Beatrix C. Hiesmayr

Detection of High-Dimensional Genuine Multipartite Entanglement of Mixed States

We derive a general framework to identify genuinely multipartite entangled mixed quantum states in arbitrary-dimensional systems and show in exemplary cases that the constructed criteria are stronger than those previously known. Our criteria are simple functions of the given quantum state and detect genuine multipartite entanglement that had not been identified so far. They are experimentally accessible without quantum state tomography and are easily computable as no optimization or eigenvalue evaluation is needed.

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.

Relativistic entanglement of two massive particles

We describe the spin and momentum degrees of freedom of a system of two massive spin--

Violation of a Bell inequality in particle physics experimentally verified

\tfrac{1}{2}

Decoherence of entangled kaons and its connection to entanglement measures

particles as a 4 qubit system. Then we explicitly show how the entanglement changes between different partitions of the qubits, when considered by different inertial observers. Although the two particle entanglement corresponding to a partition into Alices and Bobs subsystems is, as often stated in the literature, invariant under Lorentz boosts, the entanglement with respect to other partitions of the Hilbert space on the other hand, is not. It certainly does depend on the chosen inertial frame and on the initial state considered. The change of entanglement arises, because a Lorentz boost on the momenta of the particles causes a Wigner rotation of the spin, which in certain cases entangles the spin- with the momentum states. We systematically investigate the situation for different classes of initial spin states and different partitions of the 4 qubit space. Furthermore, we study the behavior of Bell inequalities for different observers and demonstrate how the maximally possible degree of violation, using the Pauli-Lubanski spin observable, can be recovered by any inertial observer.

Bell inequality and CP violation in the neutral kaon system

Relevant aspects for testing Bell inequalities with entangled meson–antimeson systems are analyzed. In particular, we argue that the results of Go [J. Mod. Opt. 51 (2004) 991], which nicely illustrate the quantum entanglement of B-meson pairs, cannot be considered as a Bell-test refuting local realism.

Optimal entanglement witnesses for qubits and qutrits

We study the time evolution of the entangled kaon system by considering the Liouville-von Neumann equation with an additional term which allows for decoherence. We choose, as generators of decoherence, the projectors to the two-particle eigenstates of the Hamiltonian. Then we compare this model with the data of the CPLEAR experiment and find in this way an upper bound on strength {lambda} of the decoherence. We also relate {lambda} to an effective decoherence parameter {zeta} considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e., von Neumann entropy S, entanglement of formation E, and concurrence C, and we relate decoherence parameter {zeta} to the loss of entanglement: 1-E.

A composite parameterization of unitary groups, density matrices and subspaces

Abstract For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furrys hypothesis.

Quantum marking and quantum erasure for neutral kaons

We study the connection between the Hilbert-Schmidt measure of entanglement (that is the minimal distance of an entangled state to the set of separable states) and entanglement witness in terms of a generalized Bell inequality which distinguishes between entangled and separable states. A method for checking the nearest separable state to a given entangled one is presented. We illustrate the general results by considering isotropic states, in particular two-qubit and two-qutrit states--and their generalizations to arbitrary dimensions--where we calculate the optimal entanglement witnesses explicitly.

Quantitative complementarity in two-path interferometry

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).