Related papers: Quantum discord for the general two-qubit case
The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlation more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010)…
The dynamics of a geometric measure of the quantum discord (GMQD) under decoherence is investigated. We show that the GMQD of a two-qubit state can be alternatively obtained through the singular values of a $3\times4$ matrix whose elements…
We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous…
Quantum discord is a measure of the quantumness of correlations. After reviewing its different versions and properties, we apply it to the questions of quantum information processing. First we show that changes in discord in the processed…
A new measure based on the tripartite information diagram is proposed for identifying quantum discord in tripartite systems. The proposed measure generalizes the mutual information underlying discord from bipartite to tripartite systems,…
Quantum metrology exploits quantum mechanical laws to improve the precision in estimating technologically relevant parameters such as phase, frequency, or magnetic fields. Probe states are usually tailored on the particular dynamics whose…
In the present paper, a general theory for the second-order matrix difference equation of bilateral type is discussed. We introduced the matrix $q$-Kummer equation of bilateral type and presented the $q$-Kummer matrix function as a series…
Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero.…
We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…
Quantum discord quantifies non-classical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible…
It has been proven that the quantum discord is a more general tool to capture non-classical correlation than quantum entanglement, because there is a non-zero quantum discord in several mixed states that could not be measured by quantum…
We study the relationship between the behavior of global quantum correlations and quantum phase transitions in XY model. We find that the two kinds of phase transitions in the studied model can be characterized by the features of global…
By using the Choi-Jamio{\l}kowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched R\'{e}nyi relative entropy. Elegant properties of the…
The minimal Bures distance of a quantum state of a bipartite system AB to the set of classical states for subsystem A defines a geometric measure of quantum discord. When A is a qubit, we show that this geometric quantum discord is given in…
Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. Cai, Miyake, D\"ur, and Briegel recently constructed a ground state of a…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
The quantum channel-state duality permits the characterization of a quantum process through a quantum state, referred to as a Choi state. This characteristic serves as the impetus for the quantum computing paradigm that utilizes Choi states…
It is demonstrated that quasi-exactly solvable models of quantum mechanics admit an interesting duality transformation which changes the form of their potentials and inverts the sign of all the exactly calculable energy levels. This…
In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the…