The paper focuses on the fact that quantum projective measurements do not necessarily conserve energy. On the other hand the Wigner-Araki-Yanase (WAY) theorem states that assuming a "standard" von Neumann measurement model and "additivity" of the total energy operator, projective measurements of a system must conserve energy as defined by the system's energy operator. This paper explores the ideas behind the WAY theorem in hopes of uncovering the origin of the contradiction. After Araki and Yanase published their proof of the WAY theorem, Yanase appended a new condition now known as the Yanase condition. Under the simplifying assumption that the observable being measured has discrete and non-degenerate eigenvalues, we prove that the Yanase condition actually follows from the hypotheses of the original WAY theorem. The paper also proves that the hypotheses of the WAY theorem, together with the simplifying assumption, imply that the energy operator for the measuring apparatus must be a multiple of the identity, which seems physically unlikely. It seems probable that this surprising conclusion, along with the Yanase condition, also holds without the simplifying assumption.The paper focuses on the fact that quantum projective measurements do not necessarily conserve energy. On the other hand the Wigner-Araki-Yanase (WAY) theorem states that assuming a "standard" von Neumann measurement model and "additivity" of the total energy operator, projective measurements of a system must conserve energy as defined by the system's energy operator. This paper explores the ideas behind the WAY theorem in hopes of uncovering the origin of the contradiction. After Araki and Yanase published their proof of the WAY theorem, Yanase appended a new condition now known as the Yanase condition. Under the simplifying assumption that the observable being measured has discrete and non-degenerate eigenvalues, we prove that the Yanase condition actually follows from the hypotheses of the original WAY theorem. The paper also proves that the hypotheses of the WAY theorem, together with the simplifying assumption, imply that the energy operator for the measuring apparatus must be a multiple of the identity, which seems physically unlikely. It seems probable that this surprising conclusion, along with the Yanase condition, also holds without the simplifying assumption.

arXiv:1610.04607Oct 14, 20160 citations

Tighter sum uncertainty relations via $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew informationTighter sum uncertainty relations via $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

Cong Huai Xu, Zhaoqi Wu, Shao-Ming Fei

We establish tighter uncertainty relations for arbitrary finite observables via $(α,β,γ)$ weighted Wigner-Yanase-Dyson ( $(α,β,γ)$ WWYD) skew information. The results are also applicable to the $(α,γ)$ weighted Wigner-Yanase-Dyson ( $(α,γ)$ WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson ( $(α,β,γ)$ MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.We establish tighter uncertainty relations for arbitrary finite observables via $(α,β,γ)$ weighted Wigner-Yanase-Dyson ($(α,β,γ)$WWYD) skew information. The results are also applicable to the $(α,γ)$ weighted Wigner-Yanase-Dyson ($(α,γ)$WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson ($(α,β,γ)$MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.

arXiv:2401.08641Dec 12, 20230 citations

Tighter sum uncertainty relations via

(α,β,γ)

weighted Wigner-Yanase-Dyson skew information

We establish tighter uncertainty relations for arbitrary finite observables via

(α,β,γ)

weighted Wigner-Yanase-Dyson (

(α,β,γ)

WWYD) skew information. The results are also applicable to the

(α,γ)

weighted Wigner-Yanase-Dyson (

(α,γ)

WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via

(α,β,γ)

modified weighted Wigner-Yanase-Dyson (

(α,β,γ)

MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.