Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
- URL: http://arxiv.org/abs/2404.16753v2
- Date: Mon, 27 May 2024 04:59:07 GMT
- Title: Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements
- Authors: Rahul Sahay, Ruben Verresen,
- Abstract summary: We characterize the patterns of many-body entanglement that can be deterministically created from measurement.
We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability.
We find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, which leads to a no-go theorem for preparing certain quantum states.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding has been restricted to fixed-point representatives of phases of matter. Here, we go beyond this and characterize the patterns of many-body entanglement that can be deterministically created from measurement. Focusing on one spatial dimension, a framework is developed for the case where a single round of measurements is the only entangling operation. We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability, which uniquely determine the preparation protocol. We use these conditions to both classify preparable quantum states and characterize their physical constraints. In particular, we find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, which leads to a no-go theorem for preparing certain quantum states. More broadly, we connect properties of the preparation protocol to the resulting phase of matter, including trivial, symmetry-breaking, and symmetry-protected topological phases -- for both uniform and modulated symmetries. This work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices.
Related papers
- Entanglement measurement based on convex hull properties [0.0]
We will propose a scheme for measuring quantum entanglement, which starts with treating the set of quantum separable states as a convex hull of quantum separable pure states.
Although a large amount of data is required in the measurement process, this method is not only applicable to 2-qubit quantum states, but also a entanglement measurement method that can be applied to any dimension and any fragment.
arXiv Detail & Related papers (2024-11-08T08:03:35Z) - Learning to Classify Quantum Phases of Matter with a Few Measurements [41.94295877935867]
We study the identification of quantum phases of matter, at zero temperature, when only part of the phase diagram is known in advance.
We show how to use our previous knowledge to construct an observable capable of classifying the phase even in the unknown region.
An important application of our findings is the classification of the phases of matter obtained in quantum simulators.
arXiv Detail & Related papers (2024-09-08T18:52:34Z) - Classification of joint quantum measurements based on entanglement cost of localization [42.72938925647165]
We propose a systematic classification of joint measurements based on entanglement cost.
We show how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.
arXiv Detail & Related papers (2024-08-01T18:00:01Z) - Finite-Depth Preparation of Tensor Network States from Measurement [0.0]
We explore criteria on the local tensors for enabling deterministic state preparation via a single round of measurements.
We use these criteria to construct families of measurement-preparable states in one and two dimensions.
Our protocol even allows one to engineer preparable quantum states with a range of desired correlation lengths and entanglement properties.
arXiv Detail & Related papers (2024-04-26T00:37:00Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
arXiv Detail & Related papers (2023-10-04T09:51:00Z) - Quantifying measurement-induced quantum-to-classical crossover using an
open-system entanglement measure [49.1574468325115]
We study the entanglement of a single particle under continuous measurements.
We find that the entanglement at intermediate time scales shows the same qualitative behavior as a function of the measurement strength.
arXiv Detail & Related papers (2023-04-06T09:45:11Z) - Decoding Measurement-Prepared Quantum Phases and Transitions: from Ising
model to gauge theory, and beyond [3.079076817894202]
Measurements allow efficient preparation of interesting quantum many-body states with long-range entanglement.
We demonstrate that the so-called conformal quantum critical points can be obtained by performing general single-site measurements.
arXiv Detail & Related papers (2022-08-24T17:59:58Z) - Quantum coherence with incomplete set of pointers and corresponding
wave-particle duality [0.0]
Quantum coherence quantifies the amount of superposition in a quantum system.
We develop the corresponding resource theory, identifying the free states and operations.
We obtain a complementarity relation between the so-defined quantum coherence and the which-path information in an interferometric set-up.
arXiv Detail & Related papers (2021-08-12T16:55:40Z) - Observing a Topological Transition in Weak-Measurement-Induced Geometric
Phases [55.41644538483948]
Weak measurements in particular, through their back-action on the system, may enable various levels of coherent control.
We measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength.
Our results open new horizons for measurement-enabled quantum control of many-body topological states.
arXiv Detail & Related papers (2021-02-10T19:00:00Z) - Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations.
We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
arXiv Detail & Related papers (2020-03-04T14:01:17Z)
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.