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New Trends in Mathematical and Theoretical Physics
October 6, 2016 13:00–13:20, Moscow, MIAN, Gubkina, 8

An example of quantum system control with coherent feed-back

Viktoryia Dubravina

Lomonosov Moscow State University
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Viktoryia Dubravina
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Abstract: There exist two specific ways of quantum system control, namely, the one described by Schrodinger equation and the one, described the reduce of state as a result of some quantum measurement. The case when no measurements acquire that can destroy coherence is said to be quantum control with coherent feed-back or coherent quantum control, otherwise it is said to be non-coherent case.
A quantum system consisting of one free electron is taken as en example. A pure state of such system can be described by en element of the space $H = L_2(\mathbb{R}^3) \times \mathbb{C}^2,$ and the mixed state is represented by a linear trace-class positively-defined self-adjoint operator from $L_1(H)$ with unitary trace. Let its spin originally has a known pure state $A \in H.$ This means that upon a measurement the state projection on some fixed direction $h_A \in \mathbb{R}^3$ equals $1$ with full probability. As a result of this quantum system control we would like to obtain the electron with spin in pure state $B,$ such that upon a measurement the state projection on orthogonal to $h_A\in \mathbb{R}^3$ direction $h_B$ equals $1$ with full probability.
The example of control under consideration exploits Stern–Gerlach experiment concept. We pose a cascade of magnetic fields so that every proceeding cascade element partially effects the system state. For large enough number for magnetic fields investigated construction provides quantum system state close enough to desired one.

Language: English

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