arXiv subjects
Publications and source records attributed to Beatrix C. Hiesmayr.
Using a recently introduced framework, we derive criteria for quantum k-separability, which are very easily computed. In the case k = 2, our criteria are equally strong to the best methods known so far, while in all other cases there are currently no comparable criteria known. We also show how the criteria can be implemented experimentally.
To determine whether a given multipartite quantum state is separable with respect to some partition we construct a family of entanglement measures R_m. This is done utilizing generalized concurrences as building blocks which are defined by flipping of M constituents and indicate states that are separable with regard to bipartitions when vanishing. Further, we provide an analytically computable lower bound for R_m via a simple ordering relation of the convex roof extension. Using the derived lower bound, we illustrate the effect of the isotropic noise on a family of four-qubit mixed states for each intermediate separability.
We present two sets of computable entanglement measures for multipartite systems where each subsystem can have different degrees of freedom (so-called qudits). One set, called 'separability' measure, reveals which of the subsystems are separable/entangled. For that we have to extend the concept of k-separability for multipartite systems to a novel unambiguous separability concept which we call γ_k-separability. The second set of entanglement measures reveals the 'kind' of entanglement, i.e. if it is bipartite, tripartite, ..., n-partite entangled and is denoted as the 'physical' measure. We show how lower bounds on both sets of measures can be obtained by the observation that any entropy may be rewritten via operational expressions known as m-concurrences. Moreover, for different classes of bipartite or multipartite qudit systems we compute the bounds explicitly and discover that they are often tight or equivalent to positive partial transposition (PPT).
Via a multidimensional complementarity relation we derive a novel operational entanglement measure for any discrete quantum system, i.e. for any multidimensional and multipartite system. This new measure admits a separation into different classes of entanglement obtained by using a flip operator 2,3,...,n times, defining a m-flip concurrence. For mixed states bounds on this m-flip concurrence can be obtained. Moreover, the information content of a n partite multidimensional system admits an intuitive interpretation. Explicitly, the three qubits system is analyzed and the physical difference in entanglement of the W-state, the GHZ state or the bi-separable state is revealed.
We test Bohr's complementary relation, which captures the most counterintuitive difference of a classical and a quantum world, for single and bipartite neutral kaons. They present a system that is naturally interfering, oscillating and decaying. Moreover, kaons break the CP symmetry (C...charge conjugation, P...parity). In detail we discuss the effect of the CP violation on Bohr's relation, i.e. the effect on the "particle-like" information and the "wave-like" information. Further we show that the quantity that complements the single partite information for bipartite kaons is indeed concurrence, a measure of entanglement, strengthening our concept of entanglement. We find that the defined entanglement measure is independent of CP violation while it has been shown that nonlocality is sensitive to CP violation.
We show that the relation between nonlocality and entanglement is subtler than one naively expects. In order to do this we consider the neutral kaon system--which is oscillating in time (particle--antiparticle mixing) and decaying--and describe it as an open quantum system. We consider a Bell--CHSH inequality and show a novel violation for non--maximally entangled states. Considering the change of purity and entanglement in time we find that, despite the fact that only two degrees of freedom at a certain time can be measured, the neutral kaon system does not behave like a bipartite qubit system.
The nonlocal property of quantum mechanics can be nicely tested in high energy physics; in particular, the neutral kaon pairs as produced at DA$Φ$NE, Frascati, are very well suited. The analogies of kaons as compared to polarized photons or spin--1/2 particles --the kaonic qubit feature-- are reviewed. However, there are also fundamental differences which occur due to the kaon time evolution and due to internal symmetries; in particular, the violation of CP symmetry is related to the violation of Bell inequalities. Two type of Bell inequalities for kaons are presented, one for the variation of the ``quasi--spin'' and the other for different detection times of the kaon.
We investigate the state space of bipartite qutrits. For states which are locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for bipartite qubits--a magic simplex W. This is obtained via the Weyl group which is a kind of ``quantization'' of classical phase space. We analyze how this simplex W is embedded in the whole state space of two qutrits and discuss symmetries and equivalences inside the simplex W. Because we are explicitly able to construct optimal entanglement witnesses we obtain the border between separable and entangled states. With our method we find also the total area of bound entangled states of the parameter subspace under intervestigation. Our considerations can also be applied to higher dimensions.
