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A Static Analysis of Entanglement

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2025)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15530))

Abstract

Managing quantum variables in quantum programs presents specific challenges due to the possible occurrence of entanglement, the quantum mechanical phenomenon for which two variables can reach a state where they cannot be separated into two distinct individual states. Such a phenomenon may lead to critical issues due to unintended measurements, which may alter the outcome of computations involving entangled variables. To address this problem, we propose a static analysis based on the abstract interpretation framework to soundly and automatically detect entanglement occurring in quantum programs. By constructing an abstract domain for the entanglement property, our analysis identifies cases where side effects from quantum operations may produce unwanted entanglement, thus reducing the possibility of unintended computational side effects.

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Notes

  1. 1.

    Danny Greenberg, Mike Horne, and Anton Zeilinger experimentally created this three-particle entanglement showing that quantum mechanics is not compatible with Einstein’s theory of ‘hidden variables’.

  2. 2.

    We refer here to the Hilbert space vector norm defined as \(\Vert \left| {\psi }\right\rangle \Vert = \sqrt{\langle \psi \rangle }\), where \(\left\langle {\psi }\right| \) is the conjugate transpose of \(\left| {\psi }\right\rangle \) and \(\langle x\rangle {y}\) is the inner product between vector \(\left| {x}\right\rangle \) and vector \(\left| {y}\right\rangle \).

  3. 3.

    In [2] we call the direct inseparability property as being at the same level.

  4. 4.

    The following GitHub repository NicolaAssolini98/EntaglementAnalysis contains our prototype implemented in Python.

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Acknowledgment

Alessandra Di Pierro was supported by INdAM - GNCS Project CUP_E53C22001930001, Isabella Mastroeni by the project SERICS (PE00000014) under the MUR National Recovery and Resilience Plan funded by the European Union - NextGenerationEU and by PRIN2022PNRR “RAP-ARA” (PE6) - MUR: P2022HXNSC.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Verona, Verona, Italy

    Nicola Assolini, Alessandra Di Pierro & Isabella Mastroeni

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  1. Nicola Assolini
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  2. Alessandra Di Pierro
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  3. Isabella Mastroeni
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Correspondence to Nicola Assolini .

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Editors and Affiliations

  1. Indian Institute of Technology Bombay, Mumbai, Maharashtra, India

    Krishna Shankaranarayanan

  2. University of Colorado Boulder, Boulder, CO, USA

    Sriram Sankaranarayanan

  3. University of Colorado Boulder, Boulder, CO, USA

    Ashutosh Trivedi

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Assolini, N., Di Pierro, A., Mastroeni, I. (2025). A Static Analysis of Entanglement. In: Shankaranarayanan, K., Sankaranarayanan, S., Trivedi, A. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2025. Lecture Notes in Computer Science, vol 15530. Springer, Cham. https://doi.org/10.1007/978-3-031-82703-7_3

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