Pith. sign in

REVIEW 3 major objections 5 minor 26 references

This paper claims that quantum teleportation can be used as a directed, tunable communication channel between musical agents, turning teleportation infidelity into a controlled parameter for improvisation.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

T0 review · deepseek-v4-flash

2026-08-01 13:03 UTC pith:TZNQX5X7

load-bearing objection A genuinely new use of teleportation as a tunable 'whisper' channel between musical agents — with a real idea in the interpreter module, but the headline fidelity claim is only shown on isolated qubits, not the entangled circuits the system actually runs. the 3 major comments →

arxiv 2607.19212 v1 pith:TZNQX5X7 submitted 2026-07-21 quant-ph cs.SD

Teleportation Game: Quantum Teleportation in Multi-Agent Systems for Interactive Music

classification quant-ph cs.SD
keywords quantum teleportationmusical agentsinteractive musicSQPAMphase kickbackNISQinterpretative distancequantum computer music
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper builds an interactive music system in which live audio is encoded into quantum states, and up to three agents pass those states to each other via quantum teleportation. The central proposal is that teleportation is not a lossy copy but a musically meaningful 'whisper': agents can imitate, transform, or diverge from what they receive. The strongest claim is that by replacing the standard Pauli correction gates in teleportation with parameterized rotations RX(θ) and RZ(θ), the degree of interpretive divergence becomes continuously controllable—larger θ yields higher state fidelity and less variation, smaller θ yields more variability. The paper argues this makes teleportation a viable and expressive interaction mechanism for agent-based computer music, with a path toward distributed agents over the Quantum Internet.

Core claim

The central discovery is a parameterized 'interpreter module' inserted into the teleportation correction stage. Standard teleportation recovers the sent state with X and Z corrections; the paper replaces those with RX(θ) and RZ(θ) gates. Simulator experiments over randomized U(θ,φ,λ) states show that as θ increases toward π, the fidelity between sender and receiver states rises and the variance across trials falls; as θ approaches zero, fidelity drops and variance grows. The paper interprets this as a continuous spectrum of interpretative distance—from faithful reproduction to free reinterpretation—and treats it as a musical parameter rather than an error. This reframes teleportation-based i

What carries the argument

SQPAM (Single Qubit Probability Amplitude Modulation) encodes melodic and rhythmic information into the probability amplitudes of single qubits via U(θ,φ,λ) rotations; PKBSE (Phase Kickback Sequencing Encoding) uses quantum phase estimation to entangle the signal qubits with a time register and place the rotations at the correct sequence positions. Teleportation moves one agent's signal qubit state to another agent's qubit via a Bell pair and classical measurements. The interpreter module—parameterized RX/RZ corrections replacing the Pauli X/Z corrections—is the knob that controls how faithfully the received state is reproduced.

Load-bearing premise

The approach assumes that the audio features (contour energy, tempo, spectral centroid, onset intensity) mapped to rotation angles, and the subsequent scale-quantized decoding, preserve enough musical structure that differences between agents' outputs after teleportation are meaningful measures of imitation versus divergence rather than artifacts of the encoding and decoding pipeline.

