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Optimization of partially isolated quantum harmonic oscillator memory systems by mean square decoherence time criteria

Igor G. Vladimirov, Ian R. Petersen

Abstract

This paper is concerned with open quantum harmonic oscillators with position-momentum system variables, whose internal dynamics and interaction with the environment are governed by linear quantum stochastic differential equations. A recently proposed approach to such systems as Heisenberg picture quantum memories exploits their ability to approximately retain initial conditions over a decoherence horizon. Using the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation of the system variables from their initial values, we apply this approach to a partially isolated subsystem of the oscillator, which is not directly affected by the external fields. The partial isolation leads to an appropriate system decomposition and a qualitatively different short-horizon asymptotic behaviour of the deviation, which yields a longer decoherence time in the high-fidelity limit. The resulting approximate decoherence time maximization over the energy parameters for improving the quantum memory performance is discussed for a coherent feedback interconnection of such systems.

Optimization of partially isolated quantum harmonic oscillator memory systems by mean square decoherence time criteria

Abstract

This paper is concerned with open quantum harmonic oscillators with position-momentum system variables, whose internal dynamics and interaction with the environment are governed by linear quantum stochastic differential equations. A recently proposed approach to such systems as Heisenberg picture quantum memories exploits their ability to approximately retain initial conditions over a decoherence horizon. Using the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation of the system variables from their initial values, we apply this approach to a partially isolated subsystem of the oscillator, which is not directly affected by the external fields. The partial isolation leads to an appropriate system decomposition and a qualitatively different short-horizon asymptotic behaviour of the deviation, which yields a longer decoherence time in the high-fidelity limit. The resulting approximate decoherence time maximization over the energy parameters for improving the quantum memory performance is discussed for a coherent feedback interconnection of such systems.
Paper Structure (6 sections, 4 theorems, 77 equations, 3 figures)

This paper contains 6 sections, 4 theorems, 77 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. QUANTUM STOCHASTIC DYNAMICS
  3. OPEN QUANTUM HARMONIC OSCILLATORS
  4. PARTIAL SUBSYSTEM ISOLATION
  5. MEAN-SQUARE MEMORY DECOHERENCE TIME
  6. MEMORY DECOHERENCE TIME MAXIMIZATION FOR OQHO INTERCONNECTION

Key Result

Lemma 1

Suppose the coupling matrix $M$ of the OQHO in (HLOQHO) satisfies Then for any $s\leqslant d$, there exists a full row rank matrix $F \in {\mathbb R}^{s\times n}$ such that the vector of $s$ time-varying self-adjoint operators on the space (fH) satisfies the ODE where $A_0$ is the matrix from (AAOQHO). $\square$

Figures (3)

  • Figure 1: An open quantum system with vectors $W$, $Y$ of input quantum Wiener processes and output fields.
  • Figure 2: A schematic representation of (\ref{['phipsi']}) as an interconnection of systems $\Phi$, $\Psi$, where $\Phi$ is affected by the external fields $W$ only through $\Psi$ which interacts with $W$.
  • Figure 3: A coherent feedback interconnection of two OQHOs, interacting with external input quantum Wiener processes $W^{(1)}$, $W^{(2)}$ and coupled to each other through a direct energy coupling (represented by a double-headed arrow) and a field-mediated coupling through the quantum Ito processes $Y^{(1)}$, $Y^{(2)}$ at the corresponding outputs.

Theorems & Definitions (8)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof