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For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements, since it requires a global reconstruction. Here we experimentally demonstrate a scheme that can be used to…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
We explore a previously unknown connection between two important problems in physics, i.e., quantum macroscopicity and the quantum phase transition. We devise a general and computable measure of quantum macroscopicity that can be applied to…
We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces $X$ homeomorphic to $\mathbb R^2$. Given a measure $\mu$ on such a space, we introduce $\mu$-quasiconformal maps $f:X \to \mathbb…
We review single-qubit quantum process tomography for trace-preserving and nontrace-preserving processes, and derive explicit forms of the general constraints for fitting experimental data. These forms provide additional insight into the…
We introduce a family of operations in quantum mechanics that one can regard as "universal quantum measurements" (UQMs). These measurements are applicable to all finite-dimensional quantum systems and entail the specification of only a…
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…
Two-photon absorption (TPA) is of fundamental importance in super-resolution imaging and spectroscopy. Its nonlinear character allows for the prospect of using quantum resources, such as entanglement, to improve measurement precision or to…
The tomographic description of a quantum state is formulated in an abstract infinite dimensional Hilbert space framework, the space of the Hilbert-Schmidt linear operators, with trace formula as scalar product. Resolutions of the unity,…
Recently a complete set of entropic conditions has been derived for the interconversion structure of states under quantum operations that respect a specified symmetry action, however the core structure of these conditions is still only…
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the…
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Husz\'ar and N.M.T.Houlsby, Phys.Rev.A 85,…
We experimentally demonstrate that loop state-preparation-and-measurement (SPAM) tomography is capable of detecting correlated errors in a two-qubit system. We prepare photon pairs in a state that approximates a Werner state, which may or…
Quantum process tomography (QPT), used to estimate the linear map that best describes a quantum operation, is usually performed using a priori assumptions about state preparation and measurement (SPAM), which yield a biased and inconsistent…
Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction…
We show that quantum designs characterize the general structure of the optimal approximation of the transpose map on quantum states. Based on this characterization, we propose an implementation of the approximate transpose map by a…
We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space…
Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of…
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory - the Poincar\'{e} symmetries. The most complete way of introducing the modifications is via the noncocommutative…