arXiv subjects

O. Jiménez

Publications and source records attributed to O. Jiménez.

15 recordsLinked to original sources

arXiv2026

Discrimination of metric theories

We study the possibility of discriminating between metric theories within the Parametrized Post-Newtonian formalism. In this approach, the two-dimensional quantum state of a massive quantum clock becomes, after propagating at low speed and in a weak gravitational field, a function of the post-Newtonian parameters and thus a signature of a metric theory. To discriminate among metric theories, we resort to quantum-state discrimination strategies such as minimum-error and unambiguous discrimination. In particular, we show that it is possible to refute the hypothesis that a particular metric theory describes spacetime with a single detection event and that it is possible to discriminate with certainty between two different metrics, also with a single detection event. In general, the success probability of the discrimination strategy is a harmonic function of the product of the difference of the proper time corresponding to each quantum clock state, the energy difference between the energy eigenstates of the quantum clock, the propagation length, and speed. It is thus possible to find suitable length and speed scales such that the success probability is close to one by selecting a quantum system with the highest energy difference and the longest natural lifetime. According to this, atomic nuclei such as thorium are considered the most suitable quantum clocks. We also show that the use of a ensemble of quantum clocks leads to a significant increase in the probability of success in discriminating between post-Newtonian parameters that differ by $10^{-5}$. This facilitates achieving a probability of success approaching unity with distances on the scale of several kilometers and velocities approximating one-thousandth of the speed of light for a ensemble of only 10 quantum clocks.

gr-qc↗

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.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

arXiv2023

Optimal high-dimensional entanglement concentration in the bipartite scenario

Considering pure quantum states, entanglement concentration is the procedure where from $N$ copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for $N=1$. However, the associated success probability can be extremely low while increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for $N=1$, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function $\mathcal{Q}$ considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of $\mathcal{Q}$. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.

quant-ph↗

arXiv2021

Enhanced discrimination of high-dimensional quantum states by concatenated optimal measurement strategies

The impossibility of deterministic and error-free discrimination among nonorthogonal quantum states lies at the core of quantum theory and constitutes a primitive for secure quantum communication. Demanding determinism leads to errors, while demanding certainty leads to some inconclusiveness. One of the most fundamental strategies developed for this task is the optimal unambiguous measurement. It encompasses conclusive results, which allow for error-free state retrodictions with the maximum success probability, and inconclusive results, which are discarded for not allowing perfect identifications. Interestingly, in high-dimensional Hilbert spaces the inconclusive results may contain valuable information about the input states. Here, we theoretically describe and experimentally demonstrate the discrimination of nonorthogonal states from both conclusive and inconclusive results in the optimal unambiguous strategy, by concatenating a minimum-error measurement at its inconclusive space. Our implementation comprises 4- and 9-dimensional spatially encoded photonic states. By accessing the inconclusive space to retrieve the information that is wasted in the conventional protocol, we achieve significant increases of up to a factor of 2.07 and 3.73, respectively, in the overall probabilities of correct retrodictions. The concept of concatenated optimal measurements demonstrated here can be extended to other strategies and will enable one to explore the full potential of high-dimensional nonorthogonal states for quantum communication with larger alphabets.

quant-ph↗

arXiv2018

Challenging local realism with human choices

A Bell test is a randomized trial that compares experimental observations against the philosophical worldview of local realism. A Bell test requires spatially distributed entanglement, fast and high-efficiency detection and unpredictable measurement settings. Although technology can satisfy the first two of these requirements, the use of physical devices to choose settings in a Bell test involves making assumptions about the physics that one aims to test. Bell himself noted this weakness in using physical setting choices and argued that human `free will' could be used rigorously to ensure unpredictability in Bell tests. Here we report a set of local-realism tests using human choices, which avoids assumptions about predictability in physics. We recruited about 100,000 human participants to play an online video game that incentivizes fast, sustained input of unpredictable selections and illustrates Bell-test methodology. The participants generated 97,347,490 binary choices, which were directed via a scalable web platform to 12 laboratories on five continents, where 13 experiments tested local realism using photons, single atoms, atomic ensembles, and superconducting devices. Over a 12-hour period on 30 November 2016, participants worldwide provided a sustained data flow of over 1,000 bits per second to the experiments, which used different human-generated data to choose each measurement setting. The observed correlations strongly contradict local realism and other realistic positions in bipartite and tripartite scenarios. Project outcomes include closing the `freedom-of-choice loophole' (the possibility that the setting choices are influenced by `hidden variables' to correlate with the particle properties), the utilization of video-game methods for rapid collection of human generated randomness, and the use of networking techniques for global participation in experimental science.

quant-ph↗

arXiv2018

Experimental quantum tomography assisted by multiply symmetric states in higher dimensions

