Quantum control theory for state transformations: Dark states and their enlightenment

Abstract

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasizes that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterized in terms of the underlying graph properties.

Basics of perfect communication through quantum networks

“…Our first observation is a consequence of the study in [24]. For real Hamiltonians, constrained to a bipartite coupling graph (which also imposes that B n = 0), the transfer phase e iφ is ±1 if the transfer distance is even and ±i if the transfer distance is odd.…”

Capacitively coupled double quantum dot system in the Kondo regime

“…The dark state ε 2 acts like a switch between the two regimes and may have applications in quantum computation. 54,56 For example, when the first discontinuity occurs, for V g /U ≈ −0.5, QD1 is in a Kondo state, however, a further decrease of V g makes it energetically more favorable for QD1 to be in an IV state, which can be accomplished by charging QD2 (by exactly one electron), this, due to the capacitive coupling, increases the effective gate potential of QD1, discharging it, and bringing it back to the IV regime. 57 As V g /U further decreases below −0.5, QD1 starts to transition from an IV to a Kondo state; when V g /U ≈ −1, again the IV state for QD1 is more favorable; this regime can now be achieved by completely avoiding the Kondo regime through the discontinuous charging of QD1 by one extra electron.…”

Characterization and control of quantum spin chains and rings

“…For example, the operation of swapping spins k and N +2−k commutes both with H 0 and H C and is therefore a symmetry. There are two further symmetries and the Lie algebra dimension is only 17, and numerical test of the optimization show that the attainable fidelity is limited, consistent with the dynamical constraints imposed by the symmetries and dark states [5].…”