Exact mean and variance of the squared Hellinger distance for random density matrices
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913513017966592 |
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| author | Kumar, Vinay Vasan, Kaushik Kumar, Santosh |
| author_facet | Kumar, Vinay Vasan, Kaushik Kumar, Santosh |
| contents | The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these properties. In this work, we derive the mean and variance of the Hellinger distance between pairs of density matrices, where one or both matrices are random. Along the way, we also obtain exact results for the mean affinity and mean square affinity. The first two cumulants of the Hellinger distance allow us to propose an approximation for the corresponding probability density function based on the gamma distribution. Our analytical results are corroborated through Monte Carlo simulations, showing excellent agreement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_14560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact mean and variance of the squared Hellinger distance for random density matrices Kumar, Vinay Vasan, Kaushik Kumar, Santosh Quantum Physics Information Theory Mathematical Physics Chaotic Dynamics 94A15, 62B10, 81P47, 60B20, 15B52 The Hellinger distance between quantum states is a significant measure in quantum information theory, known for its Riemannian and monotonic properties. It is also easier to compute than the Bures distance, another measure that shares these properties. In this work, we derive the mean and variance of the Hellinger distance between pairs of density matrices, where one or both matrices are random. Along the way, we also obtain exact results for the mean affinity and mean square affinity. The first two cumulants of the Hellinger distance allow us to propose an approximation for the corresponding probability density function based on the gamma distribution. Our analytical results are corroborated through Monte Carlo simulations, showing excellent agreement. |
| title | Exact mean and variance of the squared Hellinger distance for random density matrices |
| topic | Quantum Physics Information Theory Mathematical Physics Chaotic Dynamics 94A15, 62B10, 81P47, 60B20, 15B52 |
| url | https://arxiv.org/abs/2409.14560 |