Measurement induced uncertainties

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Bin Chen, Shao-Ming Fei

We investigate complementary measurement-induced quantum uncertainty based on metric adjusted skew information, and propose two new measures of quantum uncertainty associated with mutually unbiased measurements and general symmetric informationally complete measurements, respectively. Based on these measures of quantum uncertainty, we present two entanglement criteria and show that they detect better entanglement than the existing corresponding criteria by detailed examples.

Fei Ming, Zheng-Qiang Xu, Tao-Tao Lu +6 more

Abstract The effect of gravity is a key factor in understanding the physical phenomenon. Quantizing gravity is challenging task due to weak interactions of gravity in quantum world. The quantum nature of gravity can be witnessed by entanglement in an interferometric platform [Phys. Rev. D 105, 086024 (2022)]. A natural question arises concerning whether the quantization of gravity can be observed via other means. In this work, we propose an effective approach to witnessing the gravity-induced quantumness by quantum uncertainty relations, including entropy-based and coherence-based uncertainty relations. The theoretical frameworks for wave-particle, entropic uncertainty and coherence are established, which can prove the quantum nature of gravity. The three-measurement entropic uncertainty and coherence exhibit the oscillatory features for the gravity-induced phases in the interferometric scheme. It is found that the evolutionary dynamics of coherence is inversely correlated with the measured uncertainty. It can be interpreted that the reduction of systemic quantum resource leads to the increase of entropic uncertainty, and vice versa. When the entropic uncertainty reaches zero, systemic coherence is the maximum value, providing a viable physical explanation for the gravity-induced quantumness. It shows that the entropic uncertainty and coherence can be regarded as the reliable indicators for capturing the gravity-induced quantumness. Compared to entanglement-based gravity quantization scheme, it shows that the capabilities are equivalent for detecting the gravity-induced quantumness using entropy uncertainty, coherence, and entanglement. The results could lay a solid theoretical foundation for the potential applications of quantum gravity in quantum information science.

Alexey E. Rastegin

Abstract We study uncertainty and certainty relations for two successive measurements of two-dimensional observables. Uncertainties in successive measurement are considered within the following two scenarios. In the first scenario, the second measurement is performed on the quantum state generated after the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first-measurement state conditioned on the actual measurement outcome. Induced quantum uncertainties are characterized by means of the Tsallis entropies. For two successive projective measurement of a qubit, we obtain minimal and maximal values of related entropic measures of induced uncertainties. Some conclusions found in the second scenario are extended to arbitrary finite dimensionality. In particular, a connection with mutual unbiasedness is emphasized.

William M. Honig, Kraft, David W, Panarella, Emilio