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Interpreting quantum discord through quantum state merging (1008.4135v2)

Published 24 Aug 2010 in quant-ph, cs.IT, and math.IT

Abstract: We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. Our interpretation has an intuitive explanation based on the strong subadditivity of von Neumann entropy. We use our result to provide operational interpretations of other quantities like the local purity and quantum deficit. Finally, we discuss in brief some instances where our interpretation is valid in the single copy scenario.

Citations (282)

Summary

  • The paper offers an operational interpretation of quantum discord by linking it to increased communication costs in the quantum state merging protocol.
  • This increased cost occurs when relevant prior correlation information, quantified by quantum discord, is neglected during the merging process.
  • This framework provides a practical understanding of quantum discord's role as a resource and its potential utility in various quantum information tasks where entanglement is not dominant.

Operational Interpretation of Quantum Discord via Quantum State Merging

This paper outlines an operational interpretation of quantum discord through the lens of the quantum state merging protocol, an essential primitive in quantum information theory. Given the lack of a widely accepted operational understanding of quantum discord, the authors' approach to relate it to the cost of quantum communication is noteworthy. They posit that neglecting relevant prior information during the state merging process results in an increased communication cost which is tied to quantum discord. This perspective relies heavily on the strong subadditivity property of von Neumann entropy.

Insights on Quantum Discord

Quantum discord, originally introduced as a measure of non-classical correlations that includes, but is not limited to, entanglement, has been pivotal in quantum information science. Unlike classical mutual information and entanglement, quantum discord remains nonzero even for some separable states, indicating quantum correlations beyond entanglement. Despite its theoretical significance, previous interpretations were primarily abstract, lacking clear connections to practical quantum information tasks. By associating quantum discord with the increased cost in quantum communication processes such as state merging, Madhok and Datta offer a pragmatic viewpoint.

Quantum State Merging and Information Theory

The quantum state merging protocol adapts the classical Slepian-Wolf protocol of distributed source coding into the quantum regime. Here, two parties, Alice and Bob, share entangled quantum states, and the protocol quantifies how much quantum information Alice needs to send Bob to achieve a single, merged quantum state at his end. The authors establish that when Alice discards prior correlation information, as denoted by quantum discord, the operational communication cost increased, underlining the utility of quantum discord in optimizing resource expenditure in quantum tasks.

Strong Subadditivity and Implications

The paper leverages strong subadditivity of entropy to argue that throwing away information increases quantum discord and, consequently, the communication cost. This perspective is insightful as it explicates why quantum discord is greater than zero and tightly links the cost of state merging to the operational definition of discord. By binding the physical process of quantum state merging with the mathematical properties of entropy, the paper provides a coherent understanding of the operational implications of discord.

Theoretical and Practical Implications

Beyond providing an operational foundation for quantum discord, the paper casts light on other related quantum information quantities like local purity and quantum deficit. It suggests practical manipulations of quantum information processes in systems where discord is present but entanglement is not predominant. As quantum technologies continue to progress, understanding the role of quantum discord in quantum computation, communication, and other processing tasks may lead to more efficient utilization of quantum resources.

Future Directions and Speculations

This research opens avenues for further exploration of quantum discord's properties across various quantum systems and protocols. It raises intriguing avenues for investigating the additivity and single-letter characteristics of discord under different operations. Additionally, examining the implications for quantum systems with more complex correlations could enrich the comprehension and utility of quantum discord in diverse quantum information protocols.

Overall, the paper provides a significant methodological step towards understanding quantum discord as a resource in quantum information science, with broad theoretical and practical implications. This interpretation not only augments the operational framework for discord but also stimulates further investigation into the utilization and manipulation of quantum correlations in a practical context.