The classical-quantum boundary for correlations: discord and related measures (1112.6238v3)

Abstract: One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more actively-studied topics of quantum information theory over the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassical behavior too. Thus distinguishing quantum correlations other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half, we review the mathematical properties of the measures of quantum correlations, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures identify and quantify the deviation from classicality in various quantum-information-processing tasks, quantum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.

• The paper demonstrates that quantum discord quantifies nonclassical correlations beyond entanglement by contrasting entropic and measurement-based mutual information.
• It provides rigorous numerical analysis and formal proofs showing that discord resists decoherence unlike entanglement, as evidenced in quantum computational models like DQC1.
• The study implies that measures such as quantum deficit and MID offer deeper insights into quantum correlations, promising advancements in quantum information processing.

Overview of "The Classical-Quantum Boundary for Correlations: Discord and Related Measures"

The paper "The Classical-Quantum Boundary for Correlations: Discord and Related Measures" by Modi et al. offers a comprehensive examination of quantum correlations beyond entanglement, focusing on the concept of quantum discord. The authors review various notions and mathematical measures of quantum and classical correlations, emphasizing discord as an insightful metric distinct from entanglement. This exploration aims to delineate the subtle boundary between classical and quantum realms, particularly when considering mixed quantum states.

Key Concepts and Measures

Quantum discord emerges as a crucial measure, capturing nonclassical correlations in quantum systems that entanglement does not fully encapsulate. While entanglement has traditionally been seen as pivotal for quantum advantage, non-entangled states can still exhibit significant nonclassical properties measured by discord. Discord quantifies the difference between two expressions of mutual information: one based on a straightforward entropic definition and the other conditional upon a measurement outcome.

The paper also introduces several related measures, such as quantum deficit, measurement-induced disturbance (MID), and relative entropy of discord, each offering different insights into quantum correlations. These measures highlight the persistence of quantum properties even when entanglement is absent.

Strong Results and Claims

The authors provide clear numerical results and formal proofs supporting their claims, particularly around the robustness of discord under decoherence and its role in quantum information processing tasks. For instance, the paper shows that discord does not exhibit "sudden death" under decoherence, a contrast to entanglement's vulnerability. Additionally, in quantum computations, discord might underlie the observed advantages over classical approaches, such as in the DQC1 model, thereby challenging the notion that entanglement is the only resource for quantum computation.

Theoretical and Practical Implications

The theoretical implications of the research explore the fundamental understanding of quantum vs. classical systems, leading to deeper insights into quantum measurement theory, quantum thermodynamics, and quantum information. Practically, understanding discord and related measures could lead to enhanced quantum computation models that leverage these nonclassical correlations more effectively than traditional entanglement-focused strategies.

Future Directions

Speculating on future developments, the role of quantum discord in quantum technologies remains a fertile area of exploration. The potential for discord to serve as a resource in quantum communications and computing, particularly in scenarios with mixed states or limited entanglement, is promising. Further research could establish stronger operational links, enhancing quantum algorithm efficiency and robustness.

In conclusion, the paper presents a detailed and systematic analysis of quantum discord and related measures, broadening the understanding of quantum correlations beyond entanglement. This work not only refines the conceptual boundary between classical and quantum systems but also opens new avenues for utilizing quantum correlations in technology.