Lossless Quantum Data Compression and Quantum Kolmogorov Complexity

Rogers, Caroline; Nagarajan, Rajagopal

doi:10.1142/s0219749911007848

Cited by 2 publications

(1 citation statement)

References 23 publications

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“…In application, quantum Kolmogorov complexities have been used. Until now, quantum Kolmogorov complexities have some applications, including communication complexity theory [22], quantum key distribution (QKD) [23], bounded quantum memory [24] and quantum data compression [25].…”

Section: Quantum Kolmogorov Complexity and Quantum Information Distancementioning

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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Section: Quantum Kolmogorov Complexity and Quantum Information Distancementioning

confidence: 99%

Second quantised information distance

Dai

2022

IET Quantum Communication

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Quantum information distance

Dai

2021

Int. J. Quantum Inform.

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In this paper, we give a definition for quantum information distance. In the classical setting, information distance between two classical strings is developed based on classical Kolmogorov complexity. It is defined as the length of a shortest transition program between these two strings in a universal Turing machine. We define the quantum information distance based on Berthiaume et al.’s quantum Kolmogorov complexity. The quantum information distance between qubit strings is defined as the length of the shortest quantum transition program between these two qubit strings in a universal quantum Turing machine. We show that our definition of quantum information distance is invariant under the choice of the underlying quantum Turing machine.

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Lossless Quantum Data Compression and Quantum Kolmogorov Complexity

Cited by 2 publications

References 23 publications

Second quantised information distance

Second quantised information distance

Quantum information distance

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