Previously, it has been suggested that the GA¶del-type non-algorithmic process may be associated with consciousness. This paper discusses the halting problem and the non-computability of self-referential consciousness. Specifically, this discussion outlines the distinguishability between the halting and looping of computation, or the semantic understanding between true and false, that may be associated with the non-computability of consciousness. The nonlocality intrinsically possessed in quantum theory is one of the striking features of nature that has received a lot of attention. In particular, Bell-type inequalities have been not only extremely powerful but practical tools in quantum information technology. A numerical approach is used to describe different cases of Bell-CHSH inequalities, particularly with different numbers of the choices of measurement bases. It is shown that there are variations of inequalities that are relatively stable against measurement errors.
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes.In this paper, the answer to this question is shown to be no.A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer.Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element.The concept that this is solely a quantum effect and does not work for a classical case is also discussed.
We have recently theorized that consciousness is intrinsically connected to quantum mechanical spin since said spin is embedded in the microscopic structure of spacetime and is more fundamental than spacetime itself, that is, spin is the “mind-pixel.” Applying these ideas to the particular structures and dynamics of the brain, we have developed a qualitative model of quantum consciousness. In this paper, we express our fundamental view that spin is a primordial self-referential process driving quantum mechanics, spacetime dynamics and consciousness. To justify such a view, we will draw support from existing literatures, discuss from a reductionist perspective the essential properties said spin should possess as mind-pixel and explore further the nature of spin to see whether said properties are present. Our conclusion is that these properties are indeed endowed to spin by Nature. One of the implications from our fundamental view is that the probabilistic structure of quantum mechanics is due to the self-referential collapse of spin state that is contextual, non-local, non-computable and irreversible. Therefore, a complete theory of the self-referential spin process is necessarily semantic, that is, it should be based on internally meaningful information.
In recent years, examining the information processing aspects of nature has received significant attention. In particular, entanglement has been shown to exhibit what is arguably the most distinctive and unique aspect of quantum information science. In this note, a numerical method is applied to the Bell inequalities for examining the range of nonlocality when imperfect measurements are performed at each end. A two-qubit direct protocol is also examined such that, unlike the Bell-type inequalities, the approach is not as stable as the indirect one against measurement errors in yielding the nonlocality. On the other hand, since many applications of quantum technology involve a particular type of entanglement, it is important to have a technique to manipulate correlations. In this paper, five chained 2-level entanglements are also examined with swapping protocols applied at each joint. It is numerically shown that there exists a class of states that approximate the optimal result, i.e., the weakest link.
Multipartite nonlocality has been extensively investigated within one-dimensional quantum lattices. Previous research has primarily focused on the nonlocality measure
S, which quantifies the violation of Bell-type inequalities. However, the optimal nonlocal operators, which are related to specific experimental settings required to achieve the violation, often remain elusive. In this work, we employ a string-like nonlocal operator
S^N, characterized by a core single-site operator
p^, to investigate the optimal measurement setting in translationally invariant quantum chains. By analyzing the infinite-size transverse-field Ising, Cluster-Ising, and extended Ising models, we uncover two general results. First, for typical ground states, we find that the optimal single-site operator
p^ possesses an intrinsic mirror symmetry. Second, the optimal nonlocal operator
S^(p^) exhibits remarkable robustness: for a specific model, as the Hamiltonian parameter changes, the structure of
p^ remains stable and persists across distinct quantum phases. These findings not only redefine the numerical optimization paradigm for multipartite nonlocality, but also significantly simplify the experimental requirements by identifying fixed measurement bases. This structural stability provides practical guidance for implementing macroscopic Bell tests in large-scale quantum simulators, making it highly compatible with modern efficient measurement protocols.
We explore in the framework of Quantum Computation the notion of computability, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm that exploits the quantum adiabatic which is equivalent to the Turing halting problem and known to be mathematically noncomputable. Generalised quantum algorithms are also considered for some other mathematical noncomputables in the same and of different noncomputability classes. The key element of all these algorithms is the measurability of both the values of physical observables and of the quantum-mechanical probability distributions for these values. It is argued that computability, and thus the limits of Mathematics, ought to be determined not
We explore in the framework of quantum computation the notion of computability, which holds a central position in mathematics and theoretical computer science. A quantum algorithm that exploits the quantum adiabatic processes is considered for Hilbert's tenth problem, which is equivalent to the Turing halting problem and known to be mathematically non-computable. Generalized quantum algorithms are also considered for some other mathematical non-computables in the same and in different non-computability classes. The key element of all these algorithms is the measurability of both the values of physical observables and the quantum-mechanical probability distributions for these values. It is argued that computability, and thus the limits of mathematics, ought to be determined not solely by mathematics itself but also by physical principles.