A Universal Quantum Certainty Relation for Arbitrary Number of Observables
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908497545789440 |
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| author | Liu, Ao-Xiang Yang, Ma-Cheng Qiao, Cong-Feng |
| author_facet | Liu, Ao-Xiang Yang, Ma-Cheng Qiao, Cong-Feng |
| contents | We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of majorization relation. While the utmost lower bound coincides with $(1/N,...,1/N)$ for any two observables with orthogonal bases, the majorization certainty relation for $M\geqslant3$ is shown to be nontrivial. The universal majorization bounds for three mutually complementary observables and a more general set of observables in dimension-2 are achieved. It is found that one cannot prepare a quantum state with probability vectors of incompatible observables spreading out arbitrarily. Moreover, we also explore the connections between quantum uncertainty and quantum coherence, and obtain a complementary relation for the quantum coherence as well, which characterizes a trade-off relation of quantum coherence with different bases and is illustrated by an explicit example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_05690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Universal Quantum Certainty Relation for Arbitrary Number of Observables Liu, Ao-Xiang Yang, Ma-Cheng Qiao, Cong-Feng Quantum Physics We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system, which provides a state-independent maximum lower bound on the direct-sum of the probability vectors in terms of majorization relation. While the utmost lower bound coincides with $(1/N,...,1/N)$ for any two observables with orthogonal bases, the majorization certainty relation for $M\geqslant3$ is shown to be nontrivial. The universal majorization bounds for three mutually complementary observables and a more general set of observables in dimension-2 are achieved. It is found that one cannot prepare a quantum state with probability vectors of incompatible observables spreading out arbitrarily. Moreover, we also explore the connections between quantum uncertainty and quantum coherence, and obtain a complementary relation for the quantum coherence as well, which characterizes a trade-off relation of quantum coherence with different bases and is illustrated by an explicit example. |
| title | A Universal Quantum Certainty Relation for Arbitrary Number of Observables |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2308.05690 |