The reference system and not completely positive open quantum dynamics

Open quantum dynamics in a tripartite scenario including a system, its environment and a passive reference is shown to resolve several open questions regarding not completely positive (NCP) dynamical maps as valid descriptions of open quantum evolution. The steering states of the system and the environment with respect to the reference, reduced down to a dense, compact set of states of the system alone, provides a well defined domain of action for a bonafide dynamical map describing the open evolution of the system. The map is not restricted to being completely positive (CP) but it preserves the positivity of all states in its domain. NCP open dynamics corresponding to different initial configurations of the tripartite system are explored.Comment: 9 pages, 4 figure

Quantum Critical Environment Assisted Quantum Magnetometer

A central qubit coupled to an Ising ring of $N$ qubits, operating close to a critical point is investigated as a potential precision quantum magnetometer for estimating an applied transverse magnetic field. We compute the Quantum Fisher information for the central, probe qubit with the Ising chain initialized in its ground state or in a thermal state. The non-unitary evolution of the central qubit due to its interaction with the surrounding Ising ring enhances the accuracy of the magnetic field measurement. Near the critical point of the ring, Heisenberg-like scaling of the precision in estimating the magnetic field is obtained when the ring is initialized in its ground state. However, for finite temperatures, the Heisenberg scaling is limited to lower ranges of $N$ values.Comment: 10 pages, 9 figure

The two-qubit amplitude damping channel: characterization using quantum stabilizer codes

A protocol based on quantum error correction based characterization of quantum dynamics (QECCD) is developed for quantum process tomography on a two-qubit system interacting dissipatively with a vacuum bath. The method uses a 5-qubit quantum error correcting code that corrects arbitrary errors on the first two qubits, and also saturates the quantum Hamming bound. The dissipative interaction with a vacuum bath allows for both correlated and independent noise on the two-qubit system. We study the dependence of the degree of the correlation of the noise on evolution time and inter-qubit separation.Comment: 13 pages, 5 figure