Christoph Spengler

Entanglement detection via mutually unbiased bases

We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases (MUBs) for the detection of entanglement in arbitrarily high-dimensional quantum systems. It is shown that their properties can be exploited to construct entanglement criteria which are experimentally implementable with few local measurement settings. The introduced concepts are not restricted to bipartite finite-dimensional systems, but are also applicable to continuous variables and multipartite systems. This is demonstrated by two examples – the two-mode squeezed state and the Aharonov state. In addition, and more importantly from a theoretical point of view, we find a link between the separability problem and the maximum number of mutually unbiased bases.

A composite parameterization of unitary groups, density matrices and subspaces

Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In this paper we present a parameterization of the unitary group of arbitrary dimension d which is constructed in a composite way. We show explicitly how any element of can be composed of matrix exponential functions of generalized anti-symmetric ?-matrices and one-dimensional projectors. The specific form makes it considerably easy to identify and discard redundant parameters in several cases. In this way, redundancy-free density matrices of arbitrary rank k can be formulated. Our construction can also be used to derive an orthonormal basis of any k-dimensional subspaces of with the minimal number of parameters. As an example it is shown that this feature leads to a significant reduction of parameters in the case of investigating distillability of quantum states via lower bounds of an entanglement measure (the m-concurrence).

Lorentz invariance of entanglement classes in multipartite systems

We analyze multipartite entanglement in systems of spin-½ particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which contributes to a physical understanding of entanglement classification. We show that quantum information in a relativistic setting requires the partition of the Hilbert space into particles to be taken seriously. Furthermore, we study exemplary cases and show how the spin and momentum entanglement transforms relativistically in a multipartite setting.

Composite parameterization and Haar measure for all unitary and special unitary groups

We adopt the concept of the composite parameterization of the unitary group U(d) to the special unitary group SU(d). Furthermore, we also consider the Haar measure in terms of the introduced parameters. We show that the well-defined structure of the parameterization leads to a concise formula for the normalized Haar measure on U(d) and SU(d). With regard to possible applications of our results, we consider the computation of high-order integrals over unitary groups.

Examining the dimensionality of genuine multipartite entanglement

Entanglement in high-dimensional many-body systems plays an increasingly vital role in the foundations and applications of quantum physics. In the present paper, we introduce a theoretical concept which allows to categorize multipartite states by the number of degrees of freedom being entangled. In this regard, we derive computable and experimentally friendly criteria for arbitrary multipartite qudit systems that enable to examine in how many degrees of freedom a mixed state is genuine multipartite entangled.

Graph-state formalism for mutually unbiased bases

A pair of orthonormal bases is called mutually unbiased if all mutual overlaps between any element of one basis with an arbitrary element of the other basis coincide. In case the dimension,

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

d

Measure of genuine multipartite entanglement with computable lower bounds

, of the considered Hilbert space is a power of a prime number, complete sets of

A geometric comparison of entanglement and quantum nonlocality in discrete systems

d+1

Experimentally implementable criteria revealing substructures of genuine multipartite entanglement

mutually unbiased bases (MUBs) exist. Here, we present a novel method based on the graph-state formalism to construct such sets of MUBs. We show that for