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arXiv:2405.08568 · International Journal of Quantum Information

Generating quantum dissonance via local operations

Gökhan Torun

Published Jul 19, 2024• 1 citation
arXivHTMLPDF

Abstract

Correlations may arise in quantum systems through various means, of which the most remarkable one is quantum entanglement. Additionally, there are systems that exhibit nonclassical correlations even in the absence of entanglement. Quantum dissonance refers to how Quantum Discord (QD) — the difference between the total correlation and the classical correlation in a given quantum state — appears as a nonclassical correlation in a system without entanglement. It could be said that QD has the potential to provide a more inclusive viewpoint for discerning the nonclassical correlations. In this paper, we address the problem of manipulating the QD between two subsystems through local operations. We propose two explicit procedures for obtaining separable Werner states, a type of mixed state with nonzero QD. Both approaches involve performing local operations on classically correlated states and offers a step-by-step method for obtaining separable Werner states with nonzero discord, providing an alternative (explicit and user-friendly) to existing methods.

DOI
10.1142/s0219749924500448

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Correlations may arise in quantum systems through various means, of which the most remarkable one is quantum entanglement. Additionally, there are systems that exhibit nonclassical correlations even in the absence of entanglement. Quantum dissonance refers to how Quantum Discord (QD) — the difference between the total correlation and the classical correlation in a given quantum state — appears as a nonclassical correlation in a system without entanglement. It could be said that QD has the potential to provide a more inclusive viewpoint for discerning the nonclassical correlations. In this paper, we address the problem of manipulating the QD between two subsystems through local operations. We propose two explicit procedures for obtaining separable Werner states, a type of mixed state with nonzero QD. Both approaches involve performing local operations on classically correlated states and offers a step-by-step method for obtaining separable Werner states with nonzero discord, providing an alternative (explicit and user-friendly) to existing methods.
Quantum discord measures the fraction of the pair-wise mutual information that is locally inaccessible in a multipartite system. Nonzero quantum discord has interesting and significant applications because although non-zero entanglement guarantees the existence of quantum correlation in a bipartite quantum system, zero entanglement does not guarantee the absence of a quantum correlation. On the other hand, many quantum optics systems can be described as deformed quantum oscillators. In this work, we investigate the quantum discord of bipartite entangled nonlinear coherent states, in the context of the so-called f-deformed coherent states algebra. To calculate the quantum discord, we consider quasi- Werner mixed states bases on bipartite entangled f-deformed coherent states. Two explicit analytic expressions are derived for the quantum discord of two different nonlinear deformed coherent states. The first one considers deformed coherent states obtained as eigenstates of the annihilation deformed operator, and the second one is obtained by using a deformed displacement operator. We compare the quantum discord of those states, when the nonlinear deformation function is either associated with the SU(1,1) coherent states in the Gilmore-Perelomov or Barut-Girardello representations, respectively.
Quantum systems in mixed states can be unentangled and yet still nonclassically correlated. These correlations can be quantified by the quantum discord and might provide a resource for quantum information processing tasks. By precisely controlling the interaction of two ionic qubits with their environment, we investigate the capability of noise to generate discord. Firstly, we show that noise acting on only one quantum system can generate discord between two. States generated in this way are restricted in terms of the rank of their correlation matrix. Secondly, we show that classically correlated noise processes are capable of generating a much broader range of discordant states with correlation matrices of any rank. Our results show that noise processes prevalent in many physical systems can automatically generate nonclassical correlations and highlight fundamental differences between discord and entanglement.
The relation between genuine multipartite entanglement in the pure state of a collection of NNN qubits and the nonclassical correlations in its two-qubit subsystems is studied. Quantum discord is used as the quantifier of nonclassical correlations in the subsystem while the generalized geometric measure [A. Sen(De) and U. Sen, Phys. Rev. A 81, 012308 (2010)] is used to quantify global entanglement in the NNN-qubit state. While no definite discernible dependence between the two can be found for randomly generated global states, for those with additional structure like weighted graph states we find that local discord is indicative of global multipartite entanglement. Global states that admit efficient classical descriptions like stabilizer states furnish an exception in which, despite multipartite entanglement, nonclassical correlation is absent in two-qubit subsystems. We discuss these results in the context of mixed state quantum computation where nonclassical correlation is considered a candidate resource that enables exponential speedup over classical computers.
We give a pedagogical introduction to quantum discord and discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy. This allows us to put all correlations on an equal footing. Entanglement and dissonance jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We finally show, using relative entropy, how different notions of quantum correlations are related to each other. This gives a single theory that incorporates all correlations, quantum and classical, and different methods of quantifying them.
We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.
Measurements of quantum systems disturb their states. To quantify this nonclassical characteristic, Zurek and Ollivier [Phys. Rev. Lett. 88, 017901 (2001)] introduced the quantum discord, a quantum correlation that can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers the exponential speed-up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy. We also identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.