/Contents 3 0 R Diss. A representative example of such tools is the quantum de Finetti theorem [2], which tells us that one part of a symmetric state can be treated as a mixture of identically prepared quantum states that have no correlation between the parties. 13 0 obj << Beyond polar codes, we have recently shown how to extend the standard classical 'belief propagation' decoding algorithm to the quantum domain in specific instances [9], and how to employ efficient input 'constellations' for classical Gaussian channels to construct similarly efficient quantum codes for quantum Gaussian channels [10]. The mathematical theory of infor-mation and information processing dates to the mid-twentieth century. Quantum state tomography is the task of estimating an unknown quantum state from some measurement data, which is an essential element of current research in quantum information processing. /Filter /FlateDecode /Type /Page Combined with the quantum de Finetti theorem, such protocols enable efficient storage of a broad range of quantum states. 2 0 obj << More precisely, if we lose part of a multipartite state that has the approximate Markov structure, we can reconstruct the lost system with a recovery map that acts only locally on a small system [2]. >> xڍXM��F�ϯ�-2+����L'Y`� ��b'@ʲ�.���Hrg�߇�d�#�� ��*�E>>���&��X�U�����~J��!���eSD���Q�������� �8LO�߶�=�뻟hzZmvY��+��&yА���v�����,�'a��L�wYR�ۀ�FZW�5��d�m�v��A���t�����׫׼Z����m���ͤ�[��K�G���[�M�ؼ�J�^i��U5͕�X�T���6��mvz�]���B�Z����X��i��-�޴�C/&e������D�>I�q��,��أ;���c��Iӈĭ�;�#܋Z�{t:�2Xa]G�Ic�wʕ���Q'�ʳh/"�F� &؁�����nG��^�X��ժ�%��1��+/qoiw�a=���>�i��hFV:��4�86�A]�q�i�,-#,x�pD���'��C�' �!v� �c�^�~�p�7������܆�6����� %����C�O* David Sutter, Omar Fawzi and Renato Renner. We also developed optimal compression protocols for identically prepared quantum states [3]. It is therefore natural to ask what information-processing possibilities quantum-mechanical laws offer. ETH No. We use cookies on this site to enhance your user experience. They are characterized by the property that the conditional mutual information (CMI), an entropic quantity, vanishes. 20213 A Framework for Non-Asymptotic Quantum Information Theory A dissertation submitted to ETH ZURICH for the degree of Doctor of Sciences presented by Marco Tomamichel Dipl. Universal recovery map for approximate Markov chains. Following these seminal works, we seek to refine and extent the quantum de Finetti theorem and to apply it to various fields including cryptography, metrology, computation, and communication. Joseph M. Renes and Jean-Christian Boileau. Felipe Lacerda, Joseph M. Renes and Volkher B. Scholz, Civil, Environmental and Geomatic Engineering, Humanities, Social and Political Sciences, Information Technology and Electrical Engineering. /MediaBox [0 0 612 792] This partly entails developing new uncertainty relations. Quantum mechanics enables new phenomena, such as systems that can not only be in a state zero or one, but also in a superposition of the two. By clicking any link on this page you are giving your consent for us to set cookies. 3 0 obj << %PDF-1.4 National Centre of Competence in Research (NCCR) Quantum Science and Technology (QSIT), Eidgenössische In turn, this tool enables simple device-independent security proofs [2]. Here the connection to the uncertainty principle enables us to convert high-performance classical protocols to high-performance quantum protocols. ,�-��3�n�(c \�(���3E�w�E D�L�J14��5h��Z��ɻ�Hz3��XpB}�y���2̊l�}���R�;�D�����,�[#��0~d�p�&'*U@b�S�6���2�ԽQ����V!�"`t��h|��ߊ3?��/?zַQi������'b�ŭ#N��-V � �E�t1]W7����2L�xA��:V`50�xp�!|��E��%��\��v`׃������ܔ�Y*�ޛnh�e�y�.cFv�^���ʂ+�c��gl;�0�x���ӋW���Y�(JiZ���V��>���8S�V$��5��G�*0P��l'��o��� Yuxiang Yang, Giulio Chiribella, and Masahito Hayashi, Frederic Dupuis, Omar Fawzi and Renato Renner, Rotem Arnon-Friedman, Renato Renner and Thomas Vidick. This feature enables us to connect the concepts of Markov chains with the theory of quantum error correction. ‪Faculty of Engineering and Centre for Quantum Technologies, National University of Singapore‬ - ‪Cited by 5,326‬ - ‪Quantum Information‬ - ‪Information Theory‬ - ‪Quantum Cryptography‬ - ‪CQT‬ ETH born March 13, 1981, in St. Gallen citizen of Bosco Gurin, TI, Switzerland accepted on the recommendation of Prof. Dr. Renato Renner, examiner Matthias Christandl, Robert Koenig, Graeme Mitchison and Renato Renner, Yuxiang Yang, Ge Bai, Giulio Chiribella, Masahito Hayashi. strategies. Jinzhao Wang, Volkher B. Scholz and Renato Renner, Quantum information processing and uncertainty relations. The goal of this course is to provide a solid understanding of the mathematical foundations of quantum information theory, with which we can then examine some of the counterintuitive phe-nomena in more detail. 