Measuring unitary invariants with the quantum switch

• URL: http://arxiv.org/abs/2508.02345v1
• Date: Mon, 04 Aug 2025 12:26:55 GMT
• Title: Measuring unitary invariants with the quantum switch
• Authors: Pedro C. Azado, Rafael Wagner, Rui S. Barbosa, Ernesto F. Galvão,
• Abstract summary: We show that the quantum switch can be used to measure Bargmann invariants of arbitrary order.<n>We also show how simple Hadamard test circuits can deterministically simulate an arbitrary unitary quantum switch.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and imaginarity, nonstabilizerness, and contextuality. We show that the quantum switch, a higher-order process featuring indefinite causal order, can be used to measure Bargmann invariants of arbitrary order. We also show how simple Hadamard test circuits can deterministically simulate an arbitrary unitary quantum switch. Our results establish a solid bridge between the theory and applications of unitary invariants and higher-order maps in quantum mechanics.

Related papers

• Multi-state imaginarity and coherence in qubit systems [3.7112567233163003]
  We provide a unitary-invariant framework to pinpoint imaginarity and coherence in sets of qubit states.<n>We also show that the set of imaginarity-free multi-states is not convex, and that third-order invariants completely characterize multi-state imaginarity of single-qubits but not of higher-dimensional systems.
  arXiv  Detail & Related papers  (2025-07-20T09:34:57Z)
• Numerical ranges of Bargmann invariants [0.32634122554914]
  We provide a rigorous determination of the numerical range of Bargmann invariants for quantum systems of arbitrary finite dimension.<n>We demonstrate that any permissible value of these invariants can be achieved using either (i) pure states exhibiting circular Gram matrix symmetry or (ii) qubit states alone.<n>These results establish fundamental limits on Bargmann invariants in quantum mechanics and provide a solid mathematical foundation for their diverse applications in quantum information processing.
  arXiv  Detail & Related papers  (2025-06-16T09:04:02Z)
• Geometry of sets of Bargmann invariants [9.999750154847826]
  We develop a unified, dimension-independent formulation that characterizes the sets of the 3rd and 4th Bargmann invariants.<n>Based on the obtained results, we conjecture that the unified, dimension-independent formulation of the boundaries for sets of 3rd-order and 4th-order Bargmann invariants may extend to the general case of the $n$th-order Bargmann invariants.
  arXiv  Detail & Related papers  (2024-12-12T08:54:11Z)
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the multimode extreme bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes.<n>Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• 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)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra [0.0]
  We propose simple quantum circuits to measure weak values, KD distributions, and spectra of density matrices without the need for post-selection. An upshot is a unified view of nonclassicality in all those tasks.
  arXiv  Detail & Related papers  (2023-02-01T19:01:25Z)
• 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)
• Measuring relational information between quantum states, and applications [0.0]
  We describe how to measure Bargmann invariants using suitable generalizations of the SWAP test. As applications, we describe basis-independent tests for linear independence, coherence, and imaginarity.
  arXiv  Detail & Related papers  (2021-09-21T07:23:12Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)

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.