Physical Review APub Date : 2024-12-10DOI: 10.1103/physreva.110.062207
Nattaphong Wonglakhon, Howard M. Wiseman, Areeya Chantasri
{"title":"Completely positive trace-preserving maps for higher-order unraveling of Lindblad master equations","authors":"Nattaphong Wonglakhon, Howard M. Wiseman, Areeya Chantasri","doi":"10.1103/physreva.110.062207","DOIUrl":"https://doi.org/10.1103/physreva.110.062207","url":null,"abstract":"Theoretical tools used in processing continuous measurement records from real experiments to obtain quantum trajectories can easily lead to numerical errors due to a noninfinitesimal time resolution. In this work we propose a systematic assessment of the accuracy of a map. We perform error analyses for diffusive quantum trajectories, based on single-time-step Kraus operators proposed in the literature, and find the orders in time increments $mathrm{ensuremath{Delta}}t$, to which such operators satisfy the conditions for valid average quantum evolution (completely positive, convex linear, and trace preserving), and the orders to which they match the Lindblad solutions. Given these error analyses, we propose a Kraus operator that satisfies the valid average quantum evolution conditions and agrees with the Lindblad master equation, to second order in $mathrm{ensuremath{Delta}}t$, thus surpassing all other existing approaches. In order to test how well our proposed operator reproduces exact quantum trajectories, we analyze two examples of qubit measurement, where exact maps can be derived: a qubit subjected to a dispersive ($z$-basis) measurement and a fluorescence (dissipative) measurement. We show analytically that our proposed operator gives the smallest average trace distance to the exact quantum trajectories compared to existing approaches.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"110 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147916853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-11-20DOI: 10.1103/physreva.110.053712
Offek Tziperman, Victor Rueskov Christiansen, Ido Kaminer, Klaus Mølmer
{"title":"Parametric amplification of a quantum pulse","authors":"Offek Tziperman, Victor Rueskov Christiansen, Ido Kaminer, Klaus Mølmer","doi":"10.1103/physreva.110.053712","DOIUrl":"https://doi.org/10.1103/physreva.110.053712","url":null,"abstract":"Creating and manipulating quantum states of light requires nonlinear interactions. We present here a multimode theory for the transformation of an arbitrary quantum pulse by Hamiltonians that are quadratic in field creation and annihilation operators. We show, in particular, that any input quantum pulse will feed only one or two distinct output modes. Our result readily provides both the output modes and the quantum states after transformation of arbitrary input wave packets. While being central for applications in quantum information processing with traveling bosonic modes, e.g., in quantum networks, our theoretical method and its results are not anticipated by the conventional Bogoliubov diagonalization of the problem in many input and output eigenmodes.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"110 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147922119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-10-23DOI: 10.1103/physreva.110.043115
Je Hoi Mun, Sung-Ho Jang, Sang Ki Nam
{"title":"Quantum-optical radiative recombination between electrons and ions analyzed with a semiclassical picture","authors":"Je Hoi Mun, Sung-Ho Jang, Sang Ki Nam","doi":"10.1103/physreva.110.043115","DOIUrl":"https://doi.org/10.1103/physreva.110.043115","url":null,"abstract":"In this work, quantum-optical radiative recombinations between electrons and ions are analyzed using a semiclassical approach without losing their specific quantum-optical nature. Under moderately strong driving field conditions, the results of the quantum-optical model are consistent with the semiclassically derived results in terms of both the spectral intensity and phase. Deviations between the two models, which are observed under extremely strong driving field conditions, are investigated in the time and frequency domains to clarify the underlying reasons. In addition, the radiative recombination dynamics between a free electron and a bare ion can be simulated using our quantum model. In recent decades, the semiclassical model combined with the classical equations of light has been used as an intuitive and powerful tool to study the macroscopic buildup of nonlinearly generated light. In this macroscopic approach, the phase information of individual atomic radiations plays an essential role. Since our model can provide spectral phases of quantum-optical lights generated from individual atoms, it is now feasible to pursue the macroscopic buildup of specific quantum-optical radiations and relevant phenomena by using the conventional approach used for the semiclassical model.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"110 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147905276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dissipatively stabilized squeezed-cat qubits and their application in thermometry","authors":"Chengsong Zhao, Wenlin Li, Biao Xiong, Wei‐Jiang Gong, Ling Zhou","doi":"10.1103/physreva.110.043517","DOIUrl":"https://doi.org/10.1103/physreva.110.043517","url":null,"abstract":"Quantum error correction codes, such as noise-biased squeezed-cat qubits, hold promise for preserving quantum coherence and advancing various quantum information technologies. In this paper we demonstrate the stabilization of squeezed-cat qubits through the cooling of a mechanical oscillator. By investigating the bit-flip rate related to two-photon heating processes originating from the mechanical oscillator, we reveal the oscillator's potential as a probe for detecting environmental temperature. Moreover, we observe that the extended bit-flip lifetime of the squeezed-cat qubit significantly enhances temperature detection sensitivity. Finally, we analyze the impacts of single-photon loss and dephasing channels on thermometry.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"110 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147887780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-23DOI: 10.1103/physreva.110.032432
Sophia M. Walls, Ian J. Ford
{"title":"Memory effects in a sequence of measurements of noncommuting observables","authors":"Sophia M. Walls, Ian J. Ford","doi":"10.1103/physreva.110.032432","DOIUrl":"https://doi.org/10.1103/physreva.110.032432","url":null,"abstract":"We use continuous, stochastic quantum trajectories within a framework of quantum state diffusion (QSD) to describe alternating measurements of two noncommuting observables. Projective measurement of an observable completely destroys memory of the outcome of a previous measurement of the conjugate observable. In contrast, measurement under QSD is not projective and it is possible to vary the rate at which information about previous measurement outcomes is lost by changing the strength of measurement. We apply our methods to a spin 1/2 system and a spin 1 system undergoing alternating measurements of the <a:math xmlns:a=\"http://www.w3.org/1998/Math/MathML\"><a:msub><a:mi>S</a:mi><a:mi>z</a:mi></a:msub></a:math> and <b:math xmlns:b=\"http://www.w3.org/1998/Math/MathML\"><b:msub><b:mi>S</b:mi><b:mi>x</b:mi></b:msub></b:math> spin observables. Performing strong <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\"><c:msub><c:mi>S</c:mi><c:mi>z</c:mi></c:msub></c:math> measurements and weak <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\"><d:msub><d:mi>S</d:mi><d:mi>x</d:mi></d:msub></d:math> measurements on the spin 1 system, we demonstrate return to the same eigenstate of <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\"><e:msub><e:mi>S</e:mi><e:mi>z</e:mi></e:msub></e:math> to a degree beyond that expected from projective measurements and the Born rule. Such a memory effect appears to be greater for return to the <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\"><f:mrow><f:mo>±</f:mo><f:mn>1</f:mn></f:mrow></f:math> eigenstates than the 0 eigenstate. Furthermore, the spin 1 system follows a measurement cascade process where an initial superposition of the three eigenstates of the observable evolves into a superposition of just two, before finally collapsing into a single eigenstate, giving rise to a distinctive pattern of evolution of the spin components. Published by the American Physical Society 2024","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"110 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147896422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-19DOI: 10.1103/physreva.110.032817
Denis Mishin, Dmitry Tregubov, Nikolay Kolachevsky, Artem Golovizin
{"title":"Combined microwave and optical spectroscopy for hyperfine structure analysis in thulium atoms","authors":"Denis Mishin, Dmitry Tregubov, Nikolay Kolachevsky, Artem Golovizin","doi":"10.1103/physreva.110.032817","DOIUrl":"https://doi.org/10.1103/physreva.110.032817","url":null,"abstract":"We present refined values of the hyperfine splitting frequencies of the ground <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mo>|</mo><mi>g</mi><mo>〉</mo></mrow><mo>=</mo><mrow><mrow><mo>|</mo></mrow><mrow><mn>4</mn><msup><mi>f</mi><mn>13</mn></msup><mrow><msup><mo>(</mo><mn>2</mn></msup><msup><mi>F</mi><mi>o</mi></msup><mo>)</mo></mrow><mn>6</mn><msup><mi>s</mi><mn>2</mn></msup><mo>,</mo><mi>J</mi><mo>=</mo><mn>7</mn><mo>/</mo><mn>2</mn></mrow><mrow><mo>〉</mo></mrow></mrow></mrow></math> and clock <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mrow><mo>|</mo><mi>c</mi><mo>〉</mo></mrow><mo>=</mo><mrow><mrow><mo>|</mo></mrow><mrow><mn>4</mn><msup><mi>f</mi><mn>13</mn></msup><mrow><msup><mo>(</mo><mn>2</mn></msup><msup><mi>F</mi><mi>o</mi></msup><mo>)</mo></mrow><mn>6</mn><msup><mi>s</mi><mn>2</mn></msup><mo>,</mo><mi>J</mi><mo>=</mo><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mrow><mo>〉</mo></mrow></mrow></mrow></math> states of thulium atoms, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msubsup><mi>f</mi><mrow><mi>g</mi></mrow><mtext>HFS</mtext></msubsup><mo>=</mo><mn>1</mn><mspace width=\"0.16em\"></mspace><mn>496</mn><mspace width=\"0.16em\"></mspace><mn>550</mn><mspace width=\"0.16em\"></mspace><mn>658.23</mn><mrow><mo>(</mo><mn>3</mn><mo>)</mo></mrow></mrow></math> Hz and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msubsup><mi>f</mi><mrow><mi>c</mi></mrow><mtext>HFS</mtext></msubsup><mo>=</mo><mn>2</mn><mspace width=\"0.16em\"></mspace><mn>113</mn><mspace width=\"0.16em\"></mspace><mn>946</mn><mspace width=\"0.16em\"></mspace><mn>873.08</mn><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math> Hz, respectively. The measurements are performed on an ultracold atomic ensemble in an optical lattice using combined microwave and optical transition spectroscopy. The achieved measurement accuracy of less than 0.1 ppb represents an improvement of 2 and 7 orders of magnitude for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>f</mi><mrow><mi>g</mi></mrow><mtext>HFS</mtext></msubsup></math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mi>f</mi><mrow><mi>c</mi></mrow><mtext>HFS</mtext></msubsup></math>, respectively, compared to the previously published values. We also refine the value of the Landé <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>g</mi></math>-factor of the clock level to <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>g</mi><mi>c</mi></msub><mo>=</mo><mn>0.854</mn><mspace width=\"0.16em\"></mspace><mn>786</mn><mrow><mo>(</mo><mn>12</mn><mo>)</mo></mrow></mrow></math>. The results of this work can be used in the frequency standards and quantum simulators based on thulium atoms being developed today, as well as in a number of fundamental studies that require precise knowledge of the hyperfine structure characteristics of various elements.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"4 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-19DOI: 10.1103/physreva.110.033112
Dilfuza Umarova, Otabek Umarov, Attila Tóth, András Csehi
{"title":"Spectral evidence of vibronic Rabi oscillations in the resonance-enhanced photodissociation of MgH+","authors":"Dilfuza Umarova, Otabek Umarov, Attila Tóth, András Csehi","doi":"10.1103/physreva.110.033112","DOIUrl":"https://doi.org/10.1103/physreva.110.033112","url":null,"abstract":"We study by real-time wave-packet simulations the sequential two-photon dissociation of the <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mi>MgH</mi></mrow><mo>+</mo></msup></math> molecule, under intense ultraviolet laser pulses of narrow spectral width. By a resonant coupling, one-photon Rabi oscillations are generated between two vibrational levels of the molecule, belonging to two different bound electronic states. These vibronic Rabi oscillations are probed upon absorption of further photons from the same laser pulse, that gradually promote the molecule to a dissociative electronic state. Calculating the energy spectrum of the photofragments explicitly analytically, we elucidate the physical origin of the main spectral features—such as the splitting, shifting, asymmetry, and multipeak pattern—identified by accurate numerical simulations. We find that the pronounced spectral intensity modulations result from the interference of fragment amplitudes that are generated during the distinct Rabi cycles in the upper and lower dynamically dressed states, formed upon the resonant coupling with the laser pulse. These intensity modulations are sensitively influenced by the resonant and nonresonant Stark effects, and can be manipulated by the parameters of the applied laser pulse. Our results contribute to the understanding and control of ultrafast coherent phenomena via the energy spectrum of particles emitted during the dynamical process under investigation.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"27 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-19DOI: 10.1103/physreva.110.032816
Gregory S. Adkins, Ulrich D. Jentschura
{"title":"Relativistic and recoil corrections to vacuum polarization in muonic systems: Three-photon exchange, gauge invariance, and numerical values","authors":"Gregory S. Adkins, Ulrich D. Jentschura","doi":"10.1103/physreva.110.032816","DOIUrl":"https://doi.org/10.1103/physreva.110.032816","url":null,"abstract":"For an accurate theoretical description of muonic bound systems, it is crucial to consistently treat relativistic and recoil corrections to vacuum polarization. The one-loop vacuum-polarization effect is by far the dominant quantum electrodynamic (QED) energy correction for bound muons, being of order <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>α</mi><msup><mrow><mo>(</mo><mi>Z</mi><mi>α</mi><mo>)</mo></mrow><mn>2</mn></msup><msub><mi>m</mi><mi>r</mi></msub></mrow></math>, where <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>α</mi></math> is the fine-structure constant, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>Z</mi></math> is the nuclear charge number, and <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>m</mi><mi>r</mi></msub></math> is the reduced mass. Gauge invariance of the relativistic and recoil corrections to vacuum polarization of order <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>α</mi><msup><mrow><mo>(</mo><mi>Z</mi><mi>α</mi><mo>)</mo></mrow><mn>4</mn></msup><msub><mi>m</mi><mi>r</mi></msub></mrow></math> is investigated with respect to nonretarded and standard, renormalized variants of Coulomb gauge. The invariance is shown after including three-photon exchange diagrams. Our derivation is based on an adapted form of nonrelativistic quantum electrodynamics for bound muon systems (<math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>NRQED</mi><mi>μ</mi></msub></math>), which is a version of NRQED where the hard scale is set at the muon mass instead of the electron mass. Updated values for the gauge-independent corrections for one-muon ions with nuclear charge numbers <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>Z</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn></mrow></math> are presented.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"24 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-19DOI: 10.1103/physreva.110.033321
Alice Marché, Hironobu Yoshida, Alberto Nardin, Hosho Katsura, Leonardo Mazza
{"title":"Universality and two-body losses: Lessons from the effective non-Hermitian dynamics of two particles","authors":"Alice Marché, Hironobu Yoshida, Alberto Nardin, Hosho Katsura, Leonardo Mazza","doi":"10.1103/physreva.110.033321","DOIUrl":"https://doi.org/10.1103/physreva.110.033321","url":null,"abstract":"We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and on a lattice. The asymptotic decay rate and the universal power-law form of the decay of the number of particles are exactly computed in the whole parameter space of the problem. When in the initial state the two particles are far apart, the average number of particles in the setup decays with time <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>t</mi></math> as <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>t</mi><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math>; a different power law, <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mi>t</mi><mrow><mo>−</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup></math>, is found when the two particles overlap in the initial state. These results are valid both in the continuum and on a lattice, but in the latter case a logarithmic correction appears.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"30 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Physical Review APub Date : 2024-09-18DOI: 10.1103/physreva.110.032617
Julia A. Kunzelmann, Hermann Kampermann, Dagmar Bruß
{"title":"Multipartite multiplexing strategies for quantum routers","authors":"Julia A. Kunzelmann, Hermann Kampermann, Dagmar Bruß","doi":"10.1103/physreva.110.032617","DOIUrl":"https://doi.org/10.1103/physreva.110.032617","url":null,"abstract":"This work explores the important role of quantum routers in communication networks and investigates the increase in efficiency using memories and multiplexing strategies. Motivated by the bipartite setup introduced by Abruzzo <i>et al.</i> [<span>Phys. Rev. A</span> <b>89</b>, 012303 (2014)] for finite-range multiplexing in quantum repeaters, we extend the study to an <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math>-partite network with a router as a central station. We present a general protocol for <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math> parties after defining the underlying matching problem and we calculate the router rate for different <math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math>. We analyze the improvement due to multiplexing and analyze the secret key rate with explicit results for the tripartite network. Investigating strategic qubit selection for the Greenberger-Horne-Zeilinger measurements, we show that using cutoffs to remove qubits after a certain number of rounds and consistently combining qubits with the lowest number of storage rounds leads to an optimal secret key rate.","PeriodicalId":20146,"journal":{"name":"Physical Review A","volume":"31 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142262773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}