相关论文: Real-space RG, error correction and Petz map
We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it…
The equilibrium transport properties of an elementary nanostructured device with side-coupled geometry are computed and related to universal functions. The computation relies on a real-space formulation of the numerical…
Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical…
In this paper, we discuss the quantum data processing inequality and its refinements that are physically meaningful in the context of approximate recoverability. An important conjecture regarding this due to Seshadreesan et. al. in J. Phys.…
We present a recently-developed renormalization group scheme, the functional renormalization group (fRG), as a many-particle method suited to account for the two-particle interactions between the electrons in complex quantum dot geometries.…
The scaled relative graph (SRG) of an operator is a subset of the complex plane. It captures several salient features of an operator, such as contractiveness, and can be used to reveal the geometric nature of many of the inequality based…
We investigate the precision of the numerical implementation of the functional renormalization group based on extracting the eigenvalues from the linearized RG transformation. For this purpose, we implement the LPA and $O(\partial^2)$…
The relationship between mappings of sets and renormalization group transformations is established, and renormalization group invariants of such mappings are found. These results are valid both for continuous and discrete mappings and for…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of…
The key idea behind the renormalization group (RG) transformation is that properties of physical systems with very different microscopic makeups can be characterized by a few universal parameters. However, finding the optimal RG…
The parity operator $\cal P$ and time reversal operator $\cal T$ are two important operators in the quantum theory, in particular, in the $\cal PT$-symmetric quantum theory. By using the concrete forms of $\cal P$ and $\cal T$, we discuss…
For a noisy quantum channel, a quantum error correcting code exists if and only if the joint higher rank numerical ranges associated with the error operators of the channel is non-empty. In this paper, geometric properties of the joint…
For a diagonalizable linear operator $H:\mathscr{H}\to\mathscr{H}$ acting in a separable Hilbert space $\mathscr{H}$, i.e., an operator with a purely point spectrum, eigenvalues with finite algebraic multiplicities, and a set of…
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification in a relatively small set of…
We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller…
Trace inequalities are general techniques with many applications in quantum information theory, often replacing classical functional calculus in noncommutative settings. The physics of quantum field theory and holography, however, motivate…
The reconstruction of the state of a multipartite quantum mechanical system represents a fundamental task in quantum information science. At its most basic, it concerns a state of a bipartite quantum system whose subsystems are subjected to…
We develop a novel real-space renormalization group (RG) scheme which accurately estimates correlation length exponent $\nu$ near criticality of higher-dimensional quantum Ising and Potts models in a transverse field. Our method is…