Quantum information distance based on classical descriptions

Dai, Songsong

doi:10.1007/s42484-022-00064-2

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2022

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“…Berthiaume et al [6] defined the quantum Kolmogorov complexity of a state as the length of its shortest quantum description. Building upon their quantum Kolmogorov complexities [5,6], Dai [7,8] developed two quantum information distances, which are, respectively, based on classical and quantum descriptions. However, some quantum states have indeterminate lengths because of their superposition.…”

Section: Introductionmentioning

confidence: 99%

Second quantised information distance

Dai

2022

IET Quantum Communication

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The Kolmogorov complexity of a string is the minimum length of a programme that can produce that string. Information distance between two strings based on Kolmogorov complexity is defined as the minimum length of a programme that can transform either string into the other one, both ways. The second quantised Kolmogorov complexity of a quantum state is the minimum average length of a quantum programme that can reproduce that state. In this paper, a second quantised information distance is defined based on the second quantised Kolmogorov complexity. It is described as the minimum average length of a transformation quantum programme between two quantum states. This distance's basic properties are discussed. A practical analogue of quantum information distance is also developed based on quantum data compression.

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