What would settle it

Run the same two-agent teleportation circuit but replace the teleportation channel with a direct classical copy of agent 1's U(θ,φ,λ) parameters into agent 2's initial state (perfect transfer); if melodic correlation, Hamming distance, and fidelity distributions are statistically indistinguishable from the teleportation runs, then the observed interpretive variation is not caused by teleportation at all—it would be a property of the encoding/decoding and the parameterized corrections, not of the quantum channel.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Teleportation can mediate directed influence between musical agents without enforcing synchronization or identity; after reception, the receiver evolves independently, enabling divergence.
  • Cascading teleportation across three agents produces composite influences: downstream agents' outputs reflect both direct and indirect transmissions, and NISQ noise can reverse which influence dominates.
  • The interpreter module gives performers and composers a continuous control over interpretive distance, not just a binary success or failure of state transfer.
  • The work offers a new evaluation lens for quantum communication: fidelity can be treated as a continuum of interpretive transformation with perceptible musical meaning, potentially useful for Quantum Internet design.
  • The framework extends to distributed agents connected via quantum networks, where teleportation would carry non-local musical information that classical networks cannot transmit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The interpreter module could be generalized beyond RX/RZ to arbitrary single-qubit rotations or even non-unitary operations, creating a larger space of 'listening styles'; the paper's claim that θ is the dial suggests a family of such dials.
  • The temporal misalignment between agents' time registers, noted in the paper as a cause of divergence, could be isolated and deliberately controlled to add a rhythmic-displacement dimension independent of state fidelity.
  • A blind listening study where human listeners rate melodic similarity between agents' outputs could test whether perceptual ratings correlate with the computed fidelity continuum, giving the 'interpretative distance' metric ecological validity.
  • If hardware noise indeed inflates variance as the paper assumes, different devices or noise-injection levels could be used as a compositional parameter, making device noise an expressive resource rather than a limitation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents an interactive music system in which musical agents encode melodic and rhythmic features of a live input as quantum states (SQPAM/PKBSE), entangle these with a time register via QPE, and communicate by quantum teleportation. Two- and three-agent demonstrations on a simulator and IBM hardware are compared with melodic-correlation and Hamming-distance metrics. The central quantitative experiment (Section 5) generalizes the teleportation correction stage by replacing Pauli gates with parameterized RX(RZ) rotations and reports that increasing the correction angle theta toward pi increases sender-receiver fidelity and reduces variance, which is interpreted as a tunable 'interpreter module' that shapes musical interpretative distance. The paper frames NISQ noise and teleportation infidelity as creative resources ('quantum whispers') and positions the work toward future Quantum Internet music ensembles.

Significance. The artistic idea of treating infidelity in quantum teleportation as a continuous, tunable musical parameter is original and could be a useful proof-of-concept for quantum computer music and for human-centered evaluation of imperfect quantum state transfer. The paper is clearly written, builds on established building blocks (SQPAM, PKBSE, QPE, standard teleportation), and the Section 5 single-qubit trend is internally consistent. However, the main claims about 'systematically shaped' musical interpretation are not yet supported by experiments on the actual multi-agent entangled circuits, and the hand-built encoding/decoding pipeline lacks controls. If the follow-up experiments requested below demonstrate the trend in the full pipeline, the contribution would be significant for its community; as it stands, the result is a promising but incomplete demonstration.

major comments (3)
  1. [Section 5, Fig. 18; Eqs. (6)-(7)] The central claim of a tunable interpreter module is supported only by a standalone single-qubit teleportation circuit U(theta, phi, lambda)|0> with RX(theta)/RZ(theta) corrections (Fig. 18). In the actual agent circuits of Sections 3-4, the teleported melodic qubit is entangled with the time register and rhythm qubit through controlled-U and QFT/PKBSE, so the receiver qubit is not an isolated pure state; single-qubit sender-vs-receiver fidelity cannot quantify the resulting distortion of the multipartite state. Section 5 also states that the hardware experiment was not run and merely assumes that noise will increase variance. Please run the interpreter module on the full SQPAM/PKBSE circuit and decode the corrected states; without that, 'interpretative behaviour can be systematically shaped' as a musical parameter is unsupported.
  2. [Sections 3.1-3.2 and Tables 3-4] The conclusions about imitation/divergence and direct/indirect influence depend on a hand-built pipeline: audio features are scaled to [-10,10], mapped to U-gate angles, decoded via Eq. (3), and quantized to an F-major scale. No control condition or ablation is provided, so the melodic correlations and Hamming distances may reflect the quantizer/decoder rather than teleportation. In addition, Tables 3-4 report single runs without error bars; the simulator/hardware discrepancy for the Agent 2-3 pair (0.717 vs 0.290) is unexplained. A baseline with random replacement of the teleported state, or varying only the decoder, is needed before attributing the observed differences to teleportation.
  3. [Section 4.1, Fig. 7] The correction table appears to interchange the X and Z corrections for measurement outcomes |01> and |10> relative to the standard teleportation protocol as described (Bennett et al.). Moreover, Fig. 7 shows unconditional X and Z gates on q2 rather than classically conditioned corrections. If the corrections are not applied conditionally on the measurement outcomes, the protocol is not standard teleportation, and the Section 5 fidelity results measure a different operation. Please clarify the exact conditional correction logic and verify it on |0>, |1>, and a superposition state.
minor comments (5)
  1. [Section 5, Eq. (6)] The ranges from which theta, phi, lambda are sampled are not specified, and the number of shots is not stated. This prevents reproduction of the 100-trial experiment.
  2. [Eq. (4)] The melodic-correlation sum uses A_i and A_{i-1}; the index range should start at i=2 (or the first term should be defined separately). Also clarify the min-of-ratios convention.
  3. [Figure 19] Panel (a) is labeled 'Normal distribution for state fidelities,' but no fitted distribution or axis labels are shown. State the sample statistics and whether a normal fit was actually performed.
  4. [Abstract and Section 5] Minor typos: 'asquantum whispers' should be 'as quantum whispers'; the paragraph beginning 'For each trial, the teleportation protocol was executed...' is repeated almost verbatim.
  5. [Reference [15]] The DOI/URL for the Librosa paper is malformed: 'https://doi.org/10.25080/Majora-7b98e3ed-01ehttps://doi.org/10.25080/Majora-7b98e3ed-003'.

