Most incompatible measurements and sum-of-squares optimisation

• URL: http://arxiv.org/abs/2509.10381v1
• Date: Fri, 12 Sep 2025 16:14:59 GMT
• Title: Most incompatible measurements and sum-of-squares optimisation
• Authors: Sébastien Designolle,
• Abstract summary: Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource.<n>We show analytical universal parent measurements giving access to bounds that beat the state of the art.<n>Results find direct application for demonstrating genuine high-dimensional steering.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Measurement incompatibility, or joint measurability, is a cornerstone of quantum theory and a useful resource. For finite-dimensional systems, quantifying this resource and establishing universal bounds valid for all measurements is a long-standing problem. In this work, we exhibit analytical universal parent measurements giving access to bounds that beat the state of the art. In particular, we can show that, for relevant robustnesses, sets of anticommuting observables give rise to the most incompatible dichotomic measurements. We also formalise the construction of such universal parent measurements in the framework of sum-of-squares optimisation and obtain preliminary numerical results demonstrating the power of the method by improving on our own analytical values. All results find direct application for demonstrating genuine high-dimensional steering, that is, certifying the dimensionality of a quantum system in a one-sided device-independent manner.

Related papers

• 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)
• Effect of the readout efficiency of quantum measurement on the system entanglement [44.99833362998488]
  We quantify the entanglement for a particle on a 1d quantum random walk under inefficient monitoring. We find that the system's maximal mean entanglement at the measurement-induced quantum-to-classical crossover is in different ways by the measurement strength and inefficiency.
  arXiv  Detail & Related papers  (2024-02-29T18:10:05Z)
• The signaling dimension in generalized probabilistic theories [48.99818550820575]
  The signaling dimension of a given physical system quantifies the minimum dimension of a classical system required to reproduce all input/output correlations of the given system. We show that it suffices to consider extremal measurements with rayextremal effects, and we bound the number of elements of any such measurement in terms of the linear dimension. For systems with a finite number of extremal effects, we recast the problem of characterizing the extremal measurements with ray-extremal effects.
  arXiv  Detail & Related papers  (2023-11-22T02:09:16Z)
• 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)
• High-dimensional monitoring and the emergence of realism via multiple observers [41.94295877935867]
  Correlation is the basic mechanism of every measurement model.<n>We introduce a model that interpolates between weak and strong non-selective measurements for qudits.
  arXiv  Detail & Related papers  (2023-05-13T13:42:19Z)
• 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)
• High-dimensional entanglement certification: bounding relative entropy of entanglement in $2d+1$ experiment-friendly measurements [77.34726150561087]
  Entanglement -- the coherent correlations between parties in a quantum system -- is well-understood and quantifiable. Despite the utility of such systems, methods for quantifying high-dimensional entanglement are more limited and experimentally challenging. We present a novel certification method whose measurement requirements scale linearly with dimension subsystem.
  arXiv  Detail & Related papers  (2022-10-19T16:52:21Z)
• Naimark dilations of qubit POVMs and joint measurements [0.0]
  Measurement incompatibility is one of the cornerstones of quantum theory. numerical methods can decide any finite-dimensional and discrete joint measurability problem. Here, we take a complementary approach by asking which measurements are compatible with a given measurement.
  arXiv  Detail & Related papers  (2022-08-29T13:29:04Z)
• Equivalence between simulability of high-dimensional measurements and high-dimensional steering [0.0]
  The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. We show that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement.
  arXiv  Detail & Related papers  (2022-07-08T18:11:53Z)
• Quantifying coherence of quantum measurements [0.0]
  We show that any statistical distance can be adopted to define a coherence monotone of measurement. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components.
  arXiv  Detail & Related papers  (2020-08-10T09:57:28Z)
• Generalized Sliced Distances for Probability Distributions [47.543990188697734]
  We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs) GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation. We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
  arXiv  Detail & Related papers  (2020-02-28T04:18:00Z)

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.