One of the features of 20^{th} century art is its increasing level of abstraction from cubism and surrealism in the early years to abstract expressionism and mathematical photography later. So an interesting question is what further abstractions can we look forward to in the 21^{th} century?

Today we get an answer thanks to the work of Karl Svozil, a theoretical physicist at the University of Technology in Vienna and his pal Volkmar Putz. These guys have mapped out a way of representing music using the strange features of quantum theory. The resulting art is the quantum equivalent of music and demonstrates many of the bizarre properties of the quantum world.

Svozil and Putz begin by discussing just how it might be possible to represent a note or octave of notes in quantum form and by developing the mathematical tools for handling quantum music.

They begin by thinking of the seven notes in a quantum octave as independent events whose probabilities add up to one. In this scenario, quantum music can be represented by a mathematical structure known as a seven-dimensional Hilbert space.

A pure quantum musical state would then be made up of a linear combination of the seven notes with a specific probability associated with each. And a quantum melody would be the evolution of such a state over time.

An audience listening to such a melody would have a bizarre experience. In the classical world, every member of the audience hears the same sequence of notes. But when a quantum musical state is observed, it can collapse into any one of the notes that make it up. The note that is formed is entirely random but the probability that it occurs depends on the precise linear makeup of the state.

And since this process is random for all observer, the resulting note will *not* be the same for each member of the audience.

Svozil and Puz call this “quantum parallel musical rendition.” “A classical audience may perceive one and the same quantum musical composition very differently,” they say.

As an example they describe the properties of a quantum composition created using two notes: C and G. They show how in one case, a listener might perceive a note as a C in 64 percent of cases and as a G in 36 percent of cases.

They go on to show how a quantum melody of two notes leads to four possible outcomes: a C followed by a G, a G followed by a C, a C followed by a C, and G followed by a G. And they calculate the probability of a listener experiencing these during a given performance. “Thereby one single quantum composition can manifest itself during listening in very different ways,” say Svozil and Putz. This is the world’s first description of a quantum melody.

The researchers go on to discuss the strange quantum phenomenon of entanglement in the context of music. Entanglement is the deep connection between quantum objects that share the same existence even though they may be in different parts of the universe. So a measurement on one immediately influences the other, regardless of the distance between them.

Exactly what form this might take in the quantum musical world isn’t clear. But it opens the prospect of an audience listening to a quantum melody in one part of the universe influencing a quantum melody in another part.

Svozil and Putz also take a stab at developing a notation for quantum music (see picture above).

That takes musical composition to a new level of abstraction. “This offers possibilities of aleatorics in music far beyond the classical aleatoric methods of John Cage and his allies,” they say.

There is one obvious problem, however. Nobody knows how to create quantum music or how a human might be able to experience it. Svozil and Putz’s work is entirely theoretical.

That shouldn’t stop the authors or anybody else from performing a quantum musical composition. It ought to be straightforward to simulate the effect using an ordinary computer and a set of headphones. So instead of quantum music, we could experience a quantum music simulation.

That’s interesting work that has implications for other art forms too. How about quantum sculpture that changes for each observer or a quantum mobile that is entangled with another elsewhere in the universe.

One thing seems clear. Quantum art is coming, or at least the simulation of it.So don’t be surprised if you find a quantum melody playing at an auditorium near you someday soon.

Ref: arxiv.org/abs/1503.09045 : Quantum Music

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