Symmetric extendibility for qudits and tolerable error rates in quantum cryptography

Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit error rates

The general conditions are discussed which quantum state purification protocols have to fulfill in order to be capable of purifying Bell-diagonal qubit-pair states, provided they consist of steps that map Bell-diagonal states to Bell-diagonal states and they finally apply a suitably chosen Calderbank-Shor-Steane code to the outcome of such steps. As a main result a necessary and a sufficient co...

Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography

The concept of asymptotic correctability of Bell-diagonal quantum states is generalised to elementary quantum systems of higher dimensions. Based on these results basic properties of quantum state purification protocols are investigated which are capable of purifying tensor products of Bell-diagonal states and which are based on B-steps of the Gottesman-Lo-type with the subsequent application o...

Symmetric extendibility for a class of qudit states

The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a...

Constructive Conjugate Codes for Quantum Error Correction and Cryptography

A conjugate code pair is defined as a pair of linear codes either of which contains the dual of the other. A conjugate code pair represents the essential structure of the corresponding Calderbank-Shor-Steane (CSS) quantum error-correcting code. It is known that conjugate code pairs are applicable to quantum cryptography. In this work, a polynomial construction of conjugate code pairs is present...

Symmetric Error Structure in Stochastic DEA