Optimal tracking for pairs of qubit states

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.Comment: 15 pages, 8 figures. Extensive revision of text, optimality results extended, other physical applications include

Entanglement universality of two-qubit X-states

We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states.Comment: 24 pages, 6 figures. v2 includes new references and minor changes (accepted version

Heuristic for estimation of multiqubit genuine multipartite entanglement

For every N-qubit density matrix written in the computational basis, an associated "X-density matrix" can be obtained by vanishing all entries out of the main- and anti-diagonals. It is very simple to compute the genuine multipartite (GM) concurrence of this associated N-qubit X-state, which, moreover, lower bounds the GM-concurrence of the original (non-X) state. In this paper, we rely on these facts to introduce and benchmark a heuristic for estimating the GM-concurrence of an arbitrary multiqubit mixed state. By explicitly considering two classes of mixed states, we illustrate that our estimates are usually very close to the standard lower bound on the GM-concurrence, being significantly easier to compute. In addition, while evaluating the performance of our proposed heuristic, we provide the first characterization of GM-entanglement in the steady states of the driven Dicke model at zero temperature.Comment: 19 pages, 5 figure

Further Characterization of the Mitigation of Radiation Lethality by Protective Wounding

There continues to be a major effort in the United States to develop mitigators for the treatment of mass casualties that received high-intensity acute ionizing radiation exposures from the detonation of an improvised nuclear device during a radiological terrorist attack. The ideal countermeasure should be effective when administered after exposure, and over a wide range of absorbed doses. We have previously shown that the administration of a subcutaneous incision of a defined length, if administered within minutes after irradiation, protected young adult female C57BL/6 mice against radiation-induced lethality, and increased survival after total-body exposure to an LD50/30 X-ray dose from 50% to over 90%. We refer to this approach as "protective wounding". In this article, we report on our efforts to further optimize, characterize and demonstrate the validity of the protective wounding response by comparing the response of female and male mice, varying the radiation dose, the size of the wound, and the timing of wounding with respect to administration of the radiation dose. Both male and female mice that received a subcutaneous incision after irradiation were significantly protected from radiation lethality. We observed that the extent of protection against lethality after an LD50/30 X-ray dose was independent of the size of the subcutaneous cut, and that a 3 mm subcutaneous incision is effective at enhancing the survival of mice exposed to a broad range of radiation doses (LD15-LD100). Over the range of 6.2-6.7 Gy, the increase in survival observed in mice that received an incision was associated with an enhanced recovery of hematopoiesis. The enhanced rate of recovery of hematopoiesis was preceded by an increase in the production of a select group of cytokines. Thus, a thorough knowledge of the timing of the cytokine cascade after wounding could aid in the development of novel pharmacological radiation countermeasures that can be administered several days after the actual radiation exposure

The Relationship Between Lower Extremity Functional Strength and Aerobic Performance in Youth with Cerebral Palsy (CP)

Please refer to the pdf version of the abstract located adjacent to the title