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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07756 |
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| _version_ | 1866910045925539840 |
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| author | Root, Owen |
| author_facet | Root, Owen |
| contents | I study a promise problem for an unknown unitary operator acting on an $n$-qubit system. The operator is promised to take one of two forms: either it implements a fixed permutation of computational basis states, or it implements the same permutation together with a conditional sign change determined by a designated input qubit. I show that these two cases can be distinguished with certainty using a single query to the unknown operator and a measurement of only one qubit. The procedure requires no ancilla qubits and uses only $n+1$ Hadamard gates in addition to the oracle call. The promise is intrinsically quantum, since the two cases differ only in their relative-phase structure and therefore have no direct classical counterpart in the usual black-box model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07756 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Deterministic Discrimination of Phase-Modified Permutation Oracles via Single Qubit Measurement Root, Owen Quantum Physics I study a promise problem for an unknown unitary operator acting on an $n$-qubit system. The operator is promised to take one of two forms: either it implements a fixed permutation of computational basis states, or it implements the same permutation together with a conditional sign change determined by a designated input qubit. I show that these two cases can be distinguished with certainty using a single query to the unknown operator and a measurement of only one qubit. The procedure requires no ancilla qubits and uses only $n+1$ Hadamard gates in addition to the oracle call. The promise is intrinsically quantum, since the two cases differ only in their relative-phase structure and therefore have no direct classical counterpart in the usual black-box model. |
| title | Deterministic Discrimination of Phase-Modified Permutation Oracles via Single Qubit Measurement |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.07756 |