[Paper Review] How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation

Seid Koudia, Angela Sara Cacciapuoti+2 more|arXiv (Cornell University)|Aug 16, 2021

Quantum Information and CryptographyComputer Science160 references45 citations

TL;DR

This treatise provides a comprehensive, communication engineering-focused overview of non-classical quantum channel phenomena—superadditivity, superactivation, and causal activation—demonstrating how entanglement and indefinite causal order can dramatically enhance quantum communication capacity beyond classical limits. The paper establishes that quantum channel capacity is fundamentally non-additive and context-dependent, with key results showing that zero-capacity channels can transmit information when used in superposition or entangled configurations.

ABSTRACT

In the theory of quantum communications, a deeper structure has been recently unveiled, showing that the capacity does not completely characterize the channel ability to transmit information due to phenomena -- namely, superadditivity, superactivation and causal activation -- with no counterpart in the classical world. Although how deep goes this structure is yet to be fully uncovered, it is crucial for the communication engineering community to own the implications of these phenomena for understanding and deriving the fundamental limits of communications. Hence, the aim of this treatise is to shed light on these phenomena by providing the reader with an easy access and guide towards the relevant literature and the prominent results from a communication engineering perspective.

Motivation & Objective

• To clarify the fundamental role of quantum entanglement and indefinite causal order in enhancing quantum communication capacity.
• To bridge the gap between quantum information theory and communication engineering by translating abstract quantum phenomena into practical implications.
• To provide researchers with a guided entry point to the literature on superadditivity, superactivation, and causal activation.
• To demonstrate that quantum channel capacity is not additive and depends critically on the context of channel usage.

Proposed method

• Uses the isometric extension of quantum channels to model the joint evolution of system, receiver, and environment, enabling analysis of coherent and complementary information flows.
• Applies the Holevo information χ({px, ρx}, N) as an upper bound on classical information transfer, and coherent information Ic(ρ, N) as a measure of quantum information flow.
• Employs the quantum switch as a supermap to implement indefinite causal order, allowing channels to be placed in a quantum superposition of orders.
• Analyzes the entropy of exchange S(E) = S(N^c(ρ)) to quantify information leakage to the environment.
• Applies data processing inequalities to show that both Holevo and coherent information satisfy bottleneck constraints under sequential channel composition.
• Uses the code rate R = k/n to define achievable communication rates, with error probability vanishing as n → ∞.

Experimental results

Research questions

• RQ1 How does entanglement enable superadditivity, where the total capacity of multiple channel uses exceeds the sum of individual capacities?
• RQ2 Can zero-capacity quantum channels transmit information when used together in an entangled input state, and if so, under what conditions?
• RQ3 What role does indefinite causal order—realized via the quantum switch—play in enabling information transfer through channels that are classically incapable?
• RQ4 How do the coherent information Ic(ρ, N) and the entropy of exchange S(E) relate to the fundamental limits of quantum communication?
• RQ5 To what extent do quantum phenomena like superactivation and causal activation violate classical additivity and causality assumptions?

Key findings

• Superadditivity enables the total classical capacity of n channel uses to exceed n times the single-use capacity, demonstrating non-additivity of quantum channel capacity.
• Superactivation allows two zero-capacity channels to jointly transmit classical information when used with entangled inputs, proving that quantum capacity is strongly non-additive.
• Causal activation enables non-zero classical capacity through zero-capacity channels when placed in a quantum superposition of causal orders via the quantum switch.
• The coherent information Ic(ρ, N) = S(B) − S(E) can be negative, indicating that the sender and receiver can gain a potential for future quantum communication.
• The Holevo information χ({px, ρx}, N) provides an upper bound on classical mutual information, and is maximized over input ensembles to determine the channel's classical capacity.
• The data processing inequality f(ρ, M ◦ N) ≤ min{f(ρ, M), f(ρ, N)} holds for both Holevo and coherent information, showing that information cannot increase under sequential channel use.