arXiv subjects

L. F. Melo

Publications and source records attributed to L. F. Melo.

6 recordsLinked to original sources

arXiv2026

Quantitative wave-particle duality in uniform multipath interferometers with symmetric which-path detector states

A quantum system (quanton) traverses an interferometer with $N$ equally probable paths and interacts with another quantum system (detector) that stores path information in a set of symmetric states. In this interferometric framework, we present entropic wave-particle duality relations between quantum coherence, characterized by the relative entropy of coherence of the quanton state, and which-path knowledge, quantified by the mutual information obtained through detector-state discrimination. By applying a general optimal discrimination measurement, which has a closed-form solution and encompasses other fundamental strategies as special cases, we provide an exact quantification of which-path knowledge in a variety of scenarios. This measurement is carried out in two steps. First, an optimal separation map with a prescribed separation level $ξ\in [0,1]$ probabilistically reduces the overlaps between the input detector states with maximum success rate, or increases them in case of failure. Then, a minimum-error (ME) measurement discriminates either only the successful outputs (standard approach) or both the successful and failure outputs (concatenated approach). We show that the duality relation is tighter at $ξ=0$, where both approaches reduce to the ME measurement. For $ξ>0$, each approach yields a distinct relation that becomes less tight as $ξ$ increases, with the concatenated one providing the tighter bound. Finally, by using the discrete uncertainty principle, we determine the sets of detector states that lead to saturation of the duality relation, showing that they span $n$-dimensional subspaces of the detector space, where $n$ divides $N$. As a result, nontrivial saturation occurs only for interferometers with a nonprime number of paths. From the identified saturating sets, we highlight how the quanton-detector correlations underlie this phenomenon.

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arXiv2025

Information recycling in coherent state discrimination

The discrimination of coherent states is a crucial component in quantum communication with continuous variables, especially in quantum key distribution protocols (CV-QKD), which rely on the ability to distinguish among different coherent states to establish a shared secret key between two parties. Here, we propose and analyze a strategy for distinguishing among N phase-symmetric coherent states, which optimally takes unambiguous discrimination (UD) to the deterministic regime, at the inevitable cost of having non-zero probability of error. Despite the disturbance introduced by the separation map used in the UD process, we show that for N > 2, the "failure" states of UD retain residual information about the original input states, which can be further used for discrimination. Rather than discarding inconclusive outcomes as in conventional UD, we show that the "failure" states of UD can be optimally recycled by performing a sequential minimum-error discrimination (MED). This strategy, which we call information recycling (IR), combines the benefits of both MED and optimal UD: It always provides conclusive results while allowing for a subset of those results to be error-free, which are identifiable by an ancillary system. We characterize the disturbance introduced by the state separation map by the infidelity between input and failure states, demonstrating that it lower bounds the error probability in the recycling stage. Furthermore, in the low-amplitude regime-relevant for long-distance CV-QKD applications-we show that the state separation achieves significant success while introducing relatively low disturbance to the input states after failed events. Our results open up new possibilities for adaptive and sequential discrimination protocols in continuous-variable settings, and could potentially be used in the design of next-generation receivers in quantum communication.

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arXiv2025

Coherence based on positive operator-valued measures for standard and concatenated quantum state discrimination with inconclusive results

The optimal measurement that discriminates nonorthogonal quantum states with fixed rates of inconclusive outcomes (FRIO) can be decomposed into an assisted separation of the inputs, yielding conclusive and inconclusive outputs, followed by a minimum-error (ME) measurement for the conclusive ones (standard FRIO) or both ones (concatenated FRIO). The implementation of these measurements is underpinned by quantum resources, and here we investigate coherence based on positive operator-valued measures (POVMs) as a resource for both strategies in discriminating equally probable symmetric states of arbitrary dimension. First, we show that the POVM coherence in the assisted separation stage decomposes into the coherence of the ancillary state and the quantum discord between the system and the ancilla, evidencing coherence as a more elementary resource than quantum correlations. Next, it is demonstrated that the POVM coherence for standard and concatenated FRIO decomposes into the POVM coherence measures for state separation and ME measurement, weighted by the probabilities of occurrence of each event. Due to the ME discrimination of inconclusive states, the coherence required for the concatenated scheme is shown to be greater than that of the standard one. We discuss other general aspects of our results by characterizing the POVM coherence in the discrimination of qutrit states, with respect to the distinguishability of the inputs and the inconclusive rate. Finally, by exploiting POVM-based coherence as a quantifier of cryptographic randomness gain, we discuss the standard and concatenated FRIO strategies from the perspective of generating random bits that are secret to an eavesdropper.

