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The information content of quantum sources

Giuilio Chiribella ( University of Oxford )

Quantum states provide information about multiple, mutually complementary observables. Such information is not accessible from a single system, but becomes accessible when multiple identically prepared systems are available. In this context, an important question is how much information is contained into a given number of copies of the same state. A rigorous way to quantify such information is through the task of quantum data compression, where the goal is to store the quantum state into the smallest number of quantum bits. The problem of compressing identically prepared systems is relevant in several areas, including the design of quantum sensors that collect data and transfer them to a central location, and the design of quantum learning machines that store patterns in their internal memory. In this talk I will characterize the minimum amount of memory needed to faithfully store sequences of identically prepared quantum states, showing how the size of the memory grows with the number of particles in the sequence. In addition, I will discuss how much quantum memory can be traded with classical memory. Finally, I will conclude by showing an application of quantum compression to high precision measurements of time and frequency. 

References for this talk:  

Yang, Yuxiang, Giulio Chiribella, and Daniel Ebler. "Efficient quantum compression for ensembles of identically prepared mixed states." Physical Review Letters 116.8 (2016): 080501.
Yang, Yuxiang, Giulio Chiribella, and Masahito Hayashi. "Optimal compression for identically prepared qubit states." Physical Review Letters 117.9 (2016): 090502.  
Yang, Y., Bai, G., Chiribella, G., & Hayashi, M. (2017). Data compression for quantum population coding. arXiv preprint arXiv:1701.03372, IEEE Transactions on Information Theory, in press. 



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