Bits of Uncertainty

Oleg V. Petrov

In this paper the following information interpretation of uncertainty relation is proposed: if one bit of information was extracted from the system as a result of the measurement process, then the measurement itself adds an additional uncertainty (chaos) into the system equaled to one bit. This formulation is developed by calculating of the Shannon information entropy for the classical N-slit interference experiment. This approach allows looking differently at several quantum phenomena. Particularly, the information interpretation is used for explanation of entangled photons diffraction picture compression.

Devon Bowen

Min-Nan Chen, Wen‐Yang Sun, Ai-Jun Huang +3 more

Abstract In this work, we investigate the dynamics of quantum-memory-assisted entropic uncertainty relations under open systems, and how to steer the uncertainty under different types of decoherence. Specifically, we develop the dynamical behaviors of the uncertainty of interest under two typical categories of noise; bit flipping and depolarizing channels. It has been shown that the measurement uncertainty firstly increases and then decreases with the growth of the decoherence strength in bit flipping channels. In contrast, the uncertainty monotonically increases with the increase of the decoherence strength in depolarizing channels. Notably, and to a large degree, it is shown that the uncertainty depends on both the systematic quantum correlation and the minimal conditional entropy of the observed subsystem. Moreover, we present a possible physical interpretation for these distinctive behaviors of the uncertainty within such scenarios. Furthermore, we propose a simple and effective strategy to reduce the entropic uncertainty by means of a partially collapsed operation—quantum weak measurement. Therefore, our investigations might offer an insight into the dynamics of the measurment uncertainty under decoherence, and be of importance to quantum precision measurement in open systems.

David Wick

Noriaki Kihara

This appendix develops independently a single point compressed in section 6.3 of the related report (On the Logarithmic Map of Scale and the Separation of Scale and Quantization): that the uncertainty relation in the observable space (constant product) is derived from the sum-zero of fluctuations in the fundamental-quantity N-space. The emphasis is on the direction of the derivation: sum-zero (Delta_a + Delta_b = 0) is placed as the definition, and the constant product is the consequence, the two being connected by the logarithmic map N=log2(nu). Under sum-zero, the half-bit +/-1/2 remains irreducibly on each fundamental quantity with anti-correlated signs, and the product of the observables a*b = 2^K is fixed (whereas the product of the fluctuations delta_a*delta_b is not constant). The continuous squeeze (a hyperbola a*b = 2^K) is the trade-off where tightening one widens the other, with the fixed half-bit as its minimal unit. The +/-1/2 is treated as a posit, not a derivation; no physical identification is made; uncertainty here is not in the sense of Bell's theorem.