Superposition in quantum states of large systems plays a crucial role in quantum theory and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of such states lies in the quantum coherence, as measured by the amount of entanglement and other quantum correlations, between its microscopic and macroscopic sectors. We show that in contrast to other macroscopic superposition states, it is possible to choose the states of the macroscopic sector in a way that the resulting state, which we term as the ${H}_{C}$ state, has quantum coherence that is resistant to the twin effects of environmental noise: (a) local decoherence on all the particles and (b) loss of a finite fraction of its particles. The states of the macroscopic sector of the ${H}_{C}$ state are macroscopically distinct in terms of their violation of Bell inequality.
Superposition in quantum states of large systems plays a crucial role in quantum theory and has important fundamental as well as technological implications, ranging from quantum measurement theory to quantum computers. The power of the potential implications of such states lies in the quantum coherence, as measured by the amount of entanglement and other quantum correlations, between its microscopic and macroscopic sectors. We show that in contrast to other macroscopic superposition states, it is possible to choose the states of the macroscopic sector in a way that the resulting state, which we term as the HC state, has quantum coherence that is resistant to the twin effects of environmental noise: (a) local decoherence on all the particles and (b) loss of a finite fraction of its particles. The states of the macroscopic sector of the HC state are macroscopically distinct in terms of their violation of Bell inequality.
A quantum entangled state is a quantum superposition state. The principle of quantum superposition, and therefore the existence of quantum entanglement, is contingent upon the validity of quantum theory. Thus, the generation of quantum entanglement requires that interactions occur between small-mass particles localized in a confined spatial region, resulting in each particle’s quantum state being a bound state. In other words, the prerequisite for the validity of quantum theory must be satisfied. At the same time, conserved quantities must exist between quantum superposition states, as only quantum states with conserved quantities can undergo superposition, allowing the particle system to generate quantum entangled states. Quantum entangled states can occur between electrons within an atom, between atoms, between molecules, or between atoms and molecules. Within the atomic nucleus, quantum entanglement can exist among protons, neutrons, and the quarks. In superconductivity, superfluidity, and Bose-Einstein condensation, they manifest as macroscopic quantum entanglement, which respectively come from the statistical results of a large amount of microscopic quantum entanglement between electrons, atoms or molecules. For massive macroscopic objects, they exhibit classical properties that cannot be described by quantum theory, and the principle of quantum superposition does not hold. Therefore, no entangled state is generated. It should be particularly emphasized that even for microscopic particle systems, if they exist in a large spatial region, they cannot be described by quantum theory. In such cases, the quantum superposition principle does not hold, and quantum entanglement phenomena do not exist. Therefore, within a large spatial region, multi-electron, multi-photon, and other microscopic systems do not have quantum entangled states; under certain conditions, quantum correlated states can be generated. Consequently, in a large spatial region, the mainstream viewpoints about non-locality—such as the so-called instantaneous collapse of entangled particles during measurement, infinite propagation speed, and the “spooky action at a distance”—are all incorrect. In experiments related to quantum communication and the verification of Bell’s inequality, the quantum states used are quantum correlated states rather than quantum entangled states. Regardless of whether the systems are microscopic or macroscopic, phenomena occurring in a large spatial region must adhere to the principles of causality, realism, and locality. In other words, Einstein’s viewpoint is correct.
The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from quantum mechanics in the macroscopic limit. In this paper, we challenge this perspective and demonstrate that the behaviour of a macroscopic system can retain all aspects of the quantum formalism, in a way that is robust against decoherence, particle losses and coarse-grained (imprecise) measurements. This departure from the expected classical description of macroscopic systems is not merely mathematical but also conceptual, as we show by the explicit violation of a Bell inequality and a Leggett–Garg inequality.
The categorization of quantum states for composite systems as either separable or entangled, or alternatively as Bell local or Bell non-local states based on local hidden variable theory is outlined, focusing on simple bipartite systems. The significance of states demonstrating Bell non-locality for settling the long standing controversy between the Copenhagen interpretation of the quantum measurement process involving “collapse of the wave-function” and the alternative interpretation based on pre-existing hidden variables is emphasized. Although experiments demonstrating violations of Bell locality in microscopic systems have now been carried out, there is current interest in finding Bell non-locality in quantum systems on a macroscopic scale, since this is a regime where a classical hidden variable theory might still apply. Progress towards finding macroscopic quantum states that violate Bell inequalities is reviewed. A new test for Bell non-locality that applies when the sub-system measured quantities are spin components with large outcomes is described, and applied to four mode systems of identical massive bosons in Bose-Einstein condensates.
Theory and experiment both demonstrate that an entangled quantum state of two subsystems is neither a superposition of states of its subsystems nor a superposition of composite states but rather a coherent superposition of nonlocal correlations between incoherently mixed local states of the two subsystems. Thus, even if one subsystem happens to be macroscopic as in the entangled "Schrodinger's cat" state resulting from an ideal measurement, this state is not the paradoxical macroscopic superposition it is generally presumed to be. It is, instead, a "macroscopic correlation," a coherent quantum correlation in which one of the two correlated sub-systems happens to be macroscopic. This clarifies the physical meaning of entanglement: When a superposed quantum system A is unitarily entangled with a second quantum system B, the coherence of the original superposition of different states of A is transferred to different correlations between states of A and B, so the entangled state becomes a superposition of correlations rather than a superposition of states. This transfer preserves unitary evolution while permitting B to be macroscopic without entailing a macroscopic superposition. This resolves the "problem of outcomes" but is not a complete resolution of the measurement problem because the entangled state is still reversible.
We argue that quantum nonlocality of entangled states is not an actual phenomenon. It appears in quantum mechanics as a consequence of the inconsistency of its superposition principle with the corpuscular properties of a quantum particle. In the existing form, this principle does not distinguish between macroscopically distinct states of a particle and their superpositions: it implies introducing observables for a particle, even if it is in an entangled state. However, a particle cannot take part simultaneously in two or more alternative macroscopically distinct sub-processes. Thus, calculating the expectation values of the one-particle's observables, for entangled states, is physically meaningless: Born's formula is not applicable to such states. The same concerns the entangled states of compound quantum systems. In the {\it existing} quantum mechanics, introducing Bell's inequalities is fully legal. However, these inequalities imply averaging over an entangled state, and, hence, they have no basis for their clear physical interpretation. Experiments to confirm the violation of Bell's inequalities do not prove the existence of nonlocality in microcosm. They confirm only that correlations introduced in the existing theory of entangled states have no physical sense, for they contradict special relativity.