[Paper Review] Allowing leakage can increase quantum transmission

Vikesh Siddhu|arXiv (Cornell University)|Nov 30, 2020

Quantum Mechanics and Applications85 references4 citations

TL;DR

This paper demonstrates that intentionally leaking nearly all quantum information to the environment can increase a quantum channel's capacity to transmit entanglement, defying the conventional belief that noise destroys entanglement. By exploiting two-letter non-additivity in coherent information, the authors show a counterintuitive boost in quantum and private capacities, even when the single-use capacity vanishes.

ABSTRACT

Entanglement and quantum information lie at the root of quantum theory. These remarkable resources are generally believed to diminish when systems carrying them interact with their environment. By contrast, we find that engaging a system with its environment can increases its ability to carry quantum information. The maximum rate of transmission is given by the quantum channel capacity. We counter-intuitively boost this capacity of a channel by allowing it to leak almost all quantum information to the channel's environment. We conceptually and numerically explain this boost to arise from two-letter level super-additivity in the channel's coherent information. Such super-additivity has a far larger magnitude and a qualitatively wider extent than previously known. Our findings have a surprising implication for quantum key distribution: maximum rates for key distribution can be boosted by allowing leakage of information to the eavesdropping environment.

Motivation & Objective

• To challenge the conventional view that noise and information leakage degrade quantum entanglement.
• To investigate whether non-additivity in quantum channel capacities can be harnessed to increase entanglement transmission despite information leakage.
• To compute and analyze the quantum and private capacities of a specific noisy channel under controlled leakage.
• To demonstrate that non-additivity in coherent information can lead to a significant, measurable increase in effective quantum capacity.
• To explore implications for quantum key distribution, where controlled leakage may enhance secure key rates.

Proposed method

• Constructs a specific noisy quantum channel with tunable parameters to study entanglement transmission under controlled leakage.
• Analyzes the two-copy coherent information Δ(B⊗², Λaa) to detect non-additivity effects, using a parameterized leakage model Λaa.
• Employs a two-parameter optimization over ε and p to maximize the two-letter coherent information, with r₀ = ε and r₁ = 1−ε.
• Uses asymptotic analysis near λ₁ = 1/2 to derive analytical expressions for Δ* in the small δλ = λ₁ − λ limit.
• Applies the PPT criterion to verify entanglement in output states τaa and τcc, confirming non-separability via negative partial transpose eigenvalues.
• Numerically validates the analytical results for Δ* and δ* across varying λ values, particularly near the critical point λ₀.

Experimental results

Research questions

• RQ1 Can information leakage to the environment enhance a quantum channel’s ability to preserve entanglement?
• RQ2 What is the role of two-letter non-additivity in coherent information in enabling this counterintuitive enhancement?
• RQ3 How does the quantum capacity behave when the single-use coherent information vanishes, yet the two-copy capacity remains positive?
• RQ4 Can this mechanism be leveraged to improve secure key distribution rates in quantum key distribution protocols?
• RQ5 What is the quantitative magnitude of the capacity boost achievable through controlled leakage in a specific channel model?

Key findings

• The quantum capacity Q(B) of the channel drops to zero at λ₀, yet the two-copy coherent information Δ(B⊗², Λaa) remains positive, indicating non-additivity.
• The maximum two-copy coherent information Δ* is achieved when ε → 0 and r → 1, corresponding to near-total leakage of quantum information.
• For small δλ = λ₁ − λ, Δ* scales logarithmically with δλ, and δ* = Δ*/2 − Q¹(B) is found to be positive, indicating a non-zero effective capacity.
• The PPT criterion confirms that τaa and τcc are entangled, with negative eigenvalues of −1/4 and (3−√21)/24 respectively, validating entanglement in the output states.
• Numerical results for Δ* and δ* show excellent agreement with analytical approximations in the small δλ regime.
• The study reveals a far larger and qualitatively wider non-additivity in quantum capacity than previously known, challenging the assumption that leakage always degrades performance.