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Title: Partial time-reversal transformation and entanglement negativity in fermionic systems

Abstract

Not provided.

Authors:
; ;
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1535897
DOE Contract Number:  
SC0008692
Resource Type:
Journal Article
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 95; Journal Issue: 16; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
Materials Science; Physics

Citation Formats

Shapourian, Hassan, Shiozaki, Ken, and Ryu, Shinsei. Partial time-reversal transformation and entanglement negativity in fermionic systems. United States: N. p., 2017. Web. doi:10.1103/physrevb.95.165101.
Shapourian, Hassan, Shiozaki, Ken, & Ryu, Shinsei. Partial time-reversal transformation and entanglement negativity in fermionic systems. United States. doi:10.1103/physrevb.95.165101.
Shapourian, Hassan, Shiozaki, Ken, and Ryu, Shinsei. Sat . "Partial time-reversal transformation and entanglement negativity in fermionic systems". United States. doi:10.1103/physrevb.95.165101.
@article{osti_1535897,
title = {Partial time-reversal transformation and entanglement negativity in fermionic systems},
author = {Shapourian, Hassan and Shiozaki, Ken and Ryu, Shinsei},
abstractNote = {Not provided.},
doi = {10.1103/physrevb.95.165101},
journal = {Physical Review B},
issn = {2469-9950},
number = 16,
volume = 95,
place = {United States},
year = {2017},
month = {4}
}

