Optimal Fermionic Joint Measurements for Estimating Non-Commuting
Majorana Observables
- URL: http://arxiv.org/abs/2402.19349v1
- Date: Thu, 29 Feb 2024 16:56:35 GMT
- Title: Optimal Fermionic Joint Measurements for Estimating Non-Commuting
Majorana Observables
- Authors: Daniel McNulty, Susane Calegari and Micha{\l} Oszmaniec
- Abstract summary: In this work, we investigate efficient estimation strategies of fermionic observables based on a joint measurement.
By exploiting the symmetry properties of the Majorana observables, we show that the incompatibility robustness, i.e., the minimal classical noise necessary for joint measurability, relates to the spectral properties of the Sachdev-Ye-Kitaev (SYK) model.
- Score: 3.069335774032178
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: An important class of fermionic observables, relevant in tasks such as
fermionic partial tomography and estimating energy levels of chemical
Hamiltonians, are the binary measurements obtained from the product of
anti-commuting Majorana operators. In this work, we investigate efficient
estimation strategies of these observables based on a joint measurement which,
after classical post-processing, yields all sufficiently unsharp (noisy)
Majorana observables of even-degree. By exploiting the symmetry properties of
the Majorana observables, as described by the braid group, we show that the
incompatibility robustness, i.e., the minimal classical noise necessary for
joint measurability, relates to the spectral properties of the
Sachdev-Ye-Kitaev (SYK) model. In particular, we show that for an $n$ mode
fermionic system, the incompatibility robustness of all degree--$2k$ Majorana
observables satisfies $\Theta(n^{-k/2})$ for $k\leq 5$. Furthermore, we present
a joint measurement scheme achieving the asymptotically optimal noise,
implemented by a small number of fermionic Gaussian unitaries and sampling from
the set of all Majorana monomials. Our joint measurement, which can be
performed via a randomization over projective measurements, provides rigorous
performance guarantees for estimating fermionic observables comparable with
fermionic classical shadows.
Related papers
- Generalized Zeno effect and entanglement dynamics induced by fermion counting [0.0]
We study a one-dimensional lattice system of free fermions subjected to a generalized measurement process.
We find that instantaneous correlations and entanglement properties of free fermions subjected to fermion counting and local occupation measurements are strikingly similar.
arXiv Detail & Related papers (2024-06-11T19:46:26Z) - Exploring Supersymmetry: Interchangeability Between Jaynes-Cummings and Anti-Jaynes-Cummings Models [39.58317527488534]
The supersymmetric connection that exists between the Jaynes-Cummings (JC) and anti-Jaynes Cummings (AJC) models in quantum optics is unraveled.
A new method is proposed to obtain the temporal evolution of observables in the AJC model using supersymmetric techniques.
arXiv Detail & Related papers (2024-04-18T18:00:34Z) - Theory of free fermions dynamics under partial post-selected monitoring [49.1574468325115]
We derive a partial post-selected Schrdinger"o equation based on a microscopic description of continuous weak measurement.
We show that the passage to the monitored universality occurs abruptly at finite partial post-selection.
Our approach establishes a way to study MiPTs for arbitrary subsets of quantum trajectories.
arXiv Detail & Related papers (2023-12-21T16:53:42Z) - 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) - Evolution of many-body systems under ancilla quantum measurements [58.720142291102135]
We study the concept of implementing quantum measurements by coupling a many-body lattice system to an ancillary degree of freedom.
We find evidence of a disentangling-entangling measurement-induced transition as was previously observed in more abstract models.
arXiv Detail & Related papers (2023-03-13T13:06:40Z) - Estimating the concentration of chiral media with bright squeezed light [77.34726150561087]
We quantify the performance of Gaussian probes in estimating the concentration of chiral analytes.
Four-fold precision enhancement is achievable using state-of-the-art squeezing levels and intensity measurements.
arXiv Detail & Related papers (2022-08-21T17:18:10Z) - Estimating Quantum Hamiltonians via Joint Measurements of Noisy
Non-Commuting Observables [0.0]
We introduce a method for performing a single joint measurement that can be implemented locally.
We derive bounds on the number of experimental repetitions required to estimate energies up to a certain precision.
We adapt the joint measurement strategy to minimise the sample complexity when the implementation of measurements is assumed noisy.
arXiv Detail & Related papers (2022-06-17T17:42:54Z) - Margenau-Hill operator valued measures and joint measurability [0.0]
We characterize the incompatibility of spin observables of qubits, qutrits and 2-qubit systems.
Our results indicate that the measurement incompatibility of spin observables increases with Hilbert space dimension.
arXiv Detail & Related papers (2021-11-27T16:46:42Z) - A Random Matrix Perspective on Random Tensors [40.89521598604993]
We study the spectra of random matrices arising from contractions of a given random tensor.
Our technique yields a hitherto unknown characterization of the local maximum of the ML problem.
Our approach is versatile and can be extended to other models, such as asymmetric, non-Gaussian and higher-order ones.
arXiv Detail & Related papers (2021-08-02T10:42:22Z) - Characterizing incompatibility of quantum measurements via their Naimark
extensions [5.759887284136111]
We show that a set of POVMs is jointly measurable if and only if there exists a single Naimark extension.
We also outline as to how our result provides an alternate approach to quantifying the incompatibility of a general set of quantum measurements.
arXiv Detail & Related papers (2020-11-23T12:43:52Z) - Optimal covariant quantum measurements [0.0]
We discuss symmetric quantum measurements and the associated covariant observables modelled, respectively, as instruments and positive-operator-valued measures.
The emphasis of this work are the optimality properties of the measurements, namely, extremality, informational completeness, and the rank-1 property.
arXiv Detail & Related papers (2020-09-29T15:08:07Z)
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.