
We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neutral direction (this is a semiclassical limit), the spectrum…
It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we…
There has been growing interest in recent years in Q-matrix based cognitive diagnosis models. Parameter estimation and respondent classification under these models may suffer due to identifiability issues. Non-identifiability can be…
We formulate semi-classical field theory as an approximate decoherence-free-subspace of a finite-dimensional quantum-gravity hilbert space. A complementarity construction can be realized as a unitary transformation which changes the…
Many machine learning techniques incorporate identity-preserving transformations into their models to generalize their performance to previously unseen data. These transformations are typically selected from a set of functions that are…
Semiclassical Mechanics allows for a description of quantum systems which preserves their phase information, while using only the system's classical dynamics as an input. Over the time an identification has been developed between stationary…
I examine spectral properties of a dissipative chaotic quantum map with the help of a recently discovered semiclassical trace formula. I show that in the presence of a small amount of dissipation the traces of any finite power of the…
We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the…
A general semiclassical approach to quantum systems with system-bath interactions is developed. We study system decoherence in detail using a coherent state semiclassical wavepacket method which avoids singularity issues arising in the…
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an…