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arXiv:2606.06392

Robustness of Entanglement Manipulation for almost i.i.d. sources

Nilanjana Datta

quant-phSubmitted Jun 4, 2026• Announced Jun 5, 2026• 0 citations
v1 · Jun 4, 2026v2 · Oct 8, 2026
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Abstract

We study the robustness of asymptotic entanglement manipulation beyond the exact i.i.d. regime, focusing on Mazzola--Sutter--Renner (MSR) almost i.i.d. sources, which allow a sublinear number of deviations from a tensor-power structure. For pure MSR sources along a bipartite reference state $|φ\rangle_{AB}$, we prove that the entanglement concentration rate is robust: every rate below the entropy of entanglement $S(φ_A)$ remains achievable. Moreover, this can be done by a single Schur--Weyl concentration protocol that is universal within the MSR class, depending only on the reference state and not on the particular source sequence. For mixed MSR sources along a reference state $ρ_{AB}$, we prove a source-dependent entanglement-distillation achievability result: every rate below the coherent information $I(A\rangle B)_ρ$ of the reference state is achievable, although the entanglement distillation protocol may depend on the particular MSR source sequence. For the reverse task of entanglement dilution, we prove a rate-robustness theorem: the asymptotic entanglement cost of any MSR target sequence along $ρ_{AB}$ is at most $E_F^\infty(ρ_{AB})$, the regularized entanglement of formation of the reference state. To establish these results, we prove structural and entropic properties of MSR almost i.i.d. sequences which may be useful in other information-theoretic settings. Thus, for the achievability statements considered here, MSR almost i.i.d. perturbations exhibit the same asymptotic behaviour as their i.i.d. reference states, despite allowing sublinear deviations from a tensor-power structure.

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We study the robustness of asymptotic entanglement manipulation beyond the exact i.i.d. regime, focusing on Mazzola--Sutter--Renner (MSR) almost i.i.d. sources, which allow a sublinear number of deviations from a tensor-power structure. For pure MSR sources along a bipartite reference state ∣φ⟩AB|φ\rangle_{AB}∣φ⟩AB​, we prove that the entanglement concentration rate is robust: every rate below the entropy of entanglement S(φA)S(φ_A)S(φA​) remains achievable. Moreover, this can be done by a single Schur--Weyl concentration protocol that is universal within the MSR class, depending only on the reference state and not on the particular source sequence. For mixed MSR sources along a reference state ρABρ_{AB}ρAB​, we prove a source-dependent entanglement-distillation achievability result: every rate below the coherent information I(A⟩B)ρI(A\rangle B)_ρI(A⟩B)ρ​ of the reference state is achievable, although the entanglement distillation protocol may depend on the particular MSR source sequence. For the reverse task of entanglement dilution, we prove a rate-robustness theorem: the asymptotic entanglement cost of any MSR target sequence along ρABρ_{AB}ρAB​ is at most EF∞(ρAB)E_F^\infty(ρ_{AB})EF∞​(ρAB​), the regularized entanglement of formation of the reference state. To establish these results, we prove structural and entropic properties of MSR almost i.i.d. sequences which may be useful in other information-theoretic settings. Thus, for the achievability statements considered here, MSR almost i.i.d. perturbations exhibit the same asymptotic behaviour as their i.i.d. reference states, despite allowing sublinear deviations from a tensor-power structure.
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We present a universal entanglement distillation protocol that asymptotically achieves the distillable entanglement of any unknown bipartite state in a fixed finite dimension. That is, its ebit yield attains every rate below the optimum that would be available if the state were known, with vanishing trace-distance error. Our approach combines tomography by local operations and classical communication with an adaptive distillation routine, using a local robustness lemma to control finite-sample estimation errors. We also characterize worst-case distillation from a family of states: the optimal uniform rate is the minimum distillable entanglement on the family's closure. These results show that ignorance of the state need not incur an asymptotic rate penalty.
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