Quantum mechanical systems exist as superpositions of complementary states that collapse to classical, concrete states upon becoming entangled with the measurement apparatus of observer-participants. A musical composition its performance constitute a quantum system. and Historically, conventional musical notation has presented the appearance of a composition as a deterministic, concrete entity, with interpretation approached as an extrinsic act. This historical perspective inhabits a subspace of the available quantum space. A quantum musical system unifies the composition, instruments, situated performance and perception as a superposition of musical events that collapses to concrete musical events via the interactions and perceptions of performers and audience. A composer captures superposed musical events via implicit or explicit conditional event probabilities, and human and/or machine performers create music by collapsing interrelated probabilities to zeros and ones via observer-participancy.
Quantum mechanical systems exist as superpositions of complementary states that collapse to classical, concrete states upon becoming entangled with the measurement apparatus of observer-participants. A musical composition its performance constitute a quantum system. and Historically, conventional musical notation has presented the appearance of a composition as a deterministic, concrete entity, with interpretation approached as an extrinsic act. This historical perspective inhabits a subspace of the available quantum space. A quantum musical system unifies the composition, instruments, situated performance and perception as a superposition of musical events that collapses to concrete musical events via the interactions and perceptions of performers and audience. A composer captures superposed musical events via implicit or explicit conditional event probabilities, and human and/or machine performers create music by collapsing interrelated probabilities to zeros and ones via observer-participancy.
The composer constantly makes choices: it is the composer, in fact, who chooses a melodic, rhythmic, harmonic path among the various, infinite possible paths between point A, the beginning, and point B, the end of a composition. The choice of one path over another, a local modification of a given path, can also be influenced by external factors. As it happens for the path of a charged particle in a magnetic field, the choice of the musical path can be influenced by personal style, culture, technical characteristics of the instruments, and combinations of instruments used. Even in quantum mechanics, there are “choices”: the state of a system appears as a superposition of possible eigenstates with different probability amplitudes. The act of measurement “forces” the system to choose a particular state: the observer influences the physics of the system. Like the famous example of Schrödinger’s cat, alive and dead at the same time until the box in which it is located is opened. From the choices of notes and musical paths to decision-making systems, we present some examples of the application of quantum mechanics to music. Among the applications of quantum computing, we mention a study on robots with associated musical descriptions. In particular, we consider the distributed intelligence of a swarm of robots and its possible musical description, from some existing works to our original application.
We initiate the development of a new language and theory for quantum music, to which we refer as Quantum Concept Music (QCM). This new music formalism is based on Categorical Quantum Mechanics (CQM), and more specifically, its diagrammatic incarnation Quantum Picturalism (QPict), which is heavily based on ZX-calculus. In fact, it is naturally inherited from CQM/QPict. At its heart is the explicit notational representation of relations that exist within and between the key concepts of music composition, performance, and automation. QCM also enables one to directly translate quantum phenomena into music compositions in a both intuitively obvious, rigorous and mechanical manner. Following this pattern, we propose a score for musicians interacting like a Bell-pair under measurement, and outline examples of how it could be live performed. While most of the Western classical music notation has heavily relied on linear representation of music - which does not always adequately capture the nature of music - our approach is distinct by highlighting the fundamental relational dimension of music. In addition, this quantum-based technique not only influences the music at the profound level of composition, but also has a direct impact on a live performance, and also provides a new template for automating music, e.g.~in the context of AI-generation. All together, we initiate the creation of new music formalism that is powerful and efficient in capturing the interactive nature of music, both in terms of internal and external interactions, and goes beyond the boundaries of Western classical music notation, which allows to use it in many different genres and directions.
We initiate the development of a new language and theory for quantum music, to which we refer as Quantum Concept Music (QCM). This new music formalism is based on Categorical Quantum Mechanics (CQM), and more specifically, its diagrammatic incarnation Quantum Picturalism (QPict), which is heavily based on ZXcalculus. In fact, it is naturally inherited from CQM/QPict. At its heart is the explicit notational representation of relations that exist within and between the key concepts of music composition, performance, and automation. QCM also enables one to directly translate quantum phenomena into music compositions in a both intuitively obvious, rigorous and mechanical manner. Following this pattern, we propose a score for musicians interacting like a Bell-pair under measurement, and outline examples of how it could be live performed. While most of the Western classical music notation has heavily relied on linear representation of music - which does not always adequately capture the nature of music - our approach is distinct by highlighting the fundamental relational dimension of music. In addition, this quantumbased technique not only influences the music at the profound level of composition, but also has a direct impact on a live performance, and also provides a new template for automating music, e.g. in the context of AI-generation. All together, we initiate the creation of new music formalism that is powerful and efficient in capturing the interactive nature of music, both in terms of internal and external interactions, and goes beyond the boundaries of Western classical music notation, which allows to use it in many different genres and directions.
Analyzing two standard preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is demonstrated that four entities are the basic ingredients of the theory: the composite-system preparator-plus-object state (coming about as a result of a suitable interaction between the subsystems), a suitable preparator observable, one of its characteristic projectors called the triggering event, and, finally, the conditional object state corresponding to the occurrence of the triggering event. The concepts of a conditional state and of retrospective apparent ideal occurrence are discussed in the conventional interpretation of quantum mechanics. In the general theory of a preparator in this interpretation first-kind and second-kind preparators are distinguished. They are described by the same entities in the same way, but in terms of different physical mechanisms. In this article the relative-collapse interpretation is extended to encompass also preparators (besides measuring apparatuses). In this interpretation also the mechanisms become the same and one has only one kind of preparators.
In classical physics, the ‘state’ of a particle, at any particular time, is taken to involve a definite position in space and a definite motion; and the state of a system of particles is taken to involve a definite position in space and a definite motion for each of the particles. The situation in relation to quantum mechanics is completely different. As in classical physics, calculations can be made concerning the position and motion of a particle. However, this representation is not by means of symbols for scalar or vector quantities: it is by a more complex mathematical object. This quantum state does not indicate or represent position or motion in any direct way: what it does in substance is to enable calculation of the probability of the particle in question being found to have a position or momentum if an appropriate measurement is made.