Finite Dimensional Hilbert Spaces are Complete for Dagger Compact Closed Categories (Extended Abstract)
نویسنده
چکیده
We show that an equation follows from the axioms of dagger compact closed categories if and only if it holds in finite dimensional Hilbert spaces.
منابع مشابه
Finite dimensional Hilbert spaces are complete for dagger compact closed categories
We show that an equation follows from the axioms of dagger compact closed categories if and only if it holds in finite dimensional Hilbert spaces.
متن کاملCategories of Quantum and Classical Channels (extended abstract)
We introduce the CP*–construction on a dagger compact closed category as a generalisation of Selinger’s CPM–construction. While the latter takes a dagger compact closed category and forms its category of “abstract matrix algebras” and completely positive maps, the CP*–construction forms its category of “abstract C*-algebras” and completely positive maps. This analogy is justified by the case of...
متن کاملIdempotents in Dagger Categories: (Extended Abstract)
Dagger compact closed categories were studied by Abramsky and Coecke (under the name “strongly compact closed categories”) as an abstract presentation of the category of Hilbert spaces and linear maps, and as a framework in which to carry out the interpretation of quantum protocols. I subsequently showed that dagger compact closed categories can also describe mixed quantum computation, where th...
متن کاملDagger Compact Closed Categories and Completely Positive Maps: (Extended Abstract)
Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name “strongly compact closed categories”, as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch a proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each...
متن کاملQuantum Turing automata
A denotational semantics of quantum Turing machines having a quantum control is defined in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore-Penrose generalized inverse, a new additive trace is introduced on the restriction of this category to isometries, which trace is carried over to directed quantum Turing machines as monoidal automata. The JoyalStreet-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 270 شماره
صفحات -
تاریخ انتشار 2011