Circularity Check

0 steps flagged

No significant circularity: the Section 5 fidelity result is a direct consequence of the teleportation correction gate, not a fitted input; self-citations are methodological and not load-bearing.

full rationale

The paper's derivation chain is not circular. The SQPAM/PKBSE encoding methods are cited from the authors' prior work, but the present paper independently implements and runs the circuits on Qiskit Aer and IBM hardware, so the self-citations are not the sole support for the central claims. The Section 5 interpreter module replaces Pauli corrections with RX(θ)/RZ(θ) and measures sender-receiver fidelity; the observed increase in mean fidelity as θ approaches π follows directly from RX(π) implementing the X correction up to a global phase, and the variance trend is an empirical statistic computed over randomly sampled input states, not a parameter fitted to the data. No uniqueness theorem is invoked, no fitted parameter is renamed as a prediction, and the melodic-correlation/Hamming-distance results are computed from decoded outputs rather than being fixed by construction. The paper's main limitation—that the interpreter module was not tested on the full entangled multi-agent circuit—is an external-validity concern, not circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 2 invented entities

The central musical results depend on several hand-chosen encoding choices (feature scaling bounds, block segmentation, scale quantization), while the quantitative claim about the interpreter module depends on an unspecified sampling range and the fidelity-as-understanding assumption. The protocol math itself is standard.

