Lech Jakóbczyk

Geometry of Bloch vectors in two-qubit system

Abstract We study two-dimensional sections of a set of Bloch vectors corresponding to density matrices of two-qubit system.

Quantum interference and evolution of entanglement in a system of three-level atoms

We consider a pair of three-level atoms interacting with the vacuum. The process of disentanglement due to spontaneous emission and the role of quantum interference between principal transitions in this process, are analyzed. We show that the presence of interference can slow down disentanglement. In the limit of maximal interference, some part of initial entanglement can survive.

Noise-induced finite-time disentanglement in two-atomic system

We discuss the influence of a noisy environment on entangled states of two atoms and show that all such states disentangle in finite time.

Entanglement and nonlocality versus spontaneous emission in two-atom systems

Abstract We study evolution of entanglement of two two-level atoms in the presence of dissipation caused by spontaneous emission. We find explicit formulas for the amount of entanglement as a function of time, in the case of destruction of the initial entanglement and possible creation of a transient entanglement between atoms. We also discuss how spontaneous emission influences nonlocality of states expressed by violation of Bell–CHSH inequality. It is shown that evolving system very quickly becomes local, even if entanglement is still present or produced.

Entanglement versus entropy for a class of mixed two-qutrit states

We compute the measure of entanglement for some classes of states belonging to the simplex of Bell-diagonal states of two qutrits introduced by Baumgartner et al. [Phys. Rev. A 74, 032327 (2006)]. We discuss also partial characterization of that simplex in terms of negativity and linear entropy. A numerical exploration of the entropy-entanglement plane indicates that, in the analogy to the two-qubit case [Munro et al., Phys. Rev. A 64, 030302(R) (2001)], two-qutrit Werner states do not maximize entanglement for a given entropy.

Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane

We characterize violation of CHSH inequalities for mixed two-qubit states by their mixedness and entanglement. The class of states that have maximum degree of CHSH violation for a given linear entropy is also constructed.

Canonical quantization with indefinite inner product

Abstract In this paper an algebraic approach to canonical quantization on indefinite inner product space is presented. Concrete realization of such a quantization of a given classical system described by a symplectic space ( M , σ) is obtained by means of a so-called J ∗ -representation of CCR algebra Δ( M , σ). So-called Fock-Krein representations of Δ( M , σ) determined by some class of complex structures on ( M , σ) are studied in detail. It is shown that every Fock-Krein representation is unbounded. Starting with a fixed Fock-Krein representation of CCR sectors of non-Fock-Krein representations are constructed.

Reconstruction of Kubo–Martin–Schwinger structure from Euclidean Green functions

The explicit form of the Poisson kernel for the strip Tβ={z∈C:0<Im z<β} is used to derive some conditions for a state ω on a given C*‐algebra dynamical system (A,αt) to be a Kubo–Martin–Schwinger (KMS) state. Reflection positivity and generalized periodicity of the Euclidean Green functions corresponding to ω are established and used for an analytic continuation to real time. Reflection positivity is also used for the construction of a cyclic and faithful representation of (A,αt) on some Hilbert space. A sufficient condition for the identification of the constructed dynamics with the modular group of a von Neumann algebra generated by the representation is formulated in terms of the Euclidean Green functions.

Vacuum-induced stationary entanglement in radiatively coupled three-level atoms

We consider a pair of three-level atoms interacting with a common vacuum and analyse the process of entanglement production due to spontaneous emission. We show that in the case of closely separated atoms collective damping can generate robust entanglement of the asymptotic states.

Measures of entanglement based on decoherence

New measures of entanglement - the time of disentanglement and the rate of decoherence - of states of a compound system are proposed. They are based on the dynamical properties of the system induced by the measurement-like interaction with an environment. In particular, it is shown that in the case of two qubits the time of disentanglement may serve as a practical measure of entanglement of mixed states.