Notes on optimality of direct characterisation of quantum dynamics

A Note on Optimality of Quantum Circuits over Metaplectic Basis

Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate $R=|0\rangle \langle 0| + |1\rangle \langle 1| - |2\rangle \langle 2|$. It is arguably, a ternary basis with the simplest geometry. Recently Cui, Kliuchnikov, Wang and the Author have proposed a compilation algorithm to approximate any two-level Householder reflection to precision $\varepsilon$ by a metaplectic circuit of $R$-count at most $C \, \log_3(1/\varepsilon) + O(\log \log 1/\varepsilon)$ with $C=8$. A new result in this note takes the constant down to…

Reply to M. Ziman's "Notes on optimality of direct characterization of quantum dynamics"

Recently M. Ziman [quant-ph/0603151] criticized our approach for quantifying the required physical resources in the theory of Direct Characterization of Quantum Dynamics (DCQD) [quant-ph/0601033, quant-ph/0601034] in comparison to other quantum process tomography (QPT) schemes. Here we argue that Ziman's comments regarding optimality, quantumness, and the novelty of DCQD are inaccurate. Specifically, we demonstrate that DCQD is optimal with respect to both the required number of experimental configurations and the number of possible outcomes over all known QPT schemes in the 2^{2n} dimensional…

A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces

Entanglement witnesses (EWs) constitute one of the most important entanglement detectors in quantum systems. Nevertheless, their complete characterization, in particular with respect to the notion of optimality, is still missing, even in the decomposable case. Here we show that for any qubit-qunit decomposable EW (DEW) W the three statements are equivalent: (i) the set of product vectors obeying \bra{e,f}W\ket{e,f}=0 spans the corresponding Hilbert space, (ii) W is optimal, (iii) W=Q^Γ with Q denoting a positive operator supported on a completely entangled subspace (CES) and Γstanding for the …

A Note on Non-Additive Quantum Codes

A method to combine two quantum error-correcting codes is presented. Even when starting with additive codes, the resulting code might be non-additive. Furthermore, the notion of the erasure space is introduced which gives a full characterisation of the erasure-correcting capabilities of the codes. For the special case that the two codes are unitary images of each other, the erasure space and the pure erasure space of the resulting code can be calculated.

概率估计框架的渐近最优对抗策略

Asymptotically Optimal Adversarial Strategies for the Probability Estimation Framework

本文证明概率估计框架的渐近最优性，刻画无信令与量子受限对抗攻击，并展示其在 Bell 场景中的鲁棒性。

量子纠错的规范场形式论在逻辑门方面的注记

Note on Logical Gates by Gauge Field Formalism of Quantum Error Correction

本研究将量子CSS码的规范场形式论扩展，构造了S、Hadamard等一类逻辑门，证明其可分解为物理门且逻辑作用依赖同调类，为CSS码逻辑门提供了系统方法并揭示了相关领域的相互作用。