free parameters (5)
  • Feature-to-Ugate scaling bounds = -10 to +10
    Section 3.1: every extracted audio feature is scaled into [-10, +10] to 'prevent the features from becoming too large, while being able to move the qubit state throughout at least one rotation of the Bloch sphere.' The choice of bound is manual and affects all musical outputs.
  • Contour-energy block segmentation = 3 equal blocks
    Section 3.1: the audio stream is segmented into 3 equal blocks, one per time-register qubit. The block size Bs enters Eq. 2 directly and determines the encoded θm values; no justification is given for 3 rather than another number.
  • Scaling of decoded amplitude ai to pitches = Key of F major; quantized to scale
    Section 3.2: 'each float value in the sequences is quantised to pitches within a chosen scale' in the key of F major. The quantization mapping is not specified, and the choice of scale affects all melodic-correlation and Hamming-distance numbers.
  • Sampled parameter ranges in Section 5 = uniform over a 'predefined range'
    Section 5, Eq. 6: each parameter set p=(θ,φ,λ) is sampled uniformly from a predefined range, but the range is never stated. The reported fidelity trend is conditioned on this unspecified range.
  • Correction rotation angle θ in demonstrations = π
    Section 5: 'all instances of melodic convergence and divergence between agents were observed using the baseline teleportation protocol' with the standard Pauli corrections, i.e., θ=π. The hardware demonstrations therefore do not exercise the tunable interpreter module.
axioms (4)
  • standard math Standard quantum teleportation protocol with ideal Bell-state measurements and classical feed-forward corrections.
    Section 4.1 relies on the textbook Bennett et al. protocol; the paper notes NISQ noise but does not derive or re-derive the protocol's behavior under noise.
  • domain assumption The SQPAM representation and PKBSE phase-kickback sequencing encode musical amplitude information faithfully enough for musical purposes.
    Sections 3 and 3.1 import SQPAM from reference [9] and PKBSE from reference [20] (both author-affiliated) as the encoding foundation; no independent evaluation of the encoding's musical fidelity is provided here.
  • domain assumption Librosa feature extraction (pYIN, beat.tempo, spectral centroid, onset strength) produces musically relevant parameter values for the U gates.
    Section 3.1 maps four audio features to six U-gate angles with no ablation or validation that the mapping preserves melodic/rhythmic information.
  • domain assumption The Uhlmann-Jozsa fidelity between the teleported sender/receiver qubit states is a meaningful proxy for 'musical understanding' or 'interpretive distance'.
    Section 5 reinterprets fidelity as a measure of musical understanding; the paper itself notes that fidelity 'does not capture' what a listener perceives, which undercuts its use as the quantitative basis for the interpreter-module claims.
invented entities (2)
  • Quantum whisper no independent evidence
    purpose: Metaphor/framing for deliberately imperfect teleportation-based agent communication.
    Introduced in the abstract and Section 6 as an aesthetic concept; no falsifiable prediction is attached to it.
  • Interpreter module independent evidence
    purpose: Generalizes the teleportation correction stage by replacing Pauli X/Z corrections with parameterized RX(θ)/RZ(θ) gates to tune interpretative distance.
    The module yields a concrete, testable prediction (mean fidelity and variance of teleported states vary with θ; θ→π gives high fidelity). The paper reports a simulator fidelity trend supporting this, though on an unspecified parameter range.

pith-pipeline@v1.3.0-alltime-deepseek · 13806 in / 9395 out tokens · 78055 ms · 2026-08-01T13:03:18.906286+00:00 · methodology

0 comments
read the original abstract

This paper introduces an interactive music system with quantum musical agents that communicate by teleporting quantum states to one another. Human performers interact in real time with agents whose melodic and rhythmic behaviours are encoded as quantum states using Single Qubit Probability Amplitude Modulation (SQPAM) and structured through Quantum Phase Estimation (QPE). Up to three agents are combined within a single quantum circuit, with directed communication via quantum teleportation. We are interested in supporting ambiguous, transformative interactions reminiscent of free Jazz improvisation. Therefore, rather than treating noise and decoherence as limitations, the system embraces NISQ-era constraints as creative affordances, framing agent communication as quantum whispers, that is, deliberate, musically expressive imperfections in state transfer. We provide demonstrations and analyses based on melodic correlation, pitch-set distance, and state fidelity, where a continuum between imitation and divergence can be observed. We developed a tunable interpretation method to assess how agents reinterpret teleported states. This work positions teleportation as a promising interaction mechanism for agent-based quantum computer music and outlines future directions toward distributed ensembles connected via the Quantum Internet.

Figures

Figures reproduced from arXiv: 2607.19212 by Eduardo Reck Miranda, Scott Yeiichi Oshiro.

