11518

10581

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

نه، 72ص.

به فارسي و انگليسي

1395/07/17

رياضي

ID10581

Approximately Clean QuantumProbability Measures on a Hilbert space Maryam Ahmadian maryam ahmadian@math iut ac ir Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Mahmoud Manjegani manjgani@cc iut ac ir Advisor Dr Farid Bahrami fbahrami@cc iut ac ir 2010 MSC 05C80 05C90 Keywords Social Network Privacy Preserving Anonymous Graph Theory AbstractIn this thesis we present the mathematical rami cations of the notion of cleanness for positive operatorvalued measures This thesis is based on paper by Douglas Farenick Remus Floricel and Sarah Plosker 2013 A quantum system is represented by a Hilbert space H Let X be a set of measurementoutcomes for the system O X is a algebra of measurement events and B H is the space of allbounded linear operators acting on H A positive operator valued probability measure O X B H is represented a measurement of the system A quantum probability measure or quantummeasurement is said to be clean if it cannot be irreversibly connected to any other quantum probabilitymeasure via a quantum channel In this thesis we introduce a new descriptions of clean quantumprobability measures in the case of nite dimensional Hilbert space For Hilbert spaces of in nitedimension we introduce the notion of approximately clean quantum probability measures and thenwe characterise this property in the nite dimensional systems In chapter two the necessary background in operator theory is presented such as spectrum ofoperator compact operator trace class operator and tensor product operator In chapter three introduce the positive maps compeletly positive maps quantum channels quantumprobability measures and trace preserving completely positive linear maps B1 K B1 H forsome Hilbert spacesH and K The main results are presented in chapter four Theorem 4 1 1 which gives an analytic descriptionof the order relation 1 ap cl 2 for quantum probability measures and Theorem 4 1 4 which

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رسول نصراصفهاني، مهدي نعمتي