TY - JOUR

T1 - Non-Markovian quantum control as coherent stochastic trajectories

AU - Sakuldee, Fattah

AU - Milz, Simon

AU - Pollock, Felix A.

AU - Modi, Kavan

PY - 2018/9/14

Y1 - 2018/9/14

N2 - We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as a convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes. This division of processes is analogous to separable and entangled states. In the second half of the paper, we show, with an information theoretic game, that when a process is non-Markovian, coherent trajectories allow for decoupling from the environment while preserving arbitrary quantum information encoded into the system. We give explicit expressions for the temporal correlations (quantifying non-Markovianity) and show that, in general, there are more quantum correlations than classical ones. This shows that non-Markovian quantum processes are indeed fundamentally different from their classical counterparts. Furthermore, we demonstrate how coherent trajectories (with the aid of coherent control) could turn non-Markovianity into a resource. In the final section of the paper we explore this phenomenon in a geometric picture with a convenient set of basis trajectories.

AB - We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as a convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes. This division of processes is analogous to separable and entangled states. In the second half of the paper, we show, with an information theoretic game, that when a process is non-Markovian, coherent trajectories allow for decoupling from the environment while preserving arbitrary quantum information encoded into the system. We give explicit expressions for the temporal correlations (quantifying non-Markovianity) and show that, in general, there are more quantum correlations than classical ones. This shows that non-Markovian quantum processes are indeed fundamentally different from their classical counterparts. Furthermore, we demonstrate how coherent trajectories (with the aid of coherent control) could turn non-Markovianity into a resource. In the final section of the paper we explore this phenomenon in a geometric picture with a convenient set of basis trajectories.

KW - coherent dynamics

KW - non-Markovian

KW - stochastic trajectory

UR - http://www.scopus.com/inward/record.url?scp=85049831250&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aabb1e

DO - 10.1088/1751-8121/aabb1e

M3 - Article

AN - SCOPUS:85049831250

VL - 51

JO - Journal of Physics A-Mathematical and Theoretical

JF - Journal of Physics A-Mathematical and Theoretical

SN - 1751-8113

IS - 41

M1 - 414014

ER -