Figure 1
Figure 1. Figure 1: Quantum Agent System Pipeline. Technically, the system employs the Single Qubit Probability Amplitude Modulation (SQPAM) representation scheme [9], combined with the Quantum Phase Estimation (QPE) algorithm [25]. Melodic and rhythmic information extracted from input music is encoded into the probability amplitudes of individual qubits with SQPAM. Then, QPE is used to entangle this information with a repres… view at source ↗
Figure 2
Figure 2. Figure 2: Quantum Circuit of a single quantum agent. One set of qubits (𝑞0, 𝑞1 and 𝑞2) represents the time register. Each of the binary codes produced by the three-qubit register corresponds to eighth-note subdivisions in a 4 4 time signature. The remaining two qubits (𝑞3 and 𝑞4), referred to as signal qubits, represent the melodic (pitch) and rhythmic (duration) information at each subdivision. Through trigonometri… view at source ↗
Figure 3
Figure 3. Figure 3: Probability distribution for a single quantum agent produced on (a) Qiskit’s Aer simulator and (b) ibm fez. After obtaining the distributions presented in [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Single agent (a) melodic and rhythmic qubit signals and (b) decoded music notation produced with Aer simulator. 4 Multiple Quantum Agents with Teleportation In this section, we present practical demonstrations designed to illustrate how the agents introduced above behave and interact within a multi-agent system. Specifically, this section looks at musical results using two and three agents. These qualitati… view at source ↗
Figure 5
Figure 5. Figure 5: Single agent (a) melodic and rhythmic qubit signals and (b) decoded music notation produced with the IBM quantum hardware, ibm fez. For both demonstrations, the same core pipeline described in Section 2 is employed. These demonstrations should, however, be understood not as benchmarks of computational efficiency, but as explorations of musically meaningful behaviour under NISQ constraints. The metrics calc… view at source ↗
Figure 6
Figure 6. Figure 6: Multiagent scheme with teleportation. ∣Ψ⟩ 1 ∣0⟩ ∣0⟩ ∣Ψ⟩ 2 𝑞0 U(𝜃, 𝜙, 𝜆) H 𝑞1 H X 𝑞2 X X Z [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Quantum Teleportation Protocol Circuit 10 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Results for agent 1 executed on Qiskit’s Aer simulator. (a) Melodic and rhythmic qubit signals of agent 2. (b) Rendered musical notation of agent 2 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Results for agent 2 executed on Qiskit’s Aer simulator. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Results for agent 1 executed on the IBM quantum hardware, ibm kingston. Figures 10 and 11 show the results of this configuration when run on an IBM quantum hardware ibm kingston. The melodic correlation between the resulting melodic phrase was 0.456, showing that for this particular example, that the melodies generated from agent 1 and agent 2 on the real quantum hardware were more correlated by a factor … view at source ↗
Figure 11
Figure 11. Figure 11: Results for agent 2 executed on the IBM quantum hardware, ibm kingston. 4.3 Three Agents Example For this example, we scaled the system up to three agents arranged in a unidirectional cascade as shown in [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Results for agent 1 in a 3-agent cascading scenario executed on Qiskit’s Aer simulator. Next, Figs. 15, 16, 17 show the results for running the quantum circuit on the IBM quantum hardware, ibm fez. In this case, we observed that agent 1 and agent 2 had the highest melodic correlation with a value equal to 0.497. Agent 1 and agent 3 displayed the second-highest correlation with a slightly lower value for m… view at source ↗
Figure 13
Figure 13. Figure 13: Results for agent 2 in a 3-agent cascading scenario executed on Qiskit’s Aer simulator. (a) Melodic and rhythmic qubit signals of agent 3.) (b) Rendered musical notation of agent 3 [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Results for agent 3 in a 3-agent cascading scenario executed on Qiskit’s Aer simulator. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Results for Agent 1 in a 3-agent cascading scenario executed on IBM quantum hardware, ibm fez. 5 Analysis of Interpretative Distance This section shows preliminary results from experimenting with interpretive distance tuning pa￾rameters for quantum agent interactions embedded within the quantum teleportation protocol. The demonstrations presented above (Section 4) showed that interaction between the quant… view at source ↗
Figure 16
Figure 16. Figure 16: Results for Agent 2 in a 3-agent cascading scenario executed on IBM quantum hardware, ibm fez. (a) Agent 3 melodic and rhythmic qubit signals. (b) Agent 3 rendered musical score [PITH_FULL_IMAGE:figures/full_fig_p018_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Results for Agent 3 in a 3-agent cascading scenario executed on IBM quantum hardware, ibm fez. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: A variation of the standard quantum teleportation protocol for the interpretive distance analysis. Θ = (𝑝1, 𝑝2, 𝑝3, ...𝑝𝑘) (6) For each trial, the teleportation protocol was executed between two agents, and the resulting density matrices of the melodic and rhythmic qubits were reconstructed from measurement statistics. Fidelity was then computed pairwise between sender and receiver states. Fidelity here p… view at source ↗
Figure 19
Figure 19. Figure 19: Results of interpretive distance analysis. 20 [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

