Claudia Zander

Multiqubit systems : highly entangled states and entanglement distribution

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present results are compared with those recently reported by Brown et al (J. Phys. A: Math. Gen. 2005 38 1119). The statistical distribution of entanglement values for the aforementioned multiqubit systems is also explored.

Fidelity measure and conservation of information in general probabilistic theories

We investigate the main features of a measure of fidelity between states in a general family of probabilistic theories admitting classical probability theory and standard quantum theory as particular instances. We apply the aforementioned measure to investigate information-theoretical features of these theories related to the conservation of information during the evolution of closed physical systems. In particular, we derive a generalization of a fundamental result in quantum theory relevant for the measurement problem: Zureks recent extension of the no-cloning theorem.

Entropic entanglement criteria for fermion systems

AbstractEntanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.

Some entanglement features exhibited by two, three and four qubits interacting with an environment in a non-Markovian regime

We explore various aspects of the quantum entanglement dynamics of systems of two, three and four qubits interacting with an environment at zero temperature in a non-Markovian regime, as described by the paradigmatic model recently studied by Bellomo, Lo Franco, and Compagno [Bellomo et al. Phys. Rev. Lett. 99 (2007) 160502]. We consider important families of initial states for the alluded systems. The average, typical entanglement evolution associated with each of these families is determined, and its relation with the evolution of the global degree of mixedness of the multi-qubit system is explored. For three and four qubits we consider the family of initial states equivalent under local unitary transformations to the jGHZi and jWi states, and compare their average behavior with the average behavior exhibited by initial maximally entangled twoqubits states. Furthermore, in the case of two qubits, the evolution of other manifestations of entanglement, related to measurable quantities, is also investigated. In particular, we consider the Mintert-Buchleitner concurrence lower bound and an entanglement indicator based upon the violation of local uncertainty relations.

Positive operator valued measures and the quantum Monty Hall problem

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.

Two particles in a double well: illustrating the connection between entanglement and the speed of quantum evolution

The connection between entanglement and the speed of quantum evolution (as measured by the time needed to reach an orthogonal state) is discussed in the case of two quantum particles moving in a one-dimensional double well. The aforementioned connection offers an interesting opportunity of discussing the basic features of quantum entanglement within an elementary context, using concepts and methods usually included in university courses of quantum mechanics.

Entanglement generation through particle detection in systems of identical fermions

We investigate the generation of entanglement in systems of identical fermions through a process involving particle detection, focusing on the implications that this kind of processes have for the concept of entanglement between fermionic particles. As a paradigmatic example we discuss in detail a scheme based on a splitting-plus-detection operation. This scheme generates states with accessible entanglement starting from an initial pure state of two indistinguishable fermions exhibiting correlations due purely to antisymmetrization. It is argued that the proposed extraction of entanglement does not contravene the notion that entanglement in identical-fermion systems requires correlations beyond those purely due to their indistinguishability. In point of fact, it is shown that this concept of entanglement, here referred to as {\it fermonic entanglement}, actually helps to clarify some essential aspects of the entanglement generation process. In particular, we prove that the amount of extracted accessible entanglement equals the amount of fermionic entanglement created with the detection process. The aforementioned scheme is generalized for the case of

Entanglement and the speed of evolution of two interacting qubits

N

Revisiting Entanglement within the Bohmian Approach to Quantum Mechanics

-identical fermion systems of arbitrary dimension. It transpires from our present discussion that a proper analysis of entanglement generation during the splitting-plus-detection operation is not only consistent with the concept of fermonic entanglement, but actually reinforces this concept.

Classical analogue of the statistical operator

The time needed by a quantum system to reach a state fully distinguishable from the original one provides a natural way of determining how fast the corresponding dynamical evolution is. This orthogonality time admits a lower bound, expressible in terms of the energy’s expectation value and the energy’s standard deviation, that yields a ‘quantum speed limit’. Composite quantum systems need entanglement in order to achieve this limit. So far, most studies on the connection between entanglement and the quantum speed limit have focused on the case of non-interacting systems. The connection between quantum speed and entanglement is systematically investigated here for the case of a system of two interacting qubits, taking into consideration all possible initial states that evolve into an orthogonal one.