The quantum power of general quantum correlations and QUDIT systems

Margarita A. Man’ko, Vladimir I. Man’ko

Igor Ya. Doskoch, Margarita A. Man’ko

Xiaoguang Wang, Barry C. Sanders, Dominic William Berry

We establish the entangling power of a unitary operator on a general finite-dimensional bipartite quantum system with and without ancillas, and give relations between the entangling power based on the von Neumann entropy and the entangling power based on the linear entropy. Significantly, we demonstrate that the entangling power of a general controlled unitary operator acting on two equal-dimensional qudits is proportional to the corresponding operator entanglement if linear entropy is adopted as the quantity representing the degree of entanglement. We discuss the entangling power and operator entanglement of three representative quantum gates on qudits: the SUM, double SUM, and SWAP gates.

Andrzej Frydryszak, Lech Jakóbczyk, Piotr Ługiewicz

We advocate the step change in properties of discrete d -level quantum systems, between d = 2 and d ≥ 3. Qubit systems, or multipartite systems containing qubit subsystem, are exceptional in their relative simplicity. One faces a step in complexity in valuating measures of quantum correlations for qutrits and then other higher dimensional qudits. There is a growing number of arguments leading to such conclusion: recently found no-go theorem for generalization of the Peres-Horodecki's PPT criterion [1], change in geometry of state spaces of qubit and higher degree qudits (the so called 'generalized Bloch ball' is not a ball anymore), restricted possibilities for diagonalization of correlation matrices for bipartite systems, more difficult way for handling the set of relevant families of orthogonal projectors.

Himadri Shekhar Dhar, Amit Kumar Pal, Debraj Rakshit +2 more

Ibrahim Saideh, A. D. Ribeiro, Giulia Ferrini +3 more

We present a general strategy to derive entanglement criteria through a dichotomization procedure which consists of performing a mapping from qudits to qubits that preserves the separability of the parties and the SU(2) rotational invariance. Consequently, it is possible to apply the well-known positive partial transpose criterion to reveal the existence of quantum correlations between qudits. We discuss some examples of entangled states that are detected using the proposed strategy. Finally, we demonstrate, using our scheme, how some variance-based entanglement witnesses can be generalized from qubits to higher dimensional spin systems.