26 extracted references · 10 canonical work pages

  1. [1]

    Probabilis- tic Links Between Quantum Classification of Patterns of Boolean Functions and Hamming Distance

    Andronikos, T., Bitsakos, C., Nikas, K., Goumas, G. I., and Koziris, N. (2026). “Probabilis- tic Links Between Quantum Classification of Patterns of Boolean Functions and Hamming Distance”.Stats, 9(1): 5. DOI:https://doi.org/10.3390/stats9010005

  2. [2]

    Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen chan- nels

    Bennett, C. H., Brassard, G., Cr ´epeau, C., Jozsa, R., Peres, A., and Wootters, W. K. (1993). “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen chan- nels”.Physical Review Letters, 70(13): 1895-1899. DOI:https://doi.org/10.1103/ PhysRevLett.70.1895

  3. [3]

    (2019).Quantum Computing for Everyone

    Bernhardt, C. (2019).Quantum Computing for Everyone. The MIT Press, Cambridge, MA. ISBN: 978-0-26-203925-3

  4. [4]

    Improvizing with Genetic Algorithms: GenJam

    Biles J. A. (2007). “Improvizing with Genetic Algorithms: GenJam”. In Miranda, E.R. and Biles, J.A. (eds.),Evolutionary Computer Music. Springer, London. DOI:https://doi. org/10.1007/978-1-84628-600-1_7

  5. [5]

    Djordjevic, I. B. (2022).Quantum Communication, Quantum Networks, and Quantum Sensing. Elsevier, Amsterdam. ISBN: 978-0-12-822942-2

  6. [6]

    and Squartini, S

    Gabrielli, L. and Squartini, S. (2016).Wireless Networked Music Performance. Springer, Sin- gapore. DOI:https://doi.org/10.1007/9789811003356

  7. [7]

    and Pikrakis, A

    Giannakopoulos, T. and Pikrakis, A. (2014).Introduction to Audio Analysis. Academic Press, Cambridge, MA. ISBN: 978-0-08-099388-1

  8. [8]

    Information security through controlled quantum tele- portation networks

    Hamdoun, H. and Sagheer, A. (2020). “Information security through controlled quantum tele- portation networks”.Digital Communications and Networks, 6(4):463-470. DOI:https: //doi.org/10.1016/j.dcan.2020.04.009

  9. [9]

    Quantum Representations of Sound: From Mechanical Waves to Quantum Circuits

    Itaborai, P. V. and Miranda, E. R. (2022). “Quantum Representations of Sound: From Mechanical Waves to Quantum Circuits”. In Miranda, E.R. (Ed.)Quantum Computer Music. Springer, Cham. DOI:https://doi.org/10.1007/978-3-031-13909-3_10

  10. [10]

    Performance Monitoring of Improvisation and Score-Playing in a Turn-Taking Piano Duet: An EEG Study Using Altered Auditory Feedback

    Kim, K., Fram, N., Nerness, B., Turnbull, C., Chander, A., Georgieva, E., James, S., Wright, M. and Fujioka, T. (2024). “Performance Monitoring of Improvisation and Score-Playing in a Turn-Taking Piano Duet: An EEG Study Using Altered Auditory Feedback”Psychophysiology. Psychophysiology. 62(2):e14704.DOI:https://doi.org/10.1111/psyp.14704

  11. [11]

    Kimble, H. J. (2008).The Quantum Internet. arXiv:0806.4195:https://doi.org/10. 48550/arXiv.0806.4195

  12. [12]

    Too many notes: Computers, complexity and culture in Voyager

    Lewis, G. E. (2000). “Too many notes: Computers, complexity and culture in Voyager”.Leonardo Music Journal, 10(2): 33–39. DOI:https://doi.org/10.1162/096112100570585

  13. [13]

    Quantum fidelity measures for mixed states

    Liang, Y.-C., Yeh, Y.-H., Mendonc ¸a, P. E. M. F., Teh, R. Y., Reid, M. D. and Drummond, P. D. (2019). “Quantum fidelity measures for mixed states”.Reports on Progress in Physics, 82(7), 076001. DOI:https://doi.org/10.1088/1361-6633/ab1ca4