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arXiv2024

Experimental optimal discrimination of $N$ states of a qubit with fixed rates of inconclusive outcomes

In a general optimized measurement scheme for discriminating between nonorthogonal quantum states, the error rate is minimized under the constraint of a fixed rate of inconclusive outcomes (FRIO). This so-called optimal FRIO measurement encompasses the standard and well known minimum-error and optimal unambiguous (or maximum-confidence) discrimination strategies as particular cases. Here, we experimentally demonstrate the optimal FRIO discrimination between $N=2,3,5,$ and $7$ equally likely symmetric states of a qubit encoded in photonic path modes. Our implementation consists of applying a probabilistic quantum map which increases the distinguishability between the inputs in a controlled way, followed by a minimum-error measurement on the successfully transformed outputs. The results obtained corroborate this two-step approach and, in our experimental scheme, it can be straightforwardly extended to higher dimensions. The optimized measurement demonstrated here will be useful for quantum communication scenarios where the error rate and the inconclusive rate must be kept below the levels provided by the respective standard strategies.

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arXiv2022

Enlarging the notion of additivity of resource quantifiers

Whenever a physical quantity becomes essential to the realization of useful tasks, it is desirable to define proper measures or monotones to quantify it. In quantum mechanics, coherence, entanglement, and Bell nonlocality are examples of such quantities. Given a quantum state $\varrho$ and a quantifier ${\cal E}(\varrho)$, both arbitrary, it is a hard task to determine ${\cal E}(\varrho^{\otimes N})$. However, if the figure of merit $\cal{E}$ turns out to be additive, we simply have ${\cal E}(\varrho^{\otimes N})=N e$, with $e={\cal E}(\varrho)$. In this work we generalize this useful notion through the inner product ${\cal E}(\varrho^{\otimes N}) = \vec{N}\cdot \vec{e}$, where $\vec{e}=({\cal E}(\varrho^{\otimes i_1}), {\cal E}(\varrho^{\otimes i_2}),\dots,{\cal E}(\varrho^{\otimes i_q}) )$ is a vector whose $q$ entries are the figure of merit under study calculated for some numbers of copies smaller than $N$ ($1 \le i_1<i_2<\dots <i_q<N$), where $\vec{N}=(N_{i_1}, N_{i_2}, \dots ,N_{i_q})$, is a string of numbers that depends only on $N$ and on the set of integers $\{ {i_j}\}$. We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.

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arXiv2021

Simplest non-additive measures of quantum resources

Given an arbitrary state $ρ$ and some figure of merit ${\cal E}(ρ)$, it is usually a hard problem to determine the value of ${\cal E}(ρ^{\otimes N})$. One noticeable exception is the case of additive measures, for which we simply have ${\cal E}(ρ^{\otimes N}) = Ne$, with $e\equiv {\cal E}(ρ)$. In this work we study measures that can be described by ${\cal E}(ρ^{\otimes N}) =E(e;N) \ne Ne$, that is, measures for which the amount of resources of $N$ copies is still determined by the single real variable $e$, but in a nonlinear way. If, in addition, the measures are analytic around $e=0$, recurrence relations can be found for the Maclaurin coefficients of $E$ for larger $N$. As an example, we show that the $\ell_1$-norm of coherence is a nontrivial case of such a behavior.

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