Abstract
When analysing quantum information processing protocols, one has to deal with large entangled systems, each consisting of many subsystems. To make this analysis feasible, it is often necessary to identify some additional structures. de Finetti theorems provide such a structure for the case where certain symmetries hold. More precisely, they relate states that are invariant under permutations of subsystems to states in which the subsystems are independent of each other. This relation plays an important role in various areas, e.g., in quantum cryptography or state tomography, where permutation invariant systems are ubiquitous. The known de Finetti theorems usually refer to the internal quantum state of a system and depend on its dimension. Here, we prove a different de Finetti theorem where systems are modelled in terms of their statistics under measurements. This is necessary for a large class of applications widely considered today, such as device independent protocols, where the underlying systems and the dimensions are unknown and the entire analysis is based on the observed correlations.
Highlights
The analysis of quantum information processing protocols is a challenging task
Let it be a quantum tomography process, transmission of quantum information over a noisy channel or a cryptographic protocol – all need to be analysed under general conditions
Theorem 4, we can see how additional symmetries of the states can affect the pre-factor in the de Finetti reduction
Summary
The analysis of quantum information processing protocols is a challenging task. Let it be a quantum tomography process, transmission of quantum information over a noisy channel or a cryptographic protocol – all need to be analysed under general conditions. We are interested in a theorem that will allow us to reduce permutation invariant conditional probability distributions to a simple de Finetti-type conditional probability distribution, in a way that will be applicable in device independent protocols and, more generally, when the dimension of the underlying quantum states is unknown. As an example of an application of our theorem we prove that for protocols which are based on the violation of the CHSH and chained Bell inequalities it is sufficient to consider the case where Alice and Bob share the de Finetti state τACHB|SXHY
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
