Related papers: Reconstructing quantum states from local data
The fidelity and local unitary transformation are two widely useful notions in quantum physics. We study two constrained optimization problems in terms of the maximal and minimal fidelity between two bipartite quantum states undergoing…
Quantum state tomography is the standard technique for reconstructing a quantum state from experimental data. In the regime of finite statistics, experimental data cannot give perfect information about the quantum state. A common way to…
In this article, we investigate the problem of state reconstruction of four-level quantum systems. A realistic scenario is considered with measurement results distorted by random unitary operators. Two frames which define injective…
Quantum state tomography is an essential tool for the characterization and verification of quantum states. However, as it cannot be directly applied to systems with more than a few qubits, efficient tomography of larger states on mid-sized…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…
We consider the problem of characterizing states of a multipartite quantum system from restricted, quasi-local information, with emphasis on uniquely determined pure states. By leveraging tools from dissipative quantum control theory, we…
We consider the problem of estimating the maximal energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Denoting by $E^*(p)$ the (appropriately normalized) maximal…
Neural network approaches to approximate the ground state of quantum hamiltonians require the numerical solution of a highly nonlinear optimization problem. We introduce a statistical learning approach that makes the optimization trivial by…
We propose a general methodology for efficient statistical reconstruction of a quantum state through collection and analysis of photon counting statistics. Our approach includes both strict quantitative criteria for adequacy and…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt…
Most quantum tomographic methods can only be used for one-dimensional problems. We show how to infer the quantum state of a non-relativistic N-dimensional harmonic oscillator system by simple inverse Radon transforms. The procedure is…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
Finding a local Hamiltonian $\hat{\mathcal{H}}$ having a given many-body wavefunction $|\psi\rangle$ as its ground state, i.e. a parent Hamiltonian, is a challenge of fundamental importance in quantum technologies. Here we introduce a…
The area law conjecture states that the entanglement entropy of a region of space in the ground state of a gapped, local Hamiltonian only grows like the surface area of the region. We show that, for any quantum state that fulfills an area…
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential…
Quantum entanglement entropy has a geometric character. This is illustrated by the interpretation of Rindler space or black hole entropy as entanglement entropy. In general, one can define a "geometric entropy", associated with an event…
We consider fully many-body localized systems, i.e. isolated quantum systems where all the many-body eigenstates of the Hamiltonian are localized. We define a sense in which such systems are integrable, with localized conserved operators.…
Thermal states are thermal with respect to a fixed Hamiltonian. How much information about this Hamiltonian can we ``bootstrap'' from the subsystems of a thermal state? We attack the problem by positioning it as a subspecies of the quantum…
This report concerns the inverse problem of estimating a spacially dependent coefficient of a partial differential equation from observations of the solution at the boundary. Such a problem can be formulated as an optimal control problem…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…