  14. [14]

    pYIN: A fundamental frequency estimator using probabilistic threshold distributions

    Mauch, M. and Dixon, S. (2014). “pYIN: A fundamental frequency estimator using probabilistic threshold distributions”. InProceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 659–663. IEEE. DOI:https://doi.org/ 10.1109/ICASSP.2014.6853678

  15. [15]

    Librosa: Audio and music signal analysis in Python

    McFee, B., Raffel, C., Liang, D., Ellis, D. P. W., McVicar, M., Battenberg, E. and Nieto, O. (2015). “Librosa: Audio and music signal analysis in Python”. InProceedings of the 14th Python in Science Conference, pp. 18-25. Austix, Texas. DOI:https://doi.org/10. 25080/Majora-7b98e3ed-01ehttps://doi.org/10.25080/Majora-7b98e3ed-003 23

  16. [16]

    Available online:https://midi.org/specs(Ac- cessed on 21 December 2025)

    MIDI Association.MIDISpecifications. Available online:https://midi.org/specs(Ac- cessed on 21 December 2025)

  17. [17]

    Introduction to Quantum Computing for Musicians

    Miranda, E. R. and Weaver, J.(2022). “Introduction to Quantum Computing for Musicians”. In Miranda, E. R. (ed.),Quantum Computer Music. Springer, Cham. DOI:https://doi.org/ 10.1007/978-3-031-13909-3_1

  18. [18]

    Brain Dynamics During Music Improvisation

    Nerness, B. (2025). “Brain Dynamics During Music Improvisation” Doctoral disser- tation. Stanford University. Available online:https://stacks.stanford.edu/ file/xm667gf4960/BarbaraNerness_diss_Brain_Dynamics_Music_ Improvisation-augmented.pdf(Accessed on 19 March 2025)

  19. [19]

    (2023).Lineage and Freedom: A Quantum Computational Framework for Im- provisation

    Oshiro, S. (2023).Lineage and Freedom: A Quantum Computational Framework for Im- provisation. Doctoral dissertation. Stanford University. Available online:https://purl. stanford.edu/sg420hc4768

  20. [20]

    (2022).QuiKo: A quantum beat generation application

    Oshiro, S. (2022).QuiKo: A quantum beat generation application. Available on arXiv:2204.04370:https://doi.org/10.48550/arXiv.2204.04370

  21. [21]

    ibm.com/docs/en/api/qiskit/qiskit.circuit.library.UGate

    IBM Quantum Platform (2025).Qiskit API Reference: UGate.https://quantum.cloud. ibm.com/docs/en/api/qiskit/qiskit.circuit.library.UGate

  22. [22]

    Rohde, P. P. (2021).The Quantum Internet: The Second Quantum Revolution. Cambridge University Press, Cambridge. DOI:https://doi.org/10.1017/9781108868815

  23. [23]

    Machine listening and composing with Cypher

    Rowe, R. (1992). “Machine listening and composing with Cypher”.Computer Music Journal, 16(1): 62–73. DOI:https://www.jstor.org/stable/3680494

  24. [24]

    Spectral centroid and timbre in com- plex, multiple instrumental textures

    Schubert, E., Wolfe, J., and Tarnopolsky, A. (2004). “Spectral centroid and timbre in com- plex, multiple instrumental textures”. InProceedings of the International Conference on Music Perception and Cognition (ICMPC)

  25. [25]

    (2024).Quantum algorithms: Phase estimation

    Ueda, K. (2024).Quantum algorithms: Phase estimation. IBM Quantum Platform Courses. Available online:https://quantum.cloud.ibm.com/learning/en/courses/ utility-scale-quantum-computing/quantum-phase-estimation

  26. [26]

    Capturing coordination and intentionality in joint musical improvisation

    Vaarten, L. and Wiltshire, T. J. (2023). “Capturing coordination and intentionality in joint musical improvisation”.Psychomusicology: Music, Mind, and Brain, 33(1-4): 26–39. DOI: https://doi.org/10.1037/pmu0000299 24