Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Reversing quantum dynamics with near-optimal quantum and classical fidelity

H. Barnum, E. Knill

TL;DR

This work addresses reversing quantum dynamics under known noise to preserve entanglement or classical correlations with a reference, introducing a near-optimal reversal $\mathcal{R}_{\mathcal{A},\rho}$ that depends on the noise map and the input state. A central result proves the reversal error is at most twice the optimum for both quantum and classical information, and the reversal connects to the pretty good measurement, yielding computable bounds on fidelities such as $F_e$ and $F_{cl}$. The framework applies to finite-dimensional systems and offers practical implications for quantum algorithms, error correction, and information transmission by providing a robust decoding tool under prescribed noise. These insights enable principled comparisons between the near-optimal reversal and simpler decoding strategies, with potential impact on quantum information processing tasks and query complexity analyses.

Abstract

We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the ``noise'' dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.

Reversing quantum dynamics with near-optimal quantum and classical fidelity

TL;DR

This work addresses reversing quantum dynamics under known noise to preserve entanglement or classical correlations with a reference, introducing a near-optimal reversal that depends on the noise map and the input state. A central result proves the reversal error is at most twice the optimum for both quantum and classical information, and the reversal connects to the pretty good measurement, yielding computable bounds on fidelities such as and . The framework applies to finite-dimensional systems and offers practical implications for quantum algorithms, error correction, and information transmission by providing a robust decoding tool under prescribed noise. These insights enable principled comparisons between the near-optimal reversal and simpler decoding strategies, with potential impact on quantum information processing tasks and query complexity analyses.

Abstract

We consider the problem of reversing quantum dynamics, with the goal of preserving an initial state's quantum entanglement or classical correlation with a reference system. We exhibit an approximate reversal operation, adapted to the initial density operator and the ``noise'' dynamics to be reversed. We show that its error in preserving either quantum or classical information is no more than twice that of the optimal reversal operation. Applications to quantum algorithms and information transmission are discussed.

Paper Structure

This paper contains 7 sections, 6 theorems, 31 equations.

Table of Contents

  1. Introduction
  2. Quantum noise operations
  3. Quantifying the effects of noise
  4. The reversal operation
  5. Relationship to the "pretty good measurement"
  6. A bound on the classical fidelity of reversal
  7. Examples and applications

Key Result

Lemma 1

The definition of the reversal operation $\mathcal{R}(\mathcal{A},\rho)$ is independent of the decomposition $\{A_{i}\}_{i}$ of $\mathcal{A}$.

Theorems & Definitions (10)

  • Lemma 1
  • proof
  • Proposition 2
  • Theorem 3
  • proof
  • Corollary 4
  • Theorem 5
  • proof
  • Lemma 6
  • proof