Abstract
In this paper, analogous to the no-signaling-in-time (NSIT) conditions, a series of equalities for the change of conditional and average energy of a quantum system are given to test macrorealism. These equalities are named no-signaling-in-time conditions for conditional energy (CNSIT) and no-signaling-in-time conditions for average energy (ANSIT), respectively. Then, we investigate the violations of the NSIT conditions, the CNSIT conditions and the ANSIT conditions for a qubit in the following scenarios: pure coherent dynamics, dynamics with drive, dynamics under dissipation and dephasing. For the pure qubit, when the NSIT conditions or the CNSIT conditions are not violated, the ANSIT conditions can not be violated, and a suitable conjunction of the CNSIT conditions and the NSIT conditions may be better for testing macrorealism. While for the driven qubit, the non-violation of the CNSIT conditions implies the non-violation of the NSIT conditions, which in turn implies the non-violation of the ANSIT conditions. For dephasing and dissipative qubits, the relationships among the NSIT conditions, the CNSIT conditions and the ANSIT conditions are similar to those of the pure and driven qubits, respectively. While the degree of violations of the NSIT conditions, the CNSIT conditions and the ANSIT conditions is decreased with the increasing time interval between measurements; and if this time interval tends to a very large number, all three kinds of conditions are satisfied.
Highlights
And mathematically, quantum physics is incompatible with a view of classical world
The Leggett–Garg inequality puts limits on temporal correlation functions of pairs of consecutive measurements on the same quantum system fulfilled macrorealism, and the NSIT conditions say that a measurement does not change the outcome statistics of a later measurement
We find that the non-violation conditions of the CNSIT conditions and the ANSIT conditions both depend on the initial state, while the non-violation conditions of the NSIT conditions for the initial mixed state is the same as that of the initial pure state
Summary
And mathematically, quantum physics is incompatible with a view of classical world. The other fundamental concept, macrorealism, was proposed by Leggett and Garg in 1985, and can be described as [2]: (1) Macrorealism per se (MRps): A macroscopic object which has two or more macroscopically distinct states is in a definite one of those states at any given time; (2) Non-invasive measurability (NIM): In principle, it is possible to determine which of these states the system is in without any influence on the state itself or on the subsequent system dynamics Based on these assumptions and analogous to Bell’s theorem [1], the Leggett–Garg inequality [2,3,4] was proposed to test quantum correlations in time by Leggett and Garg. While for dissipative and dephasing qubits, the dissipation and dephasing decrease the degree of violations of the NSIT conditions, the CNSIT conditions and the ANSIT conditions, with the increasing time interval between measurements; and if this time interval tends to very large values, all three kinds of conditions can not be violated
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