We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the s...We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.展开更多
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 scen...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 affer the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first- tioned on the actual measurement outcome. Induced entropies. For two successive projective t state condiquantum uncertainties are characterized by means of the Tsallis t 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.展开更多
文摘We obtain uncertainty and certainty relations of state-independent form for the three Paufi observables with use of the Renyi entropies of order α∈ （0; 1]. It is shown that these entropic bounds are tight in the sense that they are always reached with certain pure states. A new result is the condition for equality in Renyi-entropy uncertainty relations for the Pauli observables. Upper entropic bounds in the pure-state case are also novel. Combining the presented bounds leads to a band, in which the rescaled average Renyi a-entropy ranges for a pure measured state. A width of this band is compared with the Tsallis formulation derived previously.
文摘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 affer the first measurement with completely erased information. In the second scenario, the second measurement is performed on the post-first- tioned on the actual measurement outcome. Induced entropies. For two successive projective t state condiquantum uncertainties are characterized by means of the Tsallis t 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.
