arXiv subjects

Christos Gagatsos

Publications and source records attributed to Christos Gagatsos.

4 recordsLinked to original sources

arXiv2026

Upper bounds on the purity of Wigner positive quantum states that verify the Wigner entropy conjecture

We present analytical results toward the Wigner entropy conjecture, which posits that among all physical Wigner non-negative states the Wigner entropy is minimized by pure Gaussian states for which it attains the value $1+\lnπ$. Working under a minimal set of constraints on the Wigner function, namely, non-negativity, normalization, and the pointwise bound $πW\le 1$, we construct an explicit hierarchy of lower bounds $B_n$ on $S[W]$ by combining a truncated series lower bound for $-\ln x$ with moment identities of the Wigner function. This yields closed-form sufficient conditions, expressed in terms of the state purity $μ:=\operatorname{Tr}(ρ^2)=2π\int dq\,dp\,W(q,p)^2$, ensuring $S[W]\ge 1+\lnπ$. In particular, we first prove that all physical Wigner-non-negative states with $μ\le 4-2\sqrt{3}$ satisfy the Wigner entropy conjecture. We further obtain a systematic purity-only relaxation of the hierarchy, whose limiting sufficient condition is $μ\le 2/e$. Finally, we show that the threshold $2/e$ is sharp under the relaxed constraints considered here, thereby identifying the need for additional quantum-realizability information in the remaining high-purity regime.

quant-ph↗

arXiv2022

Transceiver designs to attain the entanglement assisted communications capacity

Pre-shared entanglement can significantly boost communication rates in the high thermal noise and low-brightness transmitter regime. In this regime, for a lossy-bosonic channel with additive thermal noise, the ratio between the entanglement-assisted capacity and the Holevo capacity - the maximum reliable-communications rate permitted by quantum mechanics without any pre-shared entanglement - scales as $\log(1/{\bar N}_{\rm S})$, where the mean transmitted photon number per mode, ${\bar N}_{\rm S} \ll 1$. Thus, pre-shared entanglement, e.g., distributed by the quantum internet or a satellite-assisted quantum link, promises to significantly improve low-power radio-frequency communications. In this paper, we propose a pair of structured quantum transceiver designs that leverage continuous-variable pre-shared entanglement generated, e.g., from a down-conversion source, binary phase modulation, and non-Gaussian joint detection over a code word block, to achieve this scaling law of capacity enhancement. Further, we describe a modification to the aforesaid receiver using a front-end that uses sum-frequency generation sandwiched with dynamically-programmable in-line two-mode squeezers, and a receiver back-end that takes full advantage of the output of the receiver's front-end by employing a non-destructive multimode vacuum-or-not measurement to achieve the entanglement-assisted classical communications capacity.

quant-ph↗

arXiv2022

Quantum Multi-Parameter Adaptive Bayesian Estimation and Application to Super-Resolution Imaging

In Bayesian estimation theory, the estimator ${\hat θ} = E[θ|l]$ attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest $θ$ from the observation of $l$ through a noisy channel $P_{l|θ}$, given a prior $P_θ$ on $θ$. In quantum sensing tasks, the user gets $ρ_θ$, the quantum state that encodes $θ$. They choose a measurement, a positive-operator valued measure (POVM) $Π_l$, which induces the channel $P_{l|θ} = {\rm Tr}(ρ_θΠ_l)$ to the measurement outcome $l$, on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM $Π_l$ that minimizes the MMSE over all possible measurements, and that MMSE. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements, when $P_θ$ is unavailable. For multi-parameter estimation, i.e., when $θ$ is a vector, in Fisher quantum estimation theory, the inverse of the QFI matrix provides an operator lower bound to the covariance of an unbiased estimator. However, there has been little work on quantifying quantum limits and measurement designs, for multi-parameter quantum estimation in the {\em Bayesian} setting. In this paper, we build upon Personick's result to construct a Bayesian adaptive measurement scheme for multi-parameter estimation when $N$ copies of $ρ_θ$ are available. We illustrate an application to localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs far superior to quantum-noise-limited focal-plane direct imaging.

physics.data-an↗

arXiv2019

Efficient representation of Gaussian states for multi-mode non-Gaussian quantum state engineering via subtraction of arbitrary number of photons

We introduce a complete description of a multi-mode bosonic quantum state in the coherent-state basis (which in this work is denoted as "$K$" function ), which---up to a phase---is the square root of the well-known Husimi "$Q$" representation. We express the $K$ function of any $N$-mode Gaussian state as a function of its covariance matrix and displacement vector, and also that of a general continuous-variable cluster state in terms of the modal squeezing and graph topology of the cluster. This formalism lets us characterize the non Gaussian state left over when one measures a subset of modes of a Gaussian state using photon number resolving detection, the fidelity of the obtained non-Gaussian state with any target state, and the associated heralding probability, all analytically. We show that this probability can be expressed as a Hafnian, re-interpreting the output state of a circuit claimed to demonstrate quantum supremacy termed Gaussian boson sampling. As an example-application of our formalism, we propose a method to prepare a two-mode coherent-cat-basis Bell state with fidelity close to unity and success probability that is fundamentally higher than that of a well-known scheme that splits an approximate single-mode cat state---obtained by photon number subtraction on a squeezed vacuum mode---on a balanced beam splitter. This formalism could enable exploration of efficient generation of cat-basis entangled states, which are known to be useful for quantum error correction against photon loss.

quant-ph↗