We consider translationally invariant states of an infinite one dimensional chain of qubits or spin-1/2 particles. We maximize the entanglement shared by nearest neighbours via a variational approach based on finitely correlated states. We find an upper bound of nearest neighbour concurrence equal to C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a completely different procedure. The obtained state maximizing nearest neighbour entanglement seems to approximate the maximally entangled mixed states (MEMS). Further we investigate in detail several other properties of the so obtained optimal state.
We consider an open quantum system which contains unstable states. The time evolution of the system can be described by an effective non-hermitian Hamiltonian H_{eff}, in accord with the Wigner--Weisskopf approximation, and an additional term of the Lindblad form, the socalled dissipator. We show that, after enlarging the original Hilbert space by states which represent the decay products of the unstable states, the non-hermitian part of H_{eff} --the ``particle decay''-- can be incorporated into the dissipator of the enlarged space via a specific Lindblad operator. Thus the new formulation of the time evolution on the enlarged space has a hermitian Hamiltonian and is probability conserving. The equivalence of the new formulation with the original one demonstrates that the time evolution which is governed by a non-hermitian Hamiltonian and a dissipator of the Lindblad form is nevertheless completely positive, just as systems with hermitian Hamiltonians.
Quantum mechanics can also be tested in high energy physics; in particular, the neutral kaon system is very well suited. We show that these massive particles can be considered as qubits --kaonic qubits-- in the very same way as spin-1/2 particles or polarized photons. But they also have other important properties, namely they are instable particles and they violate the CP symmetry (C...charge conjugation, P...parity). We consider a Bell inequality and, surprisingly, the premises of local realistic theories require strict CP conservation, in contradiction to experiment. Furthermore we investigate Bohr's complementary relation in order to describe the physics of the time evolution of kaons. Finally, we discuss quantum marking and eraser experiments with kaons, which prove in a new way the very concept of a quantum eraser.
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 2-qubit and 2-qutrit states -- and their generalizations to arbitrary dimensions -- where we calculate the optimal entanglement witnesses explicitly.
We establish correspondence between macroscopic thermodynamical quantities and complementarity in wave interference. The well known visibility and predictability in a double slit--like experiment are shown to be connected to magnetic susceptibility and magnetization of a general interacting spin chain. This gives us the ability to analyze the tradeoff between thermodynamical quantities in the same information--theoretic way that is used in analyzing the wave--particle duality. We thus obtain new physical insights into usually complicated thermodynamical models, such as viewing a phase transition simply as a change from an effective single slit diffraction to a double slit interference.
The influence of the geometric phase, in particular the Berry phase, on an entangled spin-1/2 system is studied. We discuss in detail the case, where the geometric phase is generated only by one part of the Hilbert space. We are able to cancel the effects of the dynamical phase by using the ``spin-echo'' method. We analyze how the Berry phase affects the Bell angles and the maximal violation of a Bell inequality. Furthermore we suggest an experimental realization of our setup within neutron interferometry.
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 2-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 the strength $λ$ of the decoherence. We also relate $λ$ to an effective decoherence parameter $ζ$ considered previously in literature. Finally we discuss our model in the light of different measures of entanglement, i.e. the von Neumann entropy $S$, the entanglement of formation $E$ and the concurrence $C$, and we relate the decoherence parameter $ζ$ to the loss of entanglement: $1 - E$.
We investigate Bell inequalities for neutral kaon systems from Phi resonance decay to test local realism versus quantum mechanics. We emphasize the unitary time evolution of the states, that means we also include all decay product states, in contrast to other authors. Only this guarantees the use of the complete Hilbert space. We develop a general formalism for Bell inequalities including both arbitrary "quasi spin" states and different times; finally we analyze Wigner-type inequalities. They contain an additional term, a correction function h, as compared to the spin 1/2 or photon case, which changes considerably the possibility of quantum mechanics to violate the Bell inequality. Examples for special "quasi spin" states are given, especially those which are sensitive to the CP parameters epsilon and epsilon'.