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This research introduces a streaming protocol for estimating power moments of partial-transposed density matrices, enabling efficient entanglement certification in mixed quantum states without scaling qubit resources with moment order. By leveraging collective permutations and reusable ancillas, the method achieves near-optimal sample complexity while providing unbiased estimators suitable for thermal-state analysis. The study validates the approach through simulations and a three-qubit implementation on a cloud quantum processor, advancing practical tools for quantum state characterization.
Streaming the partial-transpose moment hierarchy with order-independent quantum memory
arXiv:2606.14204v3 Announce Type: replace Abstract: Partial transposition reveals mixed-state entanglement through the spectrum of $\rho_{AB}^{T_B}$, but this operator is not generally a physical state. Its power moments are accessible through collective permutations, whose coherent width grows with moment order. Here we introduce a streaming protocol that processes fresh copies sequentially while retaining one copy and a reusable ancilla. By realizing opposite cyclic permutations on the two subsystems, each measurement record yields unbiased estimators of all moments $p_2,\ldots,p_K$ through successive outcome products. For an $n$-qubit state, the protocol uses $2n+1$ active qubits independent of $K$ and $O(K\log K/\epsilon_{\rm mom}^2)$ copies, matching $\Omega(K/\epsilon_{\rm mom}^2)$ lower bounds up to a logarithmic factor, including a PT-specific isospectral construction. Higher-order moments strengthen thermal-state entanglement certification toward the exact PPT threshold. Simulations cover pure and mixed states, and a cloud quantum processor implements a three-qubit instance.
Abstract:Partial transposition reveals mixed-state entanglement through the spectrum of $\rho_{AB}^{T_B}$, but this operator is not generally a physical state. Its power moments are accessible through collective permutations, whose coherent width grows with moment order. Here we introduce a streaming protocol that processes fresh copies sequentially while retaining one copy and a reusable ancilla. By realizing opposite cyclic permutations on the two subsystems, each measurement record yields unbiased estimators of all moments $p_2,\ldots,p_K$ through successive outcome products. For an $n$-qubit state, the protocol uses $2n+1$ active qubits independent of $K$ and $O(K\log K/\epsilon_{\rm mom}^2)$ copies, matching $\Omega(K/\epsilon_{\rm mom}^2)$ lower bounds up to a logarithmic factor, including a PT-specific isospectral construction. Higher-order moments strengthen thermal-state entanglement certification toward the exact PPT threshold. Simulations cover pure and mixed states, and a cloud quantum processor implements a three-qubit instance.
Main text: 16 pages, 5 figures, 1 table; supplementary materials: 16 pages, 2 figures, 1 table; references: 3 pages. Total: 35 pages, 7 figures, 2 tables
arXiv:2606.14204 [quant-ph]
(or arXiv:2606.14204v3 [quant-ph] for this version)
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