Quantum geometric tensor determines the i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group

• URL: http://arxiv.org/abs/2411.04766v2
• Date: Wed, 19 Feb 2025 10:08:33 GMT
• Title: Quantum geometric tensor determines the i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• Authors: Koji Yamaguchi, Yosuke Mitsuhashi, Tomohiro Shitara, Hiroyasu Tajima,
• Abstract summary: The resource theory of asymmetry (RTA) is a resource-theoretic framework for investigating asymmetry as a resource to break constraints imposed by symmetries. We show that the quantum geometric tensor is an asymmetry monotone for pure states that determines the optimal approximate conversion rate. We also affirmatively prove the Marvian-Spekkens conjecture on reversible convertibility in RTA, which has remained unproven for a decade.
• Score: 0.0
• License:
• Abstract: Symmetry is one of the most significant foundational principles underlying nature. The resource theory of asymmetry (RTA) is a resource-theoretic framework for investigating asymmetry as a resource to break constraints imposed by symmetries. It has recently undergone significant developments, resulting in applications in a variety of research areas since symmetry and its breaking are ubiquitous in physics. Nevertheless, the resource conversion theory at the core of RTA remains incomplete. In the independent and identically distributed (i.i.d.) setup, where identical copies of a state are converted to identical copies of another state, conversion theory among pure states has been completed only for $U(1)$ group and finite groups. Here, we establish an i.i.d. conversion theory among any pure states in RTA for any continuous symmetry described by a compact Lie group, which includes the cases where multiple conserved quantities are involved. We show that the quantum geometric tensor is an asymmetry monotone for pure states that determines the optimal approximate asymptotic conversion rate. Our formulation achieves a unified understanding of conversion rates in prior studies for different symmetries. As a corollary of the formula, we also affirmatively prove the Marvian-Spekkens conjecture on reversible asymptotic convertibility in RTA, which has remained unproven for a decade.

Related papers

• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbour (between unit cells) Our invariant is invariant under unitary and similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• The i.i.d. State Convertibility in the Resource Theory of Asymmetry for Finite Groups and Lie groups [0.0]
  We show that the optimal rate of the i.i.d. state conversion with vanishingly small error is bounded by the ratio of the Fisher information matrices. These results are expected to significantly broaden the scope of the application of RTA.
  arXiv  Detail & Related papers  (2023-12-25T15:42:24Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• Operational interpretation and estimation of quantum trace-norm asymmetry based on weak value measurement and some bounds [0.0]
  An important and geometrically intuitive measure of translational asymmetry of a state is given by the trace-norm asymmetry. We show that the trace-norm asymmetry is equal to the average absolute imaginary part of the weak value of the generator of the translation group optimized over all possible orthonormal bases of the Hilbert space. We then use the link between the trace-norm asymmetry and the nonreal weak value to derive the relation between the trace-norm asymmetry with other basic concepts in quantum statistics.
  arXiv  Detail & Related papers  (2023-09-17T05:12:13Z)
• Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects [0.0]
  We consider two species of one-dimensional critical free theories coupled together via a conformal interface. They have an internal $U(1)$ global symmetry and we investigate the quantum fluctuations of the charge across the impurity. We give analytical predictions for the full counting statistics, the charged moments of the reduced density matrix and the symmetry resolved R'enyi entropies.
  arXiv  Detail & Related papers  (2023-02-16T10:49:14Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• Equivariant relative submajorization [0.0]
  We study a generalization of relative submajorization that compares pairs of positive operators on representation spaces of some fixed group. We find a sufficient condition for the existence of catalytic transformations and a characterization of an symmetric relaxation of the relation.
  arXiv  Detail & Related papers  (2021-08-30T13:13:21Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• Asymmetry-induced nonclassical correlation [1.5630592429258865]
  We establish the resource theory of asymmetry using quantum Fisher information (QFI) By defining the average Fisher information as a measure of asymmetry, it is shown that the discrepancy of bipartite global and local asymmetries naturally induces the nonclassical correlation between the subsystems.
  arXiv  Detail & Related papers  (2021-01-11T06:15:14Z)
• Topological Quantum Gravity of the Ricci Flow [62.997667081978825]
  We present a family of topological quantum gravity theories associated with the geometric theory of the Ricci flow. First, we use BRST quantization to construct a "primitive" topological Lifshitz-type theory for only the spatial metric. We extend the primitive theory by gauging foliation-preserving spacetime symmetries.
  arXiv  Detail & Related papers  (2020-10-29T06:15:30Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.