High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such progress has fueled the search of reliable quantum tomographic methods aiming for the characterization of these systems, being most of these methods specifically designed for a given scenario. Here, we report on a new tomographic method based on multiply symmetric states and on experimental investigations to study its performance in higher dimensions. Unlike other methods, it is guaranteed to exist in any dimension and provides a significant reduction in the number of measurement outcomes when compared to standard quantum tomography. Furthermore, in the case of odd dimensions, the method requires the least possible number of measurement outcomes. In our experiment we adopt the technique where high-dimensional quantum states are encoded using the linear transverse momentum of single photons and are controlled by spatial light modulators. Our results show that fidelities of $0.984\pm0.009$ with ensemble sizes of only $1.5\times10^5$ photons in dimension $D=15$ can be obtained in typical laboratory conditions, thus showing its practicability in higher dimensions.

quant-ph↗

arXiv2017

Parametric separation of symmetric pure quantum states

Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or independent quantum states. We obtained analytical solutions for the success probability of the maps--which is shown to be optimal--as well as explicit constructions in terms of positive operator valued measures. Our results can be used for state discrimination strategies interpolating continuously between minimum-error and unambiguous (or maximum-confidence) discrimination, which, in turn, have many applications in quantum information protocols. As an example, we show that quantum teleportation through a nonmaximally entangled quantum channel can be accomplished with higher probability than the one provided by unambiguous (or maximum-confidence) discrimination and with higher fidelity than the one achievable by minimum-error discrimination. Finally, an optical network is proposed for implementing parametric state separation.

quant-ph↗

arXiv2017

Experimental minimum-error quantum-state discrimination in high dimensions

Quantum mechanics forbids perfect discrimination among nonorthogonal states through a single shot measurement. To optimize this task, many strategies were devised that later became fundamental tools for quantum information processing. Here, we address the pioneering minimum-error (ME) measurement and give the first experimental demonstration of its application for discriminating nonorthogonal states in high dimensions. Our scheme is designed to distinguish symmetric pure states encoded in the transverse spatial modes of an optical field; the optimal measurement is performed by a projection onto the Fourier transform basis of these modes. For dimensions ranging from D = 2 to D = 21 and nearly 14000 states tested, the deviations of the experimental results from the theoretical values range from 0.3% to 3.6% (getting below 2% for the vast majority), thus showing the excellent performance of our scheme. This ME measurement is a building block for high-dimensional implementations of many quantum communication protocols, including probabilistic state discrimination, dense coding with nonmaximal entanglement, and cryptographic schemes.

quant-ph↗

arXiv2014

Deterministic and probabilistic entanglement swapping of nonmaximally entangled states assisted by optimal quantum state discrimination

We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that the success probability of achieving entanglement above a prescribed value from standard deterministic ES can be increased by applying sequential MC measurements.

quant-ph↗

arXiv2012

Quantum teleportation via maximum-confidence quantum measurements

We investigate the problem of teleporting unknown qudit states via pure quantum channels with nonmaximal Schmidt rank. This process is mapped to the problem of discriminating among nonorthogonal symmetric states which are linearly dependent and equally likely. It is shown that by applying an optimized maximum-confidence (MC) measurement for accomplishing this task, one reaches the maximum possible teleportation fidelity after a conclusive event in the discrimination process, which in turn occurs with the maximum success probability. In this case, such fidelity depends only on the Schmidt rank of the channel and it is larger than the optimal one achieved, deterministically, by the standard teleportation protocol. Furthermore, we show that there are quantum channels for which it is possible to apply a k-stage sequential MC measurement in the discrimination process such that a conclusive event at any stage leads to a teleportation fidelity above the aforementioned optimal one and, consequently, increases the overall success probability of teleportation with a fidelity above this limit.

quant-ph↗

arXiv2011

Maximum-confidence discrimination among symmetric qudit states

We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of "sequential maximum-confidence" (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.

quant-ph↗

arXiv2009

Quantum tomography via equidistant states

We study the possibility of performing quantum state tomography via equidistant states. This class of states allows us to propose a non-symmetric informationally complete POVM based tomographic scheme. The scheme is defined for odd dimensions and involves an inversion which can be analytically carried out by Fourier transform.

quant-ph↗

arXiv2007

Experimental scheme for unambiguous discrimination of linearly independent symmetric states

We propose an optimal discrimination scheme for a case of four linearly independent nonorthogonal symmetric quantum states, based on linear optics only. The probability of discrimination is in agreement with the optimal probability for unambiguous discrimination among N symmetric states [Phys. Lett. A \textbf{250}, 223 (1998)]. The experimental setup can be extended for the case of discrimination among $2^M$ nonorthogonal symmetric quantum states.

quant-ph↗