Related papers: Affine Maps of the Polarization Vector for Quantum…
Absolutely separable states $\varrho$ remain separable under arbitrary unitary transformations $U \varrho U^{\dag}$. By example of a three qubit system we show that in multipartite scenario neither full separability implies bipartite…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Convex sets of quantum states and processes play a central role in quantum theory and quantum information. Many important examples of convex sets in quantum theory are spectrahedra, that is, sets of positive operators subject to affine…
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…
We present three different matrix bases that can be used to decompose density matrices of $d$--dimensional quantum systems, so-called qudits: the \emph{generalized Gell-Mann matrix basis}, the \emph{polarization operator basis}, and the…
We demonstrate a novel experimental technique for quantum-state tomography of the collective density matrix. It is based on measurements of the polarization of light, traversing the atomic vapor. To assess the technique's robustness against…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
Non-classical joint measurements can hugely improve the efficiency with which certain figures of merit of quantum systems are measured. We use such a measurement to determine a particular figure of merit, the purity, for a polarization…
Structured optimization uses a prescribed set of atoms to assemble a solution that fits a model to data. Polarity, which extends the familiar notion of orthogonality from linear sets to general convex sets, plays a special role in a simple…
Covariant affine integral quantization of the half-plane is studied and applied to the motion of a particle on the half-line. We examine the consequences of different quantizer operators built from weight functions on the half-plane. To…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…
Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with…
The apodizing phase plate (APP) is a solid-state pupil optic that clears out a D-shaped area next to the core of the ensuing PSF. To make the APP more efficient for high-contrast imaging, its bandwidth should be as large as possible, and…
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map,…
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…
We report on the quantum storage and retrieval of photonic polarization quantum bits onto and out of a solid state storage device. The qubits are implemented with weak coherent states at the single photon level, and are stored for 500 ns in…
In this work we define the trajectory coset of an affine map and use it to study the similarity classes of affine maps. We use the trajectory coset, a tool which allows us to gain a deeper understanding of the interplay between geometry…
We show that the space of density matrices for n-qubit states, considered as a (2^n)^2 dimensional real vector space, has a basis consisting of density matrices of stabilizer states. We describe an application of this result to automated…