Quantum Uncertainties

Ming‐Jing Zhao, Yuan-Hong Tao

Abstract The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it systematically with respect to given projective measurement. Some basic concepts about uncertainty are reformulated in this context. We prove and get the form of the uncertainty preserving operations. The quantum states with maximal uncertainty are characterized. A universal decomposition of uncertainty into classical uncertainty and quantum uncertainty is provided. Furthermore, a unified and general relation among uncertainty, coherence and coherence of assistance is established. These results are independent of any explicit uncertainty measure. At last, we propose a new uncertainty measure called the geometric uncertainty based on the fidelity and link it with the geometric coherence.

Pieter Kok

Etera R. Livine

Hengyan Wang, Zhihao Ma, Shengjun Wu +8 more

As a very fundamental principle in quantum physics, uncertainty principle has been studied intensively via various uncertainty inequalities. Based on the information measure introduced by Brukner and Zeilinger in [Phys. Rev. Lett. 83, 3354 (1999)], we derive an uncertainty conservation relation in the presence of quantum memory. We show that the sum of measurement uncertainties over a complete set of mutually unbiased bases on a subsystem is equal to a total uncertainty determined by the initial bipartite state. Hence for a given bipartite system the uncertainty is conserved and the uncertainty relation is given by an equality. When the total uncertainty vanishes, all the uncertainties related to every mutually unbiased base measurement are zero, which is substantially different from the uncertainty relation given by Berta et. al. [Nat. Phys. 6, 659 (2010)] where an uncertainty inequality is presented. By directly measuring the corresponding quantum mechanical observables on a 5-qubit spin system, we experimentally verify the uncertainty conservation relation in the presence of quantum memory without quantum state tomography.

Etera R. Livine

Zidan Afidah, Bambang Supriadi, Novi Rahmawati +3 more

This study aims to find the uncertainty value of Helium Ion Momentum (𝐻𝑒+) by using the Heisenberg Uncertainty Approach to Quantum Numbers 𝑛 ≤ 3. This type of research uses non-experimental research. The research was conducted by developing previously existing theories. This research is to calculate the expectation value of the position to find out how often electrons can appear, and determine the uncertainty of the momentum of Helium Ion (𝐻𝑒+) by using the Heisenberg uncertainty approach at number 𝑛 ≤ 3. Based on the results and discussion, it can be concluded that the uncertainty of helium ion momentum (𝐻𝑒+) by using the Heisenberg uncertainty approach to quantum numbers 𝑛 ≤ 3. The uncertainty of helium ion momentum is influenced by the main quantum number (n) and the azimuthal quantum number (l). By entering the values of n and l, the results can be obtained at quantum numbers 𝑛 = 1 with 𝑙 = 0 obtained ∆𝑃𝑟 = 2,977504663 × 10−24. At the quantum number 𝑛 = 2 with 𝑙 = 0 obtained ∆𝑃𝑟 = 8,06312759 × 10−24 and 𝑙 = 1 obtained ∆𝑃𝑟 = 2,03048 × 10−23. At the quantum number 𝑛 = 3 with 𝑙 = 0 obtained ∆𝑃𝑟 = 1,50366086 × 10−23, and 𝑙 = 1 obtained ∆𝑃𝑟 = 3,481407588 × 10−23 and 𝑙 = 2 obtained ∆𝑃𝑟 = 4,47363642 × 10−22. Based on these results, it can be concluded that the uncertainty value of momentum is getting bigger as the two values of n and l increase. This is also proven by using simulation and the results of momentum uncertainty are not much different and only a difference of a few decimal places.