Quantum Measurements Cannot be Proved to be Random
We show that it is impossible to prove that the outcome of a quantum measurement is random.
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arXiv subjects
Caroline Rogers
Publications and source records attributed to Caroline Rogers.
Lossless Quantum Prefix Compression for Communication Channels that are Always Open
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length of a quantum string is the maximal length in the superposition). This complements work by Schumacher and Westmoreland who calculated the corresponding rate for minimizing the output's average length. Our compressed code words are prefix-free indeterminate-length quantum bit strings which can be concatenated in the case of multiple sources. Therefore, we generalize the known theory of prefix-free quantum codes to the case of strings with indeterminate length. Moreover, we describe a communication model which allows the lossless transmission of the compressed code words. The benefit of compression is then the reduction of transmission errors in the presence of noise.
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Second Quantized Kolmogorov Complexity
The Kolmogorov complexity of a string is the length of its shortest description. We define a second quantised Kolmogorov complexity where the length of a description is defined to be the average length of its superposition. We discuss this complexity's basic properties. We define the corresponding prefix complexity and show that the inequalities obeyed by this prefix complexity are also obeyed by von Neumann entropy.
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The Second Quantized Quantum Turing Machine and Kolmogorov Complexity
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two advantages to our approach - our measure of second quantized Kolmogorov complexity is closer to physical reality and unlike other quantum Kolmogorov complexities it is continuous. We give examples where second quantized and quantum Kolmogorov complexity differ.
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Quantum Bit Strings and Prefix-Free Hilbert Spaces
We give a mathematical framework for manipulating indeterminate-length quantum bit strings. In particular, we define prefixes, fragments, tensor products and concatenation of such strings of qubits, and study their properties and relationships. The results are then used to define prefix-free Hilbert spaces in a more general way than in previous work, without assuming the existence of a basis of length eigenstates. We prove a quantum analogue of the Kraft inequality, illustrate the results with some examples and discuss the relevance of prefix-free Hilbert spaces for lossless compression.
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Lossless Quantum Compression
We describe lossless quantum compression of unknown mixtures (of non-orthogonal states) and give an expression of the optimal rate of compression.
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