Related papers: Mixed-State Berry Curvature in quantum multiparame…
Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is at the core of modern physics. The Quantum Geometric Tensor (QGT) is a central physical object in this regard, encoding…
This post is the author's doctoral dissertation back in 1997. The dissertation covers following four kinds of problems: First, it studies achievable Cramer-Rao type bounds of various multi-parameter pure state models. Second, it relates…
We study and present the results of Berry connection for the topological states in quantum matter. The Berry connection plays a central role in the geometric phase and topological phenomenon in quantum many-body system. We present the…
The standard quantum mechanical electronic state calculations for molecules and solids uses the Schroedinger representation where the momentum conjugate to the coordinate $q_r$ is given by $-hbar {partial over {partial q_r}}$. This…
The local geometry of the parameter space of a quantum system is described by the quantum metric tensor and the Berry curvature, which are two fundamental objects that play a crucial role in understanding geometrical aspects of condensed…
The eigenvalues of a parameter-dependent Hamiltonian matrix form a band structure in parameter space. In such $N$-band systems, the quantum geometric tensor (QGT), consisting of the Berry curvature and quantum metric tensors, is usually…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
The quantum geometric tensor (QGT) is a fundamental concept for characterizing the local geometry of quantum states. After casting the geometry of pure quantum states and extracting the QGT, we generalize the geometry to mixed quantum…
We discuss single adaptive measurements for the estimation of mixed quantum states of qubits. The results are compared to the optimal estimation schemes using collective measurements. We also demonstrate that the advantage of collective…
We analytically investigate the non-equilibrium pumping for a double quantum dots system on the basis of the quantum master equation (QME), where the double quantum dots are connected to two external leads by the spin coupling. Each of…
We experimentally observe the quantum geometric tensor, namely the quantum metric and the Berry curvature, for a square lattice of radiatively coupled plasmonic nanoparticles. We observe a non-zero Berry curvature and show that it arises…
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…
The geometry of quantum states has profound implications in quantum multiparameter estimation. While the Riemannian structure of quantum state space is well understood, the full understanding of the curvature structure of mixed quantum…
Two representations of mixed states by state-vectors, known as purified state and thermal vacuum, have been realized on quantum computers. While the two representations look similar, they differ by a partial transposition in the ancilla…
We study a coarse-graining map arising from incomplete and imperfect addressing of particles in a multipartite quantum system. In its simplest form, corresponding to a two-qubit state, the resulting channel produces a convex mixture of the…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We present a scheme that allows integration of the Berry curvature and thus determination of the Chern number of a qubit eigenstate manifold. Our proposal continuously couples the qubit with a meter system while it explores a…
In quantum mechanics it is often required to describe in a semiclassical approximation the motion of particles moving within a given energy band. Such a representation leads to the appearance of an analogues of fictitious forces in the…