arXiv subjects

Matthew Simon Tan

Publications and source records attributed to Matthew Simon Tan.

4 recordsLinked to original sources

arXiv2026

Fully quantum fidelity-based entropic continuity bounds

We present a continuity bound for quantum conditional entropies in terms of fidelity, with no dependence on the dimension of the conditioning system. Our results encompass both the von Neumann entropy and one version of sandwiched Rényi entropy, which is particularly relevant for applications in quantum key distribution (QKD). In such applications, this bound should provide improved results as compared to previous continuity bounds based on trace distance. We also show that the bounds can be sharpened as expected for classical-quantum states, and verify that they hold when the conditioning system has countably infinite dimension. Finally, we present several variants tailored for exponential functions of the Rényi entropies instead, which should be relevant for QKD applications.

quant-ph↗

arXiv2026

Making the most of leftovers: Improved privacy amplification for quantum key distribution

The amount of secret key that can be obtained from a quantum key distribution run depends on both the physically observed error rates and the mathematical bounds used to certify security. For finite datasets, conservative bounds force users to discard a substantial fraction of the potentially available key. Here we further refine and extend the privacy amplification bounds achievable through the recent leftover hash lemma of Regula and Tomamichel [arXiv:2603.04493] and incorporate them into the security analysis of quantum key distribution based on entropic uncertainty relations. This improves on state-of-the-art key rates in finite-block regimes, certifying more secret key from the same experimental data without changes to the protocol, and outperforming techniques based on entropy accumulation. The results illustrate how sharper mathematical estimates can directly increase the usable output of a quantum communication system.

quant-ph↗

arXiv2026

Tight Contraction Rates for Primitive Channels under Quantum $f$-Divergences

Data-processing inequalities capture the phenomenon that two probability distributions can only become less distinguishable under any common post-processing. For more fine-grained inequalities, one turns to strong data-processing inequality (SDPI) constants, which give the strongest inequalities for a given channel and reference state for a fixed measure of distinguishability. These quantities have been used to quantify the rate at which time-homogeneous Markov chains contract towards a fixed point both in the classical and quantum setting. In this work, we establish that quantum $f$-divergences satisfy a local reverse Pinsker inequality, which implies the asymptotic contraction rate of a primitive channel to its stationary state is upper bounded by the SDPI constant of any non-commutative $χ^2$-divergence. Using quantum-detailed balance, we establish a sufficient condition for these bounds to be tight. Finally, we apply these results to Petz, Matsumoto, and Hirche-Tomamichel $f$-divergences, establishing new and strengthening previously known results.

quant-ph↗

arXiv2026

Approximate virtual quantum broadcasting

The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels.

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