28 (2018). /Length 588 The EAT ensures that the operationally relevant quantities of a multiparty system (the smooth min-and max-entropies) can be bounded by the sum of the von Neumann entropies of its individual parts viewed in a worst-case scenario. Quantum information processing is constrained by the uncertainty principle. Systems with permutation symmetry are prevalent in physics. The connection to classical codes via the uncertainty principle also leads to insight into the structure of classical polar codes [8]. stream Theoretically, it amounts to constructing an estimator using only the data from measurements on a finite number of copies of a state. Technische Hochschule Zürich. /ProcSet [ /PDF /Text ] We explore various aspects of quantum information theory, with implications for both our fundamental understanding of the laws of quantum physics and their technological uses. In: Approximate Quantum Markov Chains. Joseph M. Renes, Frederic Dupuis and Renato Renner. Current research efforts aim to generalize this result and applying it to areas beyond quantum cryptography. Matthias Christandl, Robert König and Renato Renner. xڅSMo�@��Wp�l؅�Bom�Tn��VPzhz�۴|X�H��|�����Ha=���͛�R('�?9~�z�>�]ݪ�ID2�t�H���������j�/T�j���]6ϗn�yҭ3��m8w����h����~���'p-����H���������0t?Wi=e�ֈ����(ǗZ$�}����豶&T�n�� �U��$���qw�+�����m�L����ۑA ���ܔ�t5�m��Q�C쎏�8�$�p䚕!Z�Hy3q��O��Y�.��a\n �g�!�MŴ�G�"4�|����Q�mH���~j7�li�8ؑ+��ԃݟ����j��OJ)�0�C��cj����-TL!�ء:m�-aH��Ҏ���M �+l���V��`K���c #\26=�6y��NЕ�/����]䖃YC���ˣ0��J���F�)H� ���dɛ$�Rb=L����)��+�xn� �p � ��K�ӆ�W M_ڲ/&q�l�EG�u�)���]�Q꒟'����ⅲ��*s~�՗;�n���)O�2J��5�K��U�Jf�t��RI�endstream Their quantum counterpart remains the only explicitly known code family that can achieve the coherent information of arbitrary channels, and brought efficient encoding and decoding operations for high-rate codes into the quantum realm for the first time. Mario Berta, Matthias Christandl, Roger Colbeck, Joseph M. Renes and Renato Renner. /Filter /FlateDecode We have also recently discovered that the entropic uncertainty relation implies a duality between pairs of quantum channels, so that the performance of one channel (for instance, its ability to transmit information) very tightly constrains the performance of the other [3]. The group is part of the Institute for Theoretical Physics in the Department of … Our research also involves developing new ways to bound the performance of information processing protocols. /Font << /F24 6 0 R /F1 9 0 R >> Theoretically, it amounts to constructing an estimator using only the data from measurements on a finite number of copies of a state. An important direction in our research is the study and development of tools to harness symmetry in quantum information, to efficiently tackle the complexity. >> endobj Marco Tomamichel, Mario Berta and Joseph M. Renes. quantum mechanics, classical information theory is actually a (practically significant) special case of quantum information theory. Information Quantum information processing as a distinct, widely recognized field of scientific inquiry has arisen only recently, since the early 1990s. We study states that have a CMI that is non-zero but small, the so-called approximate quantum Markov chains [1]. The best example is our construction of quantum polar codes from classical polar codes [7]. More recently we have formulated error–disturbance tradeoffs for quantities that are more directly operationally relevant, which for instance implies that wave–duality relations can be understood as error-disturbance uncertainty relations [6]. Alternatively, by extending classical statistical methods to the quantum setting, we proposed a different scheme that significantly improves the error estimates of the previous method [3]. Quantum computers, by contrast, rely on a more fundamental physical theory — quantum mechanics. endobj One major difficulty in proving the security of cryptographic protocols is the fact that an adversary could utilize complicated strategies to attack the scheme. For example, we have formulated a bound on the performance of quantum error-correcting codes in terms of a semidefinite program [1], and more recently extended this technique to find tight bounds on the performance of quantum data compression [2].


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