Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors

• URL: http://arxiv.org/abs/2403.19440v1
• Date: Thu, 28 Mar 2024 14:10:48 GMT
• Title: Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors
• Authors: Kin-ya Oda, Naoya Ogawa,
• Abstract summary: We show that our joint measurement smoothly interpolates between the projective measurements of position and momentum. We obtain the Lee-Tsutsui (LT) error and the refined Lee error for the position-momentum measurement.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty principle, in line with the universal framework of error, disturbance, and their uncertainty relations developed by Lee and Tsutsui. We show that our joint measurement in the Gaussian phase space, being a Positive Operator-Valued Measure (POVM) measurement, smoothly interpolates between the projective measurements of position and momentum. We, for the first time, have obtained the Lee-Tsutsui (LT) error and the refined Lee error for the position-momentum measurement. We find that the LT uncertainty relation becomes trivial, $0=0$, in the limiting case of projective measurement of either position or momentum. Remarkably, in contrast to the LT relation, the refined Lee uncertainty relation, which assesses errors for local representability, provides a constant lower bound unaffected by these limits and is invariably saturated, for a pure Gaussian initial state. The obtained lower bound is in agreement with Heisenberg's value.

Related papers

• Experimental investigation of the uncertainty relation in pre- and postselected systems [28.111582622994597]
  Uncertainty principle is one of the fundamental principles of quantum mechanics. We experimentally investigate the Robertson-Heisenberg-type uncertainty relation for two incompatible observables in a PPS system.
  arXiv  Detail & Related papers  (2024-12-18T00:29:23Z)
• Measurement incompatibility is strictly stronger than disturbance [44.99833362998488]
  Heisenberg argued that measurements irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. This article shows that measurement incompatibility is indeed a sufficient condition for irreversibility of measurement disturbance. However, we exhibit a toy theory, termed the minimal classical theory (MCT), that is a counterexample for the converse implication.
  arXiv  Detail & Related papers  (2023-05-26T13:47:00Z)
• Model-Based Uncertainty in Value Functions [89.31922008981735]
  We focus on characterizing the variance over values induced by a distribution over MDPs. Previous work upper bounds the posterior variance over values by solving a so-called uncertainty Bellman equation. We propose a new uncertainty Bellman equation whose solution converges to the true posterior variance over values.
  arXiv  Detail & Related papers  (2023-02-24T09:18:27Z)
• Tight Exponential Analysis for Smoothing the Max-Relative Entropy and for Quantum Privacy Amplification [56.61325554836984]
  The max-relative entropy together with its smoothed version is a basic tool in quantum information theory. We derive the exact exponent for the decay of the small modification of the quantum state in smoothing the max-relative entropy based on purified distance.
  arXiv  Detail & Related papers  (2021-11-01T16:35:41Z)
• Enhanced nonlinear quantum metrology with weakly coupled solitons and particle losses [58.720142291102135]
  We offer an interferometric procedure for phase parameters estimation at the Heisenberg (up to 1/N) and super-Heisenberg scaling levels. The heart of our setup is the novel soliton Josephson Junction (SJJ) system providing the formation of the quantum probe. We illustrate that such states are close to the optimal ones even with moderate losses.
  arXiv  Detail & Related papers  (2021-08-07T09:29:23Z)
• Linear simultaneous measurements of position and momentum with minimum error-trade-off in each minimum uncertainty state [0.0]
  Heisenberg's uncertainty relations are the most famous of them but are not universally valid and violated in general. We show that an error-trade-off relation (ETR), called the Branciard-Ozawa ETR, for simultaneous measurements of position and momentum gives the achievable bound in minimum uncertainty states.
  arXiv  Detail & Related papers  (2021-01-15T15:26:14Z)
• Linear position measurements with minimum error-disturbance in each minimum uncertainty state [0.0]
  We construct position measurements with minimum error-disturbance in each minimum uncertainty state. We show the theorem that gives a necessary and sufficient condition for a linear position measurement to achieve its lower bound in a minimum uncertainty state. It is expected to construct measurements with minimum error-disturbance in a broader class of states in the future.
  arXiv  Detail & Related papers  (2020-12-23T14:36:19Z)
• Incorporating Heisenberg's Uncertainty Principle into Quantum Multiparameter Estimation [0.44237366129994526]
  We find a correspondence relationship between the inaccuracy of a measurement for estimating the unknown parameter with the measurement error. For pure quantum states, this tradeoff relation is tight, so it can reveal the true quantum limits on individual estimation errors. We show that our approach can be readily used to derive the tradeoff between the errors of jointly estimating the phase shift and phase diffusion.
  arXiv  Detail & Related papers  (2020-08-20T10:56:45Z)
• Towards Better Performance and More Explainable Uncertainty for 3D Object Detection of Autonomous Vehicles [33.0319422469465]
  We propose a novel form of the loss function to increase the performance of LiDAR-based 3d object detection. With the new loss function, the performance of our method on the val split of KITTI dataset shows up to a 15% increase in terms of Average Precision.
  arXiv  Detail & Related papers  (2020-06-22T05:49:58Z)
• A Universal Formulation of Uncertainty Relation for Error and Disturbance [0.9479435599284545]
  We present a universal formulation of uncertainty relation valid for any conceivable quantum measurement. Owing to its simplicity and operational tangibility, our general relation is also experimentally verifiable.
  arXiv  Detail & Related papers  (2020-04-13T17:57:41Z)
• Geometric Formulation of Universally Valid Uncertainty Relation for Error [1.696974372855528]
  We present a new geometric formulation of uncertainty relation valid for any quantum measurements of statistical nature. Owing to its simplicity and tangibility, our relation is universally valid and experimentally viable.
  arXiv  Detail & Related papers  (2020-02-10T18:31:54Z)

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.