Afham @afhamash.bsky.social · 01/10/2026FPLS has fast classical postprocessing, is rank-preserving, and converges at 1/N. The rank-preservation allows one to return channel estimates with low rank, where that is desirable. This, and other properties, make FPLS particularly good at QPT of low Choi rank channels. 000
Afham @afhamash.bsky.social · 01/10/2026New preprint with @sayantansen.bsky.social and @marcotomamichel.bsky.social!! In Fast and Sure-ious QPT, we describe a simple and rigorous way to lift any QST algorithm (in fidelity) to a QPT algorithm, while allowing for all guarantees to transfer! scirate.com/arxiv/2609.3... 122
Afham @afhamash.bsky.social · 04/09/2026New preprint out! Paradoxical: both my first 'solo-authored' and first LLM-assisted paper. Projected Riemannian Gradient Descent for the Bures-Wasserstein Barycenter: Dimension-Independent Linear Convergence at Unit Step Size scirate.com/arxiv/2609.0... Also an ML paper with applications to QI? 110
Afham @afhamash.bsky.social · 17/02/2026As applications, we show that 1. Pretty good measurement is the fidelity/Bures projection of the ensemble to POVMs, providing new interpretation for PGM. 2. Petz map is the projection of a CP map constructed (rather naturally) from the channel-state pair to the set of reverse channels. 110
Afham @afhamash.bsky.social · 17/02/2026In the 'fixed-marginal' setting, is projection is given by a simple closed-form. If the marginal is Identity, then this recovers a standard 'partial-normalization' operation used widely in the literature. We show that this partial normalization is not just easy to write down, but optimal! 110
Afham @afhamash.bsky.social · 17/02/2026We use the condition for the saturation of DPI for fidelity, along with properties of the matrix geometric mean, to derive a closed-form for certain projection problems. For 'nice' problems, the projection is given by the 'Gamma map'. 100
Afham @afhamash.bsky.social · 17/02/2026The feasible sets are the PSD preimage of a channel and an output matrix. Examples include sets of 1. Bi- (& multi-)partite states with a given marginal on 1 of the spaces. Eg: Choi matrices of CPTP maps. 2. PSD decomposition of a given matrix. Eg: Set of all POVMs. 110
Afham @afhamash.bsky.social · 17/02/2026New preprint out with @marcotomamichel.bsky.social ! Projections with Respect to Bures Distance and Fidelity: Closed-Forms and Applications scirate.com/arxiv/2602.1... We derive simple closed-form solutions for fidelity / Bures/purified distance projections to various sets of interest. 1102
Afham @afhamash.bsky.social · 23/03/2025Thanks for the reply! But the example you posted has complex e.vals which are conjugates of each other with +ve real part, hence the trace and det condition will be satisfied without the e.vals being (real) positive. 110
Afham @afhamash.bsky.social · 14/03/2025Here is a 'simple' 3-line proof for this statement! (Although the simplicity hides behind the form and properties of the matrix geometric mean.) 1152