SESSION 2: Information theory and quantum communicationChair: (Philippe Faist (California Institute of Technology))
|Graeme Smith, University of Colorado Boulder
Progress on the quantum channel capacity problems
|Abstract. I will review what we know about the communication capacities of quantum channels, and give a flavor for why this problem is so challenging. I will also present some recent progress that allows us to tame low-noise channels, and gain new insights into high-noise channels.
|Patrick Coles, Los Alamos National Laboratory
Reliable numerical key rates for quantum key distribution
|Abstract. The holy grail of quantum key distribution (QKD) theory is a robust, quantitative method to explore novel protocol ideas and to investigate the effects of device imperfections on the key rate. We argue that numerical methods are superior to analytical ones for this purpose. However, new challenges arise with numerical approaches, including the efficiency (i.e., possibly long computation times) and reliability of the calculation. In this work, we present a reliable, efficient, and tight numerical method for calculating key rates for finite-dimensional QKD protocols. We illustrate our approach by finding higher key rates than those previously reported in the literature for several interesting scenarios (e.g., the Trojan-horse attack and the phase-coherent BB84 protocol). Our method will ultimately improve our ability to automate key rate calculations and, hence, to develop a user-friendly software package that could be used widely by QKD researchers.
|Kaushik Seshadreesan, University of Arizona
Renyi relative entropies of quantum Gaussian states
|Abstract. The quantum Rényi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory. On a different thread, quantum Gaussian states have been intensely investigated theoretically, motivated by the fact that they are more readily accessible in the laboratory than are other, more exotic quantum states. In this talk, we discuss the derivation of formulas for the quantum Rényi relative entropies of quantum Gaussian states. We consider both the traditional (Petz) Rényi relative entropy as well as the more recent sandwiched Rényi relative entropy, finding formulas that are expressed solely in terms of the mean vectors and covariance matrices of the underlying quantum Gaussian states. Our development handles the hitherto elusive case for the Petz-Rényi relative entropy when the Rényi parameter is larger than one. Finally, we also derive a formula for the max-relative entropy of two quantum Gaussian states, and we discuss some applications of the formulas derived here.
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