The unease of understanding quantum theory (QT) began<br />at the very beginning of its establishment. The famous<br />Bohr–Einstein debate inspired a lively controversy on<br />quantum foundations. QT is surely an empirically successful<br />theory, with huge applications ranging from subatomic<br />world to cosmology. However, why does it attract such a<br />heated debate over its whole history? The controversial<br />issues on quantum foundations mainly focus on two<br />aspects: (Q1) What does a wave function (or a quantum<br />state) really mean? (Q2) Is the so-called quantum<br />measurement problem really a problem? The first axiom of<br />the standard QT states that a system’s wave function<br />provides a complete description of the system. But<br />accepting the wave function as QT’s central entity, what is<br />the physical meaning of the wave function itself? In this<br />regard, there are two alternatives that the quantum state<br />might be either a state about an experimenter’s knowledge<br />or information about some aspects of reality—an epistemic<br />viewpoint—or a state of physical reality—an ontic<br />viewpoint A recent result on this issue seems to support the<br />reality of quantum states, yet with ongoing controversy<br />On the contrary, the quantum measurement problem is<br />perhaps the most controversial one on quantum<br />foundations. According to the orthodox interpretation<br />(namely, the Copenhagen interpretation (of QT, a quantum<br />system in a superposition of different states evolves<br />deterministically according to the Schrodinger equation,<br />but actual mea-¨ surements always collapse, in a truly<br />random way, the system into a definite state, with a<br />probability determined by the probability amplitude<br />according to the Born rule. When, where, and how the<br />quantum state really collapses are out of the reach of QTas<br />it is either “uninteresting or unscientific to discuss reality<br />before measurement”<br />Our classical world view implies that there exists a world<br />that is objective and independent of any observations. By<br />sharp contrast, what is observed on a quantum system is<br />dependent upon the choice of experimental arrangements;<br />mutually exclusive (or complementary) properties cannot<br />choice underlies the Pusey–Barrett–Rudolph theorem<br />and the derivation of Bell’s inequalities However, one could<br />ask the following: What does a free will or a freedom of<br />choice mean physically and particularly, and what is the<br />physical system that encodes information about the free<br />will or freedom of choice?<br />Thus, in the orthodox interpretation, classical concepts<br />are necessary for the description of measurements (which<br />type of measurements to choose and the particular<br />measurement results for chosen measurement) in QT,<br />although the measurement apparatus can indeed be<br />described quantum mechanically, as done by von Neumann<br />Seen from its very structure, quantum mechanics “contains<br />classical mechanics as a limiting case, yet at the same time,<br />it requires this limiting case for its own formulation In this<br />sense, the current QT has a classical-quantum hybrid<br />feature. At a cosmological scale, the orthodox<br />interpretation rules out the possibility of assigning a wave<br />function to the whole Universe, as no external observer<br />could exist to measure the Universe.<br />Facing with the interpretational difficulties, various<br />interpretations on QT were proposed by many brilliant<br />thoughts, such as the hidden-variable theory (initiated by<br />the famous Einstein–Podolsky–Rosen paper questioning<br />the completeness of QT), many-worlds interpretation the<br />relational interpretation the decoherence theory and the<br />WISE (wavefunction is the system entity) interpretation to<br /><br />feature. At a cosmological scale, the orthodox<br />interpretation rules out the possibility of assigning a wave<br />function to the whole Universe, as no external observer<br />could exist to measure the Universe.<br />Facing with the interpretational difficulties, various<br />interpretations on QT were proposed by many brilliant<br />thoughts, such as the hidden-variable theory (initiated by<br />the famous Einstein–Podolsky–Rosen paper questioning<br />the completeness of QT), many-worlds interpretation the<br />relational interpretationthe decoherence theory and the<br />WISE (wavefunction is the system entity) interpretation to<br />mention a few. Thus, “questions concerning the over mention a few. Thus, “questions concerning the over<br />