The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing

• URL: http://arxiv.org/abs/2001.04440v1
• Date: Mon, 13 Jan 2020 18:20:53 GMT
• Title: The quantum marginal problem for symmetric states: applications to variational optimization, nonlocality and self-testing
• Authors: Albert Aloy, Matteo Fadel, Jordi Tura
• Abstract summary: We present a method to solve the quantum marginal problem for symmetric $d$-level systems. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present a method to solve the quantum marginal problem for symmetric $d$-level systems. The method is built upon an efficient semi-definite program that determines the compatibility conditions of an $m$-body reduced density with a global $n$-body density matrix supported on the symmetric space. We illustrate the applicability of the method in central quantum information problems with several exemplary case studies. Namely, (i) a fast variational ansatz to optimize local Hamiltonians over symmetric states, (ii) a method to optimize symmetric, few-body Bell operators over symmetric states and (iii) a set of sufficient conditions to determine which symmetric states cannot be self-tested from few-body observables. As a by-product of our findings, we also provide a generic, analytical correspondence between arbitrary superpositions of $n$-qubit Dicke states and translationally-invariant diagonal matrix product states of bond dimension $n$.

Related papers

• Solving the homogeneous Bethe-Salpeter equation with a quantum annealer [34.173566188833156]
  The homogeneous Bethe-Salpeter equation (hBSE) was solved for the first time by using a D-Wave quantum annealer. A broad numerical analysis of the proposed algorithms was carried out using both the proprietary simulated-anneaing package and the D-Wave Advantage 4.1 system.
  arXiv  Detail & Related papers  (2024-06-26T18:12:53Z)
• Symmetry enforced entanglement in maximally mixed states [3.5602863178766966]
  Entanglement in quantum many-body systems is typically fragile to interactions with the environment. We analyze the entanglement and correlations of the maximally mixed state in the invariant sector. For all Abelian symmetries, the MMIS is separable, and for all non-Abelian symmetries, the MMIS is entangled.
  arXiv  Detail & Related papers  (2024-06-12T18:00:00Z)
• Dimension matters: precision and incompatibility in multi-parameter quantum estimation models [44.99833362998488]
  We study the role of probe dimension in determining the bounds of precision in quantum estimation problems. We also critically examine the performance of the so-called incompatibility (AI) in characterizing the difference between the Holevo-Cram'er-Rao bound and the Symmetric Logarithmic Derivative (SLD) one.
  arXiv  Detail & Related papers  (2024-03-11T18:59:56Z)
• Multipartite entanglement in the diagonal symmetric subspace [41.94295877935867]
  For diagonal symmetric states, we show that there is no bound entanglement for $d = 3,4 $ and $N = 3$. We present a constructive algorithm to map multipartite diagonal symmetric states of qudits onto bipartite symmetric states of larger local dimension.
  arXiv  Detail & Related papers  (2024-03-08T12:06:16Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• 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)
• Tapping into Permutation Symmetry for Improved Detection of k-Symmetric Extensions [3.501108734684888]
  In this study, we introduce an approach that adeptly leverages permutation symmetry. By fine-tuning the SDP problem for detecting ( k )-symmetric extensions, our method markedly diminishes the searching space dimensionality. This leads to an algorithmic enhancement, reducing the complexity from ( O(d2k) ) to ( O(kd2) ) in the qudit ( k )-symmetric extension scenario.
  arXiv  Detail & Related papers  (2023-09-08T06:05:56Z)
• Towards Antisymmetric Neural Ansatz Separation [48.80300074254758]
  We study separations between two fundamental models of antisymmetric functions, that is, functions $f$ of the form $f(x_sigma(1), ldots, x_sigma(N)) These arise in the context of quantum chemistry, and are the basic modeling tool for wavefunctions of Fermionic systems.
  arXiv  Detail & Related papers  (2022-08-05T16:35:24Z)
• $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks [107.86545461433616]
  We propose permutation-equivariant architectures, on which a determinant Slater is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
  arXiv  Detail & Related papers  (2022-05-26T07:44:54Z)
• Noncommutative polynomial optimization under symmetry [0.0]
  We present a general framework to exploit the symmetries present in the Navascu'es-Pironio-Ac'in semidefinite relaxations. We put equal emphasis on the moment and sum-of-squares dual approaches.
  arXiv  Detail & Related papers  (2021-12-20T19:02:16Z)
• Discriminating an Arbitrary Number of Pure Quantum States by the Combined $\mathcal{CPT}$ and Hermitian Measurements [1.840931826951159]
  It's possible to distinguish an arbitrary number of pure quantum states by an appropriate choice of the parameters of $mathcalPT$-symmetric Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-16T17:05:50Z)

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.