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<span class="author">Illuminati, Fabrizio</span> ; <span class="author">INFN Sezione di Napoli-Gruppo Collegato di Salerno, Via S. Allende, 84081 Baronissi, SA</span> <span class="text-muted pubdata"> - Physical Review. A</span> </span> </div> <div class="abstract">We study the entanglement of general (pure or mixed) two-mode Gaussian states of continuous-variable systems by comparing the two available classes of computable measures of entanglement: entropy-inspired Gaussian convex-roof measures and positive partial transposition-inspired measures (negativity and logarithmic negativity). We first review the formalism of Gaussian measures of entanglement, adopting the framework introduced in M. M. Wolf et al., Phys. Rev. A 69, 052320 (2004), where the Gaussian entanglement of formation was defined. We compute explicitly Gaussian measures of entanglement for two important families of nonsymmetric two-mode Gaussian state: namely, the states of extremal (maximal and minimal) negativities at fixed<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> global and local purities, introduced in G. Adesso et al., Phys. Rev. Lett. 92, 087901 (2004). This analysis allows us to compare the different orderings induced on the set of entangled two-mode Gaussian states by the negativities and by the Gaussian measures of entanglement. We find that in a certain range of values of the global and local purities (characterizing the covariance matrix of the corresponding extremal states), states of minimum negativity can have more Gaussian entanglement of formation than states of maximum negativity. Consequently, Gaussian measures and negativities are definitely inequivalent measures of entanglement on nonsymmetric two-mode Gaussian states, even when restricted to a class of extremal states. On the other hand, the two families of entanglement measures are completely equivalent on symmetric states, for which the Gaussian entanglement of formation coincides with the true entanglement of formation. Finally, we show that the inequivalence between the two families of continuous-variable entanglement measures is somehow limited. Namely, we rigorously prove that, at fixed negativities, the Gaussian measures of entanglement are bounded from below. Moreover, we provide some strong evidence suggesting that they are as well bounded from above.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PhysRevA.72.032334" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20718520" data-product-type="Journal Article" data-product-subtype="" >10.1103/PhysRevA.72.032334</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/22220730-speed-disentanglement-multiqubit-systems-under-depolarizing-channel" itemprop="url">Speed of disentanglement in multiqubit systems under a depolarizing channel</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Zhang, Fu-Lin, E-mail: flzhang@tju.edu.cn</span> ; <span class="author">Jiang, Yue</span> ; <span class="author">Liang, Mai-Lin, E-mail: mailinliang@yahoo.com.cn</span> <span class="text-muted pubdata"> - Annals of Physics (New York)</span> </span> </div> <div class="abstract">We investigate the speed of disentanglement in the multiqubit systems under the local depolarizing channel, in which each qubit is independently coupled to the environment. We focus on the bipartition entanglement between one qubit and the remaining qubits constituting the system, which is measured by the negativity. For the two-qubit system, the speed for the pure state completely depends on its entanglement. The upper and lower bounds of the speed for arbitrary two-qubit states, and the necessary conditions for a state achieving them, are obtained. For the three-qubit system, we study the speed for pure states, whose entanglement properties can<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> be completely described by five local-unitary-transformation invariants. An analytical expression of the relation between the speed and the invariants is derived. The speed is enhanced by the three-tangle which is the entanglement among the three qubits, but reduced by the two-qubit correlations outside the concurrence. The decay of the negativity can be restrained by the other two negativity with the coequal sense. The unbalance between two qubits can reduce the speed of disentanglement of the remaining qubit in the system, and even can retrieve the entanglement partially. For the k-qubit systems in an arbitrary superposition of Greenberger–Horne–Zeilinger state and W state, the speed depends almost entirely on the amount of the negativity when k increases to five or six. An alternative quantitative definition for the robustness of entanglement is presented based on the speed of disentanglement, with comparison to the widely studied robustness measured by the critical amount of noise parameter where the entanglement vanishes. In the limit of large number of particles, the alternative robustness of the Greenberger–Horne–Zeilinger-type states is inversely proportional to k, and the one of the W states approaches 1/√(k)</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1016/J.AOP.2013.03.003" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="22220730" data-product-type="Journal Article" data-product-subtype="AC" >10.1016/J.AOP.2013.03.003</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1469298-photonic-topological-insulator-broken-time-reversal-symmetry" itemprop="url">Photonic topological insulator with broken time-reversal symmetry</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">He, Cheng</span> ; <span class="author">Sun, Xiao-Chen</span> ; <span class="author">Liu, Xiao-Ping</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Proceedings of the National Academy of Sciences of the United States of America</span> </span> </div> <div class="abstract">A topological insulator is a material with an insulating interior but time-reversal symmetry-protected conducting edge states. Since its prediction and discovery almost a decade ago, such a symmetry-protected topological phase has been explored beyond electronic systems in the realm of photonics. Electrons are spin-1/2 particles, whereas photons are spin-1 particles. The distinct spin difference between these two kinds of particles means that their corresponding symmetry is fundamentally different. It is well understood that an electronic topological insulator is protected by the electron’s spin-1/2 (fermionic) time-reversal symmetry <b>T<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> $$2\atop{f}$$ = -1</b>. However, the same protection does not exist under normal circumstances for a photonic topological insulator, due to photon’s spin-1 (bosonic) time-reversal symmetry <b>T$$2\atop{b}$$ = -1</b>. Here, we report a design of photonic topological insulator using the Tellegen magnetoelectric coupling as the photonic pseudospin orbit interaction for left and right circularly polarized helical spin states. The Tellegen magnetoelectric coupling breaks bosonic time-reversal symmetry but instead gives rise to a conserved artificial fermionic-like-pseudo time-reversal symmetry, T <sub>p</sub> ( <b>T$$2\atop{p}$$ = -1</b>), due to the electromagnetic duality. Surprisingly, we find that, in this system, the helical edge states are, in fact, protected by this fermionic-like pseudo time-reversal symmetry T <sub>p</sub> rather than by the bosonic time-reversal symmetry T <sub>b</sub>. This remarkable finding is expected to pave a new path to understanding the symmetry protection mechanism for topological phases of other fundamental particles and to searching for novel implementations for topological insulators.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 77<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1073/pnas.1525502113" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1469298" data-product-type="Journal Article" data-product-subtype="AM" >10.1073/pnas.1525502113</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1469298" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1469298" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/20786455-temperature-dependence-interaction-induced-entanglement" itemprop="url">Temperature dependence of interaction-induced entanglement</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Khasin, Michael</span> ; <span class="author">Kosloff, Ronnie</span> <span class="text-muted pubdata"> - Physical Review. A</span> </span> </div> <div class="abstract">Both direct and indirect weak nonresonant interactions are shown to produce entanglement between two initially disentangled systems prepared as a tensor product of thermal states, provided the initial temperature is sufficiently low. Entanglement is determined by the Peres-Horodecki criterion, which establishes that a composite state is entangled if its partial transpose is not positive. If the initial temperature of the thermal states is higher than an upper critical value T{sub uc} the minimal eigenvalue of the partially transposed density matrix of the composite state remains positive in the course of the evolution. If the initial temperature of the thermal states<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> is lower than a lower critical value T{sub lc}{<=}T{sub uc} the minimal eigenvalue of the partially transposed density matrix of the composite state becomes negative, which means that entanglement develops. We calculate the lower bound T{sub lb} for T{sub lc} and show that the negativity of the composite state is negligibly small in the interval T{sub lb}<T<T{sub uc}. Therefore the lower-bound temperature T{sub lb} can be considered as the critical temperature for the generation of entanglement. It is conjectured that above this critical temperature a composite quantum system could be simulated using classical computers.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1103/PHYSREVA.72.0" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="20786455" data-product-type="Journal Article" data-product-subtype="" >10.1103/PHYSREVA.72.0</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/22403505-probing-planckian-physics-de-sitter-space-quantum-correlations" itemprop="url">Probing Planckian physics in de Sitter space with quantum correlations</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Feng, Jun, E-mail: j.feng1@uq.edu.au</span> ; <span class="author">Zhang, Yao-Zhong</span> ; <span class="author">Gould, Mark D.</span> ; <span class="author">...</span> <span class="text-muted pubdata"> - Annals of Physics (New York)</span> </span> </div> <div class="abstract">We study the quantum correlