Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Influence of Noninertial Dynamics on Static Quantum Resource Theories

Saveetha Harikrishnan, Tim Byrnes, Chandrashekar Radhakrishnan

TL;DR

The paper presents a CPTP-map formulation of noninertial dynamics, showing that the Unruh effect acts as a bosonic amplifier channel for multipartite systems. Using Stinespring dilation, it links inertial quantum resource theories to their noninertial evolution and analyzes how free states, free operations, and resource quantifiers transform. It introduces NRNG resource theories, demonstrates that free-state geometry is preserved when the noninertial map is free, and proves that convex monotones, robustness-based, and contractive distance-based quantifiers remain valid under noninertial motion. The work provides a practical open-system framework for relativistic quantum information tasks and outlines extensions to curved spacetime.

Abstract

The effect of noninertial dynamics on static quantum resource theories is investigated. To this end, we first show the equivalence between noninertial effects and a completely positive, trace-preserving (CPTP) map. In this formulation, the Unruh effect is equivalent to a bosonic amplifier channel. The effect of this map on a generic quantum resource is investigated by studying the role of the CPTP map on the three core ingredients of a resource theory, namely, the free states, the free operations and the resource quantifiers. We show several general statements can be made about these three components of a resource theory in the presence of noninertial motion.

Influence of Noninertial Dynamics on Static Quantum Resource Theories

TL;DR

The paper presents a CPTP-map formulation of noninertial dynamics, showing that the Unruh effect acts as a bosonic amplifier channel for multipartite systems. Using Stinespring dilation, it links inertial quantum resource theories to their noninertial evolution and analyzes how free states, free operations, and resource quantifiers transform. It introduces NRNG resource theories, demonstrates that free-state geometry is preserved when the noninertial map is free, and proves that convex monotones, robustness-based, and contractive distance-based quantifiers remain valid under noninertial motion. The work provides a practical open-system framework for relativistic quantum information tasks and outlines extensions to curved spacetime.

Abstract

The effect of noninertial dynamics on static quantum resource theories is investigated. To this end, we first show the equivalence between noninertial effects and a completely positive, trace-preserving (CPTP) map. In this formulation, the Unruh effect is equivalent to a bosonic amplifier channel. The effect of this map on a generic quantum resource is investigated by studying the role of the CPTP map on the three core ingredients of a resource theory, namely, the free states, the free operations and the resource quantifiers. We show several general statements can be made about these three components of a resource theory in the presence of noninertial motion.
Paper Structure (22 sections, 9 theorems, 76 equations, 2 figures)

This paper contains 22 sections, 9 theorems, 76 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Relativistic dynamics of bosonic modes
  3. Noisy quantum channels
  4. Noninertial dynamics as a CPTP map
  5. Kraus operator
  6. Properties of the Map
  7. Linearity
  8. Trace preserving
  9. Positive map
  10. Completely Positive
  11. Summary
  12. Effect on quantum resource theories
  13. Quantum resource theories
  14. Stinespring dilation
  15. Free states under noninertial motion
  16. ...and 7 more sections

Key Result

Theorem 1

For a $N$-partite system in which $M$ subsystems are under non-inertial motion, the Unruh effect can be represented by a CPTP map given by and $\rho'$ is the state where all $N$ parties are in inertial motion. Here, the Kraus operator $A_{k}$ is given by where $\mathcal{I}$ is the identity operator which acts on the sector of $N-M$ inertial qudits and ${\mathcal{A}}_{k}$ is the operator acting o

Figures (2)

  • Figure 1: Minkowski space represented by the $(z,t)$ plane is divided into four regions of Rindler coordinates. In this figure, $H$ denotes the horizon. The future $F$ and past $P$ event horizons are represented by solid lines and the accelerated observers path are represented by the dashed lines.
  • Figure 2: Relationship between the operator spaces and free states under inertial and noninertial motion. The top left corresponds to the operator space $\mathcal{D}(\mathcal{H}_{\mathcal{M}})$ for the system under inertial motion. Within it are the free states $\mathcal{F}_{\mathcal{M}}$. Under Stinespring dilation, the operator space expands to $\mathcal{D}( \mathcal{H}_{R})$. Tracing out Rindler mode II results in the operator space for Rindler mode I $\mathcal{D}(\mathcal{H}_{\mathrm I})$ with its associated free state $\mathcal{F}_{\mathrm I}$. We show the case where $\mathcal{E}$ is a free operation of the resource theory (NRNG map), such that the mapped free states $\mathcal{E}( \mathcal{F}_{\mathcal{M}})$ are within $\mathcal{F}_{\mathrm I}$.

Theorems & Definitions (19)

  • Theorem 1
  • proof
  • Definition 1: Noninertial Resource Nongenerating (NRNG)
  • Theorem 2: Free operations under noninertial motion
  • proof
  • Theorem 3: Geometry of free states under noninertial maps
  • proof
  • Theorem 4: Composition with relativistic evolution
  • proof
  • Theorem 5: Convex mixtures after embedding
  • ...and 9 more