Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916017996824576 |
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| author | Dutta, Soumyojyoti Tushar |
| author_facet | Dutta, Soumyojyoti Tushar |
| contents | We introduce Magic Secret Sharing (MSS), a quantum cryptographic primitive in which the secret is the computational capability of a quantum state rather than its classical description. In the resource theory of magic, non-stabilizer states fuel universal quantum computation via non-Clifford gates; MSS distributes this resource with an (n-1,n) threshold structure using a pre-shared GHZ state and a single local phase gate P(phi) = diag(1, exp(i*phi)). Any individual party holds the maximally mixed state I/2, with Wigner distance C(I/2) = 0, so no local operation can yield non-Clifford computational advantage regardless of what operations are applied or what noise acts on the device. The authorised coalition reconstructs magic content C(phi) = (|sin(phi)| + |cos(phi)| - 1)/2 exactly, enabling a logical T gate via gate teleportation in multi-server blind quantum computation (BQC). Among diagonal parametric gates, phase gates are the unique class satisfying the security condition, characterised via an exact column-sum condition. The protocol is elevated to a one-sided device-independent (1SDI) setting via a steering inequality: the assemblage produced on the recipient's side certifies magic delivery without trusting the coalition's devices. We demonstrate the (2,3) instance on ibm_marrakesh (156-qubit IBM Heron): security (C(rho_Bob) = 0.000, below LP reconstruction tolerance) holds in all runs, and state fidelity reaches 0.959-0.986 for the authorised party, with faithfulness confirmed for all four test values of phi including near-exact recovery (C = 0.154 vs theory 0.153) for phi = pi/8. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16614 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement Dutta, Soumyojyoti Tushar Quantum Physics 81P45, 81P94, 81P68 We introduce Magic Secret Sharing (MSS), a quantum cryptographic primitive in which the secret is the computational capability of a quantum state rather than its classical description. In the resource theory of magic, non-stabilizer states fuel universal quantum computation via non-Clifford gates; MSS distributes this resource with an (n-1,n) threshold structure using a pre-shared GHZ state and a single local phase gate P(phi) = diag(1, exp(i*phi)). Any individual party holds the maximally mixed state I/2, with Wigner distance C(I/2) = 0, so no local operation can yield non-Clifford computational advantage regardless of what operations are applied or what noise acts on the device. The authorised coalition reconstructs magic content C(phi) = (|sin(phi)| + |cos(phi)| - 1)/2 exactly, enabling a logical T gate via gate teleportation in multi-server blind quantum computation (BQC). Among diagonal parametric gates, phase gates are the unique class satisfying the security condition, characterised via an exact column-sum condition. The protocol is elevated to a one-sided device-independent (1SDI) setting via a steering inequality: the assemblage produced on the recipient's side certifies magic delivery without trusting the coalition's devices. We demonstrate the (2,3) instance on ibm_marrakesh (156-qubit IBM Heron): security (C(rho_Bob) = 0.000, below LP reconstruction tolerance) holds in all runs, and state fidelity reaches 0.959-0.986 for the authorised party, with faithfulness confirmed for all four test values of phi including near-exact recovery (C = 0.154 vs theory 0.153) for phi = pi/8. |
| title | Magic Secret Sharing: Threshold Control of Quantum Computational Power via GHZ Entanglement |
| topic | Quantum Physics 81P45, 81P94, 81P68 |
| url | https://arxiv.org/abs/2605.16614 |