[Paper Review] Reduction of correlations by quantum indefinite causal structure

Ding Jia|arXiv (Cornell University)|Jun 6, 2018

Noncommutative and Quantum Gravity Theories3 references3 citations

TL;DR

This paper proposes that quantum indefinite causal structure generically reduces two-party quantum correlations, offering a model-independent ultraviolet (UV) regularization mechanism in quantum gravity. Using the process matrix formalism, it proves that under specific conditions—such as symmetric causal relations and strong environmental correlations—correlations (quantified by coherent information) are reduced to zero, implying a natural suppression of short-distance divergences without relying on classical spacetime or specific microscopic models.

ABSTRACT

We show that quantum indefinite causal structure generically reduce two-party correlations. For significant indefiniteness in the causal structure captured by some general conditions, the correlation is shown to be reduced down to zero. The result offers an operational model-independent ultraviolet regularization mechanism. It may be applied to various approaches of quantum gravity that allow quantum indefinite spacetime causal structure.

Motivation & Objective

• To address the challenge of ultraviolet (UV) divergences in quantum field theory without relying on classical spacetime or specific quantum gravity models.
• To investigate whether quantum indefinite causal structure can serve as a generic, operational mechanism for UV regularization.
• To identify general conditions under which indefinite causal structure reduces quantum correlations, particularly using coherent information as a measure.
• To develop a framework independent of background spacetime, microscopic spacetime structure, or modified propagators.
• To establish a connection between quantum gravity effects and the suppression of field correlations at short distances.

Proposed method

• Employing the process matrix formalism to describe correlations in scenarios with indefinite causal order, treating local operations as standard quantum operations.
• Using the purified density operator of the process matrix to derive entropic constraints via strong subadditivity (SSA) and normalization conditions.
• Applying the coherent information measure $ I^B(W^{AB}) = S^B - S^{AB} $ to quantify correlations, with negative values indicating quantum correlations.
• Deriving upper bounds on coherent information using entropic inequalities, particularly $ S^{a_1b_2} ightarrow S^{b_1e_1} $ and $ S^{b_1} ightarrow S^{e_1} $, under symmetry and purity assumptions.
• Utilizing the complementarity of subsystems (e.g., $ e = e_1 ar{e} $) to apply strong subadditivity and tighten bounds on the coherent information.
• Demonstrating that under symmetric and balanced causal conditions, the coherent information is bounded above by zero, implying vanishing quantum correlations.

Experimental results

Research questions

• RQ1 Can quantum indefinite causal structure serve as a generic, model-independent mechanism for ultraviolet regularization in quantum field theory?
• RQ2 Under what conditions does indefinite causal structure reduce two-party quantum correlations to zero?
• RQ3 Can the process matrix framework describe correlations in quantum gravity scenarios without assuming a classical spacetime background?
• RQ4 Is the reduction of correlations by indefinite causal structure a continuous and generic phenomenon, or limited to special cases?
• RQ5 Can local operations increase the coherent information in systems with highly indefinite causal structure, as in Theorem 7?

Key findings

• Under sufficient conditions—specifically, symmetric process matrices and strong environmental correlations ($ S^{b_1} ightarrow S^{e_1} $, $ S^{a_1b_2} ightarrow S^{b_1e_1} $)—the coherent information $ I^B(W^{AB}) $ is bounded above by zero, implying vanishing quantum correlations.
• The result is robust under continuity: correlations close to these conditions but with weaker indefinite causal structure are also suppressed, indicating a generic reduction effect.
• The process matrix formalism allows a background-independent, operational description of correlations, avoiding assumptions about classical spacetime or specific quantum gravity models.
• The reduction of coherent information implies a corresponding reduction in mutual information, confirming that both quantum and classical correlations are suppressed.
• An explicit example is provided where equal amplitudes for all three causal relations (A→B, B→A, indefinite) lead to zero coherent information, confirming the bound.
• The mechanism is inherently UV-regulating: as detectors approach each other, if indefinite causal structure becomes significant, correlations are forced to zero, preventing divergences.