Related papers: Computing complexity measures for quantum states b…
If the system is known to be in one of two non-orthogonal quantum states, $|\psi_1\rangle$ or $|\psi_2\rangle$, $\mathcal{PT}$-symmetric quantum mechanics can discriminate them, \textit{in principle}, by a single measurement. We extend this…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
Understanding the mechanisms responsible for the equilibration of isolated quantum many-body systems is a long-standing open problem. In this work we obtain a statistical relationship between the equilibration properties of Hamiltonians and…
A central challenge in quantum simulation is to prepare low-energy states of strongly interacting many-body systems. In this work, we study the problem of preparing a quantum state that optimizes a random all-to-all, sparse or dense, spin…
A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to…
Single-qubit thermometry presents the simplest tool to measure the temperature of thermal baths with reduced invasivity. At thermal equilibrium, the temperature uncertainty is linked to the heat capacity of the qubit, however the best…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The detection of multipartite entanglement in arbitrary dimensional systems is investigated. We derive useful $k$-separability criteria of mixed $n$-partite ($n\geq 3$) quantum states to detect $k$-nonseparable $n$-partite quantum states.…
We study the complexity of computational problems from quantum physics. Typically, they are studied using the complexity class QMA (quantum counterpart of NP) but some natural computational problems appear to be slightly harder than QMA. We…
When it comes to discriminating between two quantum states, trace distance is one of the well-known metrics used in quantum computation and quantum information theory. While there are several quantum algorithms for calculating the trace…
Motivated by the Kronecker product approximation technique, we have developed a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix. For any…
In this paper, we examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum state tomography. We find that, in some important circumstances, an elaborate…
The minimal memory required to model a given stochastic process - known as the statistical complexity - is a widely adopted quantifier of structure in complexity science. Here, we ask if quantum mechanics can fundamentally change the…
An equilibrium state can be represented by a pure quantum state, which we call a thermal pure quantum (TPQ) state. We propose a new TPQ state and a simple method of obtaining it. A single realization of the TPQ state suffices for…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
We consider the task of approximating the ground state energy of two-local quantum Hamiltonians on bounded-degree graphs. Most existing algorithms optimize the energy over the set of product states. Here we describe a family of shallow…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
This thesis aims to establish notions of symmetry for quantum states and channels as well as describe algorithms to test for these properties on quantum computers. Ideally, the work will serve as a self-contained overview of the subject. We…
The complexity of the quantum state of a multiparticle system and the maximum possible accuracy of its quantum description are connected by a relation similar to the coordinate-momentum uncertainty relation. The coefficient in this relation…
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For…