Partial Transposition Research Articles

To be or not to be: The crossroad between individual remote self-consumption and renewable energy communities in front of Italian public administrations and local authorities

The topic of energy cooperation has been discussed internationally for over twenty years, with its historical roots going back to the early 1900s. The Directive 2018/2001/EU on renewable energy (REDII) established a unified definition of "Renewable Energy Community" (REC) as an autonomous entity controlled by local members, aimed at providing environmental, economic, and social benefits. This shift encourages end users to participate in energy management and consumption, involving complex technological and organizational dynamics among various stakeholders, including citizens, SMEs, local authorities, and public administrations. In Italy, after the early, partial transposition of RED II in 2019 that lead to over a hundred active RECs by early 2024, the final regulations expanded the operational scope and allowed for greater participation in energy sharing and self-consumption processes. The paper focus on the role of public administrations in promoting RECs, examining potential legal forms and strategic choices, especially regarding the inclusion of the Remote Individual Self-Consumer (RISC or AID in Italian Acronym). While this new configuration seeks to accommodate those who cannot join a community, it may create ambiguity for local authorities, as they may choose between individualism and community-focused approaches. Given the complexity and novelty of these developments, further reflection is needed to assess the opportunities and risks associated with new configurations in the energy landscape.

Note on quantum discord

Quantum discord goes beyond entanglement and exists in a wide range of quantum states that may be separable, playing a crucial role in quantum information tasks. In this paper, we firstly proposed a zero-discord criterion for two-qubit system based on the partial transposition of density matrix, and then extended it to the qubit–qudit system. By detailed examples we demonstrate the effectiveness of these criteria in detecting discord. Moreover, we provide an analytical lower bound of geometric quantum discord(GQD) using eigenvalue vectors of density matrix. Finally, we presented a one-way work deficit lower bound based on our lower bound of GQD.

Limit distribution of partial transposition of block random matrices

It is well known that, under some assumptions, the limit distribution of block random matrices and their partial transposition converges to the distributions of random variables in some non-commutative probability spaces. Using free probability theory, we obtain the relation between the free cumulants of the corresponding random variables. As an application, we can derive a new family of co-completely positive and [Formula: see text]-positive maps by using the Wishart ensemble.

Performance Comparison of Cables With Partial Transposition

Performance Comparison of Cables With Partial Transposition

Naturalization of Philosophical Concepts Underlying Interculturality and Proposal of the Neurocognitive Model 'Elemental Intercultural Imprint'

Objective: The study proposes an exploration of dyads (philosophy-cognitive neuroscience) that constitute the basis of interculturality, leading to the postulation of the Elemental Intercultural Imprint as a neurocognitive model that impacts the ontological notion of 'interculturality,' viewed under the naturalizing project. Methodology: An analytical conceptual methodology was implemented, aiming to demonstrate the modes of naturalization of philosophical concepts descriptively and critically. The following hypothesis is maintained: the progressive naturalization of consciousness, self-control, identity, social mind, alterity, and morality can reveal the neurocognitive mechanisms of interculturality in individuals. To this end, thenaturalization of consciousness as attention, identity as self-reference memory, self-control as self-regulation, mind (social) as Theory of Mind, alterity as empathy, and morality as moral cognition are analyzed. Results: The conceptual analysis in the reviewed studies found that partial epistemological transposition and methodologicalsymmetry are the most common mechanisms of naturalization of the components of interculturality, and that its neurocognitive architecture allows for the incorporation of other components. Conclusions: It is concluded that the proposed neurocognitive basis is indispensable for the empirical study of interculturality.

Analysis of the effect of different facial nerve managements applied to tumor resection in the jugular foramen region

Objective:To summarize the results of different facial nerve management modalities applied to tumor resection in the jugular foramen region. Methods:The clinical data of 54 patients with tumors in the jugular foramen region who underwent surgery from January 2015 to March 2023 were retrospectively analyzed: 18 males and 36 females; Age ranges from 21 to 67 years, with an average age of 44.4 years; and median follow-up time: 12 months. The House-Brackmann（HB） grading system was applied to assess the patients' facial nerve function before surgery, 1-2 weeks after surgery and at the final follow-up （HBⅠ-Ⅱ grade for good function）: 42 cases with preoperative HB grades Ⅰ-Ⅱ; partial facial nerve transposition（9 cases）, complete facial nerve transposition（28 cases）, and facial nerve excision and re-construction（17 cases） were used, respectively（stage Ⅰor Ⅱ）. Relevant factors affecting postoperative facial nerve function were analyzed. Results:Postoperative pathology confirmed 39 cases of paraganglioma, 9 cases of nerve sheath tumor, 3 cases of meningioma, and 1 case each of fibromucinous sarcoma, chondrosarcoma, and intravascular myofibroma. Facial nerve function after partial facial nerve transposition was HB grade Ⅰ-Ⅱ in 89%（8/9）; after complete facial nerve transposition was HB grade Ⅰ-Ⅱ in 86%（24/28） in 28 cases; after facial nerve severance and reconstruction was HB grade Ⅰ-Ⅱ in 2/7（Stage Ⅰ） and 0/3（Stage Ⅱ）, respectively. Tumor size and surgical approach were correlated with postoperative facial nerve function in patients with facial nerve transposition（P<0.05）. There was no statistically significant difference in facial nerve function after complete and partial facial nerve transposition（P>0.05）. Conclusion:Intraoperative stretching of the facial nerve may be an important factor affecting facial nerve function during surgical treatment of tumors in the jugular venous foramen region; for patients with facial nerve dissection, facial nerve reconstruction should be adopted according to the situation, aiming at the recovery of facial nerve function.

Symmetry resolution of the computable cross-norm negativity of two disjoint intervals in the massless Dirac field theory

We investigate how entanglement in the mixed state of a quantum field theory can be described using the cross-computable norm or realignment (CCNR) criterion, employing a recently introduced negativity. We study its symmetry resolution for two disjoint intervals in the ground state of the massless Dirac fermion field theory, extending previous results for the case of adjacent intervals. By applying the replica trick, this problem boils down to computing the charged moments of the realignment matrix. We show that, for two disjoint intervals, they correspond to the partition function of the theory on a torus with a non-contractible charged loop. This confers a great advantage compared to the negativity based on the partial transposition, for which the Riemann surfaces generated by the replica trick have higher genus. This result empowers us to carry out the replica limit, yielding analytic expressions for the symmetry-resolved CCNR negativity. Furthermore, these expressions provide also the symmetry decomposition of other related quantities such as the operator entanglement of the reduced density matrix or the reflected entropy.

Special features of the Weyl–Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states

Abstract Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl–Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies an equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of positive partial transposition (PPT)-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.

Parameterized entanglement measures based on Rényi-&lt;i&gt;α&lt;/i&gt; entropy

Parameterized entanglement measures have demonstrated their superiority compared with kinds of unparameterized entanglement measures. Entanglement concurrence has been widely used to describe entanglement in quantum experiments. As an entanglement measure it is related to specific quantum Rényi-&lt;i&gt;α&lt;/i&gt; entropy. In the work, we propose a parameterized bipartite entanglement measure based on the general Rényi-&lt;i&gt;α&lt;/i&gt; entropy, which is named &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence. This measure, different from existing parameterized measures, is defined first for pure states, then extended to the mixed states. Furthermore, we verify three necessary conditions for &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence to satisfy the entanglement measures. We show that this measure is easy to calculate for pure states. However, for mixed states, analytical calculations are only suitable for special two-qubit states or special higher-dimensional mixed states. Therefore, we devote our efforts to developing the analytical lower bound of the-logarithmic concurrence for general bipartite states. Surprisingly, this lower bound is a function on positive partial transposition criterion and realignment criterion of this mixed state. This shows the connection among the three entanglement measures. The interesting feature is that the lower bound depends on the entropy parameter associated with the detailed state. This allows us to choose appropriate parameter &lt;i&gt;α&lt;/i&gt; such that &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ G_\alpha({\boldsymbol{\rho}})\gg0$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; for experimental entanglement detection of specific state &lt;i&gt;ρ&lt;/i&gt;. Moreover, we calculate expressions of the &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence for isotropic states, and give a the analytic expressions for isotropic states with &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ d = 2$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. Finally, the monogamy of the &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence is also discussed. We set up a mathematical formulation for the monogamous property in terms of &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence. Here we set up the functional relation between concurrence and &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence in two qubit systems. Then we obtain some useful properties of this function, and by combining the Coffman–Kundu–Wootters (CKW) inequality, we establish the monogamy inequality about &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence. We finally prove that the monogamy inequality holds true for &lt;i&gt;α&lt;/i&gt;-logarithmic concurrence.

Quadripartite entanglement from two-port resonator with second-order harmonic generation

Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.

Methods to Minimize the Effects of Geometric Asymmetry of Multi-Circuit, Multi-Voltage Overhead Lines on Transmission Network Operation

Multi-circuit, multi-voltage overhead lines (MMOLs) are becoming a favorable solution in the perspective of ensuring the efficient transmission of electrical energy and limitations relating to the expansion of the transmission network. The main part of this manuscript contains a method that minimizes the effects of risks on the operation of the power system due to asymmetrical MMOLs, with particular emphasis on the circuit with the lowest-rated voltage. The selected set of criteria includes elements such as the determination of the neutral point displacement voltage in the network with the lowest-rated voltage (zero voltage, U0), selected voltage quality factors, and short-circuit analyses to examine the impact of differences between the use of accurate and simplified mathematical models on the calculation of short-circuit currents. Methods to minimize the effects of MMOL geometric asymmetry have been proposed using simple technical steps, such as selecting the appropriate pole silhouette (indication of the methodology for identifying such supporting structures), changing the way of supplying individual circuits, or using partial transposition in the circuit with the lowest-rated voltage. The proposed methods are verified by analyzing a case study of the development of the transmission network in Poland.

From entanglement to discord: A perspective based on partial transposition

From entanglement to discord: A perspective based on partial transposition

Boundary chaos: Exact entanglement dynamics

We compute the dynamics of entanglement in the minimal setup producing ergodic and mixing quantum many-body dynamics, which we previously dubbed boundary chaos. This consists of a free, non-interacting brickwork quantum circuit, in which chaos and ergodicity is induced by an impurity interaction, i.e., an entangling two-qudit gate, placed at the system’s boundary. We compute both the conventional bipartite entanglement entropy with respect to a connected subsystem including the impurity interaction for initial product states as well as the so-called operator entanglement entropy of initial local operators. Thereby we provide exact results in a particular scaling limit of both time and system size going to infinity for either very small or very large subsystems. We show that different classes of impurity interactions lead to very distinct entanglement dynamics. For impurity gates preserving a local product state forming the bulk of the initial state, entanglement entropies of states show persistent spikes with period set by the system size and suppressed entanglement in between, contrary to the expected linear growth in ergodic systems. We observe similar dynamics of operator entanglement for generic impurities. In contrast, for T-dual impurities, which remain unitary under partial transposition, we find entanglement entropies of both states and operators to grow linearly in time with the maximum possible speed allowed by the geometry of the system. The intensive nature of interactions in all cases causes entanglement to grow on extensive time scales proportional to system size.

Royal Decree 601/2019 on justification and optimization: Practical aspects

The Royal Decree 601/2019 of 18th October is the result of the partial transposition into the Spanish legal system of the Euratom Directive 59/2013. This Royal Decree includes the mandates of the Directive related to the need to justify and optimize medical exposure, including that of asymptomatic people, proposal of stricter requirements regarding the information that must be provided to the patient, registration and notification of the doses of medical-radiological procedures, use of reference levels for diagnosis and the availability of dose-indicating devices. The article reviews the most relevant aspects and novelties related to the principles of justification, optimization, dose control and the obligations derived from the right to information and consent. This Royal Decree considers essential for radiologists to develop a high level of competence and a new list of responsibilities and functions, which are detailed and analysed in this article.

Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity

In two recent works, we studied the symmetry resolved Rényi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically characterised. In this paper we extend this line of investigation by providing analytical and numerical evidence that a similar universal behavior arises for the symmetry resolved negativity. In particular, we compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. These are “fused” versions of the more traditionally used branch point twist fields and were introduced in a previous work. The use of twist operators allows us to perform the computation in an arbitrary number of spacial dimensions. We show that, in the large-volume limit, only the commutation relations between the twist operators and local fields matter, and computations reduce to a purely combinatorial problem. We address some specific issues regarding fermionic excitations, whose treatment requires the notion of partial time-reversal transformation, and we discuss the differences and analogies with their bosonic counterpart. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons as well as for a large variety of very different states, ranging from simple qubit states to the excited states of free quantum field theories. Our predictions are tested numerically on a 1D Fermi chain.

Modified Nishida Procedure Combined with Lateral Rectus Disabling for Duane Retraction Syndrome

ABSTRACT Duane retraction syndrome (DRS) is a complex congenital cranial dysinnervation disorder. The choice of surgical procedure in esotropic-DRS depends upon several factors that include: the amount of esotropia in the primary position, the presence and severity of palpebral fissure narrowing, globe retraction, presence of medial rectus muscle (MR) contracture, the likelihood of improving abduction, age of the patient, and the presence of binocularity and stereopsis. In the presence of MR contracture, MR recession is performed either alone (unilaterally or bilaterally) or in conjunction with Y splitting plus recession of the lateral rectus muscle (LR) for reducing globe retraction. MR recession, with or without adjustable sutures, may be simultaneously combined with partial thickness vertical rectus muscle transposition (VRT) or with superior rectus muscle transposition (SRT). We describe a novel combination of surgical procedures in the management of esotropic-DRS in two patients. In our first patient, following an initial MR recession combined with LR disinsertion and periosteal fixation (LRDAPF), a modified Nishida procedure was performed. In our second patient following a prior simultaneous MR recession and LR Y splitting with recession, we combined periosteal fixation of the LR with a modified Nishida procedure of the vertical rectus muscles.

The Effect of Quantum Noise on Multipartite Entanglement from a Cascaded Parametric Amplifier

The tripartite entanglement generated from a cascaded parametric amplifier is always present in the whole gain region in the ideal condition. However, in practical applications, the quantum entanglement is very fragile and easily deteriorated by quantum noise from interactions with external environments, e.g., the avoidable attenuation and amplification operations may lead to some degradation effects on the quantum entanglement. Therefore, in this work, bipartite entanglement for the three pairs and tripartite entanglement in this cascaded parametric amplifier under the circumstances of attenuation and amplification operations are analyzed by using positivity under partial transposition criterion. The results show that tripartite entanglement is robust to the deterioration effects from the attenuation and amplification operations rather than bipartite entanglement. Our results may find some practical applications of multipartite quantum entanglement in quantum secure communications.

Comparing bound entanglement of bell diagonal pairs of qutrits and ququarts

We compare the classification as entangled or separable of Bell diagonal bipartite qudits with positive partial transposition (PPT) and their properties for different dimensions. For dimension d ge 3, a form of entanglement exists that is hard to detect and called bound entanglement due to the fact that such entangled states cannot be used for entanglement distillation. Up to this date, no efficient solution is known to differentiate bound entangled from separable states. We address and compare this problem named separability problem for a family of bipartite Bell diagonal qudits with special algebraic and geometric structures and applications in quantum information processing tasks in different dimensions. Extending analytical and numerical methods and results for Bell diagonal qutrits (d=3), we successfully classify more than 75% of representative Bell diagonal PPT states for d=4. Via those representative states we are able to estimate the volumes of separable and bound entangled states among PPT ququarts (d=4). We find that at least 75.7% of all PPT states are separable, 1.7% bound entangled and for 22.6% it remains unclear whether they are separable or bound entangled. Comparing the structure of bound entangled states and their detectors, we find considerable differences in the detection capabilities for different dimensions and relate those to differences of the Euclidean geometry for qutrits (d=3) and ququarts (d=4). Finally, using a detailed visual analysis of the set of separable and bound entangled Bell diagonal states in both dimensions, qualitative observations are made that allow to better distinguish bound entangled from separable states.

Real Decreto 601/2019 sobre justificación y optimización: aspectos prácticos

The Royal Decree 601/2019 of 18th october is the result of the partial transposition into the Spanish legal system of the EURATOM Directive 59/2013. This Royal Decree includes the mandates of the Directive related to the need to justify and optimize medical exposure, including that of asymptomatic people, proposal of stricter requirements regarding the information that must be provided to the patient, registration and notification of the doses of medical-radiological procedures, use of reference levels for diagnosis and the availability of dose-indicating devices. The article reviews the most relevant aspects and novelties related to the principles of justification, optimization, dose control and the obligations derived from the right to information and consent. This Royal Decree considers essential for radiologists to develop a high level of competence and a new list of responsibilities and functions, which are detailed and analysed in this article.

Experimental demonstration on quantum coherence evolution of two-mode squeezed state

As one of the most remarkable features of quantum mechanics, quantum coherence is regarded as an important quantum resource in the quantum information processing. The one-mode squeezed state and the two-mode squeezed state (Einstein-Podolsky-Rosen (EPR) entangled states) as the most representative examples of nonclassical states both have quantum coherence. The squeezing property of the squeezed state is described by the variance of quadrature components, and the positive partial transposition (PPT) criterion is used to describe the entanglement of the EPR entangled states. The research of the quantum coherence of Gaussian states is also a bridge between the properties of squeezing and entanglement. It has been shown that the quantum coherence with infinite-dimensional systems can be quantified by relative entropy. One of the widely used effective methods to obtain the value of quantum coherence experimentally is the quantum tomography. The covariance matrices of the quantum states are reconstructed via balanced homodyne detection and then taken into quantum coherence expression to calculate the corresponding value. The main factors affecting quantum coherence are the classical and uncorrelated noise in the actual experimental generation processing and the decoherence effect caused by the coupling between quantum resources and the surrounding environment. And the quantum coherence evolution in the generation and transmission process of the quantum resources is essential for the practical applications. Therefore, we analyze in detail the influences of the impurity of quantum resource on squeezing, entanglement and quantum coherence. The evolutions of quantum coherence of these Gaussian states in the lossy channels are demonstrated experimentally. The quantum coherence is shown to be robust against the loss in the lossy channels, which is similar to the case of squeezing and entanglement. The quantum coherences of the squeezed states and the EPR entangled states are robust against the thermal photons in the actual experimental generation processing, although the squeezing and entanglement of Gaussian states disappear at a certain number of thermal photons. Our research results provide a reference for the practical applications of quantum coherence of the squeezed state and entangled states in the lossy environment.