Linear position measurements with minimum error-disturbance in each minimum uncertainty state

• URL: http://arxiv.org/abs/2012.12707v1
• Date: Wed, 23 Dec 2020 14:36:19 GMT
• Title: Linear position measurements with minimum error-disturbance in each minimum uncertainty state
• Authors: Kazuya Okamura
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In quantum theory, measuring process is an important physical process; it is a quantum description of the interaction between the system of interest and the measuring device. Error and disturbance are used to quantitatively check the performance of the measurement, and are defined by using measuring process. Uncertainty relations are a general term for relations that provide constraints on them, and actively studied. However, the true error-disturbance bound for position measurements is not known yet. Here we concretely construct linear position measurements with minimum error-disturbance in each minimum uncertainty state. We focus on an error-disturbance relation (EDR), called the Branciard-Ozawa EDR, for position measurements. It is based on a quantum root-mean-square (q-rms) error and a q-rms disturbance. 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, and explicitly give exactly solvable linear position measurements achieving its lower bound in the state. We then give probability distributions and states after the measurement when using them. It is expected to construct measurements with minimum error-disturbance in a broader class of states in the future, which will lead to a new understanding of quantum limits, including uncertainty relations.

Related papers

• Optimal Allocation of Pauli Measurements for Low-rank Quantum State Tomography [26.844092519401617]
  A key challenge of quantum state tomography (QST) is to find out how the accuracy of the reconstruction depends on the number of state copies used in the measurements. We establish a theoretical understanding of the trade-off between the number of measurement settings and the number of repeated measurements per setting in QST.
  arXiv  Detail & Related papers  (2024-11-07T05:59:04Z)
• Quantum state testing with restricted measurements [30.641152457827527]
  We develop an information-theoretic framework that yields unified copy complexity lower bounds for restricted families of non-adaptive measurements. We demonstrate a separation between these two schemes, showing the power of randomized measurement schemes over fixed ones.
  arXiv  Detail & Related papers  (2024-08-30T17:48:00Z)
• Gaussian Formalism: Concrete Realization of Joint Measurement for Heisenberg's Uncertainty Relation for Errors [0.0]
  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.
  arXiv  Detail & Related papers  (2024-03-28T14:10:48Z)
• The role of shared randomness in quantum state certification with unentangled measurements [36.19846254657676]
  We study quantum state certification using unentangled quantum measurements. $Theta(d2/varepsilon2)$ copies are necessary and sufficient for state certification. We develop a unified lower bound framework for both fixed and randomized measurements.
  arXiv  Detail & Related papers  (2024-01-17T23:44:52Z)
• On the negative-result experiments in quantum mechanics [0.0]
  We comment on the so-called negative-result experiments (also known as null measurements, interaction-free measurements, and so on) in quantum mechanics (QM) All experiments of this kind (null-measurements) can be understood as improper measurements with an intentionally biased detector set up, which introduces exclusion or selection of certain events. The verification of the prediction made by a null-measurement requires eventually a standard unbiased measurement involving the microsystem-macroscopic detector interactions.
  arXiv  Detail & Related papers  (2023-10-03T10:56:26Z)
• Measurement sharpness and disturbance tradeoff [0.0]
  Postmeasurement states for a given measurement are not unique and highly rely on the chosen measurement model. We show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces. In particular, we show there are different tradeoff relations between the sharpness of this measurement and the average fidelity of the premeasurement and postmeasurement state spaces.
  arXiv  Detail & Related papers  (2023-08-08T08:43:39Z)
• 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)
• Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach [24.52459180982653]
  We propose a kernel-based nonparametric estimator for the causal effect when the cause is corrupted by error. We empirically show that our proposed method, MEKIV, improves over baselines and is robust under changes in the strength of measurement error.
  arXiv  Detail & Related papers  (2022-06-18T11:47:25Z)
• Experimentally determining the incompatibility of two qubit measurements [55.41644538483948]
  We describe and realize an experimental procedure for assessing the incompatibility of two qubit measurements. We demonstrate this fact in an optical setup, where the qubit states are encoded into the photons' polarization degrees of freedom.
  arXiv  Detail & Related papers  (2021-12-15T19:01:44Z)
• Entanglement detection in quantum many-body systems using entropic uncertainty relations [0.0]
  We study experimentally accessible lower bounds on entanglement measures based on entropic uncertainty relations. We derive an improved entanglement bound for bipartite systems, which requires measuring joint probability distributions in only two different measurement settings per subsystem.
  arXiv  Detail & Related papers  (2021-01-21T20:50:11Z)
• 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)

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.