arXiv subjects

Pablo V. Parellada

Publications and source records attributed to Pablo V. Parellada.

5 recordsLinked to original sources

arXiv2026

Riemannian optimization for linear optical problems

Many applications of linear optics in quantum science involve searching for some optimal configuration of a multiport interferometer. For example, to find heralded state preparations, one can optimize the interferometer to maximize the fidelity and success probability of the state preparation. In this paper, we derive a closed analytical formula for the Riemannian gradient of any differentiable function defined over the interferometer unitaries. We use this gradient in Riemannian optimization algorithms, such as gradient descent or BFGS, to find the optimal setup of the interferometer. As an interesting use case, we search for linear optical state preparations, improving some of the success probabilities reported in the literature for NOON or photon catalysis preparations. Finally, we show that our optimizer is orders of magnitude faster than other methods in the literature, opening the door for solving linear optical problems involving more modes and photons.

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arXiv2026

Lie algebraic invariants in quantum linear optics

Quantum linear optics without post-selection is not powerful enough to produce any quantum state from a given input state. This limits its utility since some applications require entangled resources that are difficult to prepare. Thus, a deeper understanding of linear optical state preparation is needed. In this work, we give a recipe to derive conserved quantities in the evolution of arbitrary states along any possible passive linear interferometer. One example of such an invariant is the spectrum of a density matrix mapped onto the Lie algebra of passive linear optical Hamiltonians. These invariants give necessary conditions for exact state preparation: if the input and output states have different invariants, it is impossible to design a passive linear interferometer that evolves one into the other. Moreover, we provide a lower bound to the distance between an output and target state based on the distance between their invariants. This gives a necessary condition for approximate or heralded state preparations. Therefore, the invariants allow us to narrow the search when trying to prepare useful entangled states, like NOON states, from easy-to-prepare states, like Fock states. We conclude that future exact and approximate state preparation methods will need to consider the necessary conditions given by our invariants to weed out impossible linear optical evolutions.

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arXiv2026

Finite-size quantum key distribution rates from Rényi entropies using conic optimization

Finite-size general security proofs for quantum key distribution based on Rényi entropies have recently been introduced. These approaches are more flexible and provide tighter bounds on the secret key rate than traditional formulations based on the von Neumann entropy. However, deploying them requires minimizing the conditional Rényi entropy, a difficult optimization problem that has hitherto been tackled using ad-hoc techniques based on the Frank-Wolfe algorithm, which are unstable and can only handle particular cases. In this work, we introduce a method based on non-symmetric conic optimization for solving this problem. Our technique is fast, reliable, and completely general. We illustrate its performance on several protocols, whose results represent an improvement over the state of the art.

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arXiv2025

Quantum key distribution rates from non-symmetric conic optimization

Computing key rates in quantum key distribution (QKD) numerically is essential to unlock more powerful protocols, that use more sophisticated measurement bases or quantum systems of higher dimension. It is a difficult optimization problem, that depends on minimizing a convex non-linear function: the (quantum) relative entropy. Standard conic optimization techniques have for a long time been unable to handle the relative entropy cone, as it is a non-symmetric cone, and the standard algorithms can only handle symmetric ones. Recently, however, a practical algorithm has been discovered for optimizing over non-symmetric cones, including the relative entropy. Here we adapt this algorithm to the problem of computation of key rates, obtaining an efficient technique for lower bounding them. In comparison to previous techniques it has the advantages of flexibility, ease of use, and above all performance.

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arXiv2023

No-go theorems for photon state transformations in quantum linear optics

We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity that appears in all allowed optical transformations. We comment some examples and numerical applications, with example code, and give three general no-go results. These include (i) the impossibility of deterministic transformations which redistribute the photons from one to two different modes, (ii) a proof that it is impossible to generate a perfect Bell state in heralded schemes with a separable input for any number of ancillary photons and modes and a fixed herald and (iii) a restriction for the conversion between different types of entanglement (converting GHZ to W states).

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