Approximate quasi-orthogonality of operator algebras and relative quantum privacy

نویسندگان

چکیده

We show that the approximate quasi-orthogonality of two operator algebras is equivalent to being approximately private relative their conditional expectation quantum channels. Our analysis based on a characterization measure orthogonality in terms Choi matrices and Kraus operators for completely positive maps. present examples drawn from different areas information.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Approximate Birkhoff-James Orthogonality and Approximate $ast$-orthogonality in $C^ast$-algebras

We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary  $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.

متن کامل

Linear Orthogonality Preservers of Standard Operator Algebras

In 2003, Araujo and Jarosz showed that every bijective linear map θ : A → B between unital standard operator algebras preserving zero products in two ways is a scalar multiple of an inner automorphism. Later in 2007, Zhao and Hou showed that similar results hold if both A,B are unital standard algebras on Hilbert spaces and θ preserves range or domain orthogonality. In particular, such maps are...

متن کامل

Expanding Quasi-MV Algebras by a Quantum Operator

We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety p 0QMV of such p 0 quasi-MV algebras has a subquasivariety whose members called cartesian can be obtained in an appropriate way out of MV algebras. After showing that cartesian p 0 quasi-MV algebras generate p 0QMV, we prove a standard completeness theorem for p 0QMV w.r.t. an algebra over t...

متن کامل

Commutative Quantum Operator Algebras

A key notion bridging the gap between quantum operator algebras [22] and vertex operator algebras [4][8] is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. The main purpose of the current paper is to begin laying the foundations for a co...

متن کامل

On Quantum and Approximate Privacy

This paper studies privacy and secure function evaluation in communication complexity. The focus is on quantum versions of the model and on protocols with only approximate privacy against honest players. We show that the privacy loss (the minimum divulged information) in computing a function can be decreased exponentially by using quantum protocols, while the class of privately computable funct...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Reports on Mathematical Physics

سال: 2021

ISSN: ['0034-4877', '1879-0674']

DOI: https://doi.org/10.1016/s0034-4877(21)00024-0