Complexity of Bose-Einstein condensates at finite temperature
- URL: http://arxiv.org/abs/2503.13979v1
- Date: Tue, 18 Mar 2025 07:28:16 GMT
- Title: Complexity of Bose-Einstein condensates at finite temperature
- Authors: Chang-Yan Wang,
- Abstract summary: We investigate the geometric quantum complexity of Bose-Einstein condensate (BEC) at finite temperature.<n>We use the Bures and Sj"oqvist metrics -- generalizations of the Fubini-Study metric for mixed quantum states.<n>In the Nielsen complexity approach, we rigorously handle the gauge freedoms associated with mixed state purification and non-uniqueness unitary operations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-sa/4.0/
- Abstract: We investigate the geometric quantum complexity of Bose-Einstein condensate (BEC) at finite temperature. Specifically, we use the Bures and Sj\"oqvist metrics -- generalizations of the Fubini-Study metric for mixed quantum states, as well as the Nielsen geometric complexity approach based on purification of mixed states. Starting from the Bogoliubov Hamiltonian of BEC, which exhibits an $SU(1,1)$ symmetry, we explicitly derive and compare the complexities arising from these three distinct measures. For the Bures and Sj\"oqvist metrics, analytical and numerical evaluations of the corresponding geodesics are provided, revealing characteristic scaling behaviors with respect to temperature. In the Nielsen complexity approach, we rigorously handle the gauge freedoms associated with mixed state purification and non-uniqueness unitary operations, demonstrating that the resulting complexity aligns precisely with the Bures metric. Our work provides a compara
Related papers
- Symmetry breaking in chaotic many-body quantum systems at finite temperature [0.0]
Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described.
We build upon this result to investigate the universal symmetry-breaking properties of such eigenstates.
arXiv Detail & Related papers (2025-04-08T15:41:54Z) - Reducing the sampling complexity of energy estimation in quantum many-body systems using empirical variance information [45.18582668677648]
We consider the problem of estimating the energy of a quantum state preparation for a given Hamiltonian in Pauli decomposition.<n>We construct an adaptive estimator using the state's actual variance.
arXiv Detail & Related papers (2025-02-03T19:00:01Z) - Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
arXiv Detail & Related papers (2025-02-03T15:57:50Z) - Hilbert space geometry and quantum chaos [39.58317527488534]
We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians.
We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
arXiv Detail & Related papers (2024-11-18T19:00:17Z) - Third quantization with Hartree approximation for open-system bosonic transport [49.1574468325115]
We present a self-consistent formalism for solving the open-system bosonic Lindblad equation with weak interactions in the steady state.<n>The method allows us to characterize and predict large-system behavior of quantum transport in interacting bosonic systems relevant to cold-atom experiments.
arXiv Detail & Related papers (2024-08-23T15:50:48Z) - Geometric aspects of mixed quantum states inside the Bloch sphere [0.0]
We discuss the differences between the Bures and the Sj"oqvist metrics inside a Bloch sphere.
We show that the relative ranking based on the concept of finite distance among mixed quantum states is not preserved when comparing distances determined with the Bures and the Sj"oqvist metrics.
arXiv Detail & Related papers (2023-12-04T16:25:31Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [43.80709028066351]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.<n>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) - Comparing metrics for mixed quantum states: Sjoqvist and Bures [3.3873470587012893]
We discuss the relation between the Sjoqvist metric and the Bures metric for arbitrary nondegenerate mixed quantum states.
We show the difference between these two metrics in the case of a simple physical system characterized by a spin-qubit in an arbitrarily oriented uniform.
arXiv Detail & Related papers (2023-03-03T03:08:04Z) - Complexity of Pure and Mixed Qubit Geodesic Paths on Curved Manifolds [0.0]
We propose an information geometric theoretical construct to describe and understand the complex behavior of evolutions of quantum systems in pure and mixed states.
We analytically show that the evolution of mixed quantum states in the Bloch ball is more complex than the evolution of pure states on the Bloch sphere.
arXiv Detail & Related papers (2022-09-21T21:11:31Z) - Full counting statistics of interacting lattice gases after an
expansion: The role of the condensate depletion in the many-body coherence [55.41644538483948]
We study the full counting statistics (FCS) of quantum gases in samples of thousands of interacting bosons.
FCS reveals the many-body coherence from which we characterize iconic states of interacting lattice bosons.
arXiv Detail & Related papers (2022-07-28T13:21:57Z) - Geometry of quantum complexity [0.0]
Computational complexity is a new quantum information concept that may play an important role in holography.
We consider quantum computational complexity for $n$ qubits using Nielsen's geometrical approach.
arXiv Detail & Related papers (2020-11-15T18:41:19Z)
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.