Related papers: Random unitary maps for quantum state reconstructi…
We analyse the reconstruction of an unknown pure qubit state. We derive the optimal guess that can be inferred from any set of measurements on N identical copies of the system with the fidelity as a figure of merit. We study in detail the…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
Spatial qudit states can be realized by using multi-slits to discretize the transverse momentum of a photon. The merit of this kind of spatial qudit states is that the implementation of higher dimensional qudits is relatively easy. As we…
Motivated by recent quantum gas microscope experiments for fermions in optical lattices, we present proof of principle calculations showing that it is possible to obtain the complete information about the quantum state on a small subsystem…
Neutral atom systems are an appealing platform for the development and testing of quantum control and measurement techniques. This dissertation presents experimental investigations of control and measurement tools using as a testbed the…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We present strategies how to reconstruct (estimate) properties of a quantum channel described by the map E based on incomplete measurements. In a particular case of a qubit channel a complete reconstruction of the map E can be performed via…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
To certify that an experimentally implemented quantum transformation is a certain unitary operation U on a d-dimensional Hilbert space, it suffices to determine fidelities of output states for d+1 suitably chosen pure input states [Reich et…
We propose a quantum algorithm that emulates the action of an unknown unitary transformation on a given input state, using multiple copies of some unknown sample input states of the unitary and their corresponding output states. The…
The techniques of low-rank matrix recovery were adapted for Quantum State Tomography (QST) previously by D. Gross et al. [Phys. Rev. Lett. 105, 150401 (2010)], where they consider the tomography of $n$ spin-$1/2$ systems. For the density…
We present a formalism for self-calibrating tomography of arbitrary dimensional systems. Self-calibrating quantum state tomography was first introduced in the context of qubits, and allows the reconstruction of the density matrix of an…
It has been recently shown that a state generated by a one-dimensional noisy quantum computer is well approximated by a matrix product operator with a finite bond dimension independent of the number of qubits. We show that full quantum…
We study the ability to implement unitary maps on states of the $I=9/2$ nuclear spin in \textsuperscript{87}Sr, a $d=10$ dimensional (qudecimal) Hilbert space, using quantum optimal control. Through a combination of nuclear spin-resonance…
A state in a d-dimensional Hilbert space can be simulated by a state defined in a different dimension with high fidelity. We assess how faithfully such the approximated state can perform quantum protocols, using an example of the squeezed…
We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
For any finite dimensional Hilbert space, we construct explicitly five orthonormal bases such that the corresponding measurements allow for efficient tomography of an arbitrary pure quantum state. This means that such measurements can be…
The efficient quantum state reconstruction algorithm described in [P. Six et al., Phys. Rev. A 93, 012109 (2016)] is experimentally implemented on the non-local state of two microwave cavities entangled by a circular Rydberg atom. We use…
We find quantum signatures of classical chaos in various metrics of information gain in quantum tomography. We employ a quantum state estimator based on weak collective measurements of an ensemble of identically prepared systems. The…