Related papers: Implementing positive maps with multiple copies of…
Continuity properties of the output entropy of positive linear maps between Banach spaces of trace class operators are investigated with the special attention to the classes of quantum channels and operations. It is shown that finiteness of…
Comparison of statistical models (experiments) is an important branch of mathematical statistics, which gives deep insights in many aspects of foundation of statistics. So far, there are two quantum versions of the concept: Comparison with…
We consider complete positivity of dynamics regarding subsystems of an open composite quantum system, which is subject of a completely positive dynamics. By "completely positive dynamics", we assume the dynamical maps called the completely…
Quantum entanglement is essential to the development of quantum computation, communications, and technology. The controlled SWAP test, widely used for state comparison, can be adapted to an efficient and useful test for entanglement of a…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
We study the problem of quantum-state tomography under the assumption that the state of the system is close to pure. In this context, an efficient measurements that one typically formulates uniquely identify a pure state from within the set…
We construct entangled states with positive partial transposes using indecomposable positive linear maps between matrix algebras. We also exhibit concrete examples of entangled states with positive partial transposes arising in this way,…
The constraints imposed by the initial system-environment correlation can lead to nonpositive Dynamical maps. We find the conditions for positivity and complete positivity of such dynamical maps by using the concept of an assignment map.…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…
The common wisdom in the field of quantum information theory is that when a system is initially correlated with its environment, the map describing its evolution may fail to be completely positive. If true, this would have practical and…
Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of…
We show that quantum designs characterize the general structure of the optimal approximation of the transpose map on quantum states. Based on this characterization, we propose an implementation of the approximate transpose map by a…
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of…
We consider the quantum memory assisted quantum state verification task, where an adversary prepare independent multipartite entangled states and send to the local verifiers, who then store several copies in the quantum memory and measure…
Entanglement plays a central role in quantum information processing, indicating the non-local correlation of quantum matters. However, few effective ways are known to detect the amount of entanglement of an unknown quantum state. In this…
Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N- qubit state and linear entropy of reduced single qubit…
We provide necessary and sufficient conditions for separability of mixed states of n-particle systems. The conditions are formulated in terms of maps which are positive on product states of $n-1$ particles. The method of providing of the…
Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on…
We study the problem of universal quantum cloning -- taking several identical copies of a pure but unknown quantum state and producing further copies. While it is well known that it is impossible to perfectly reproduce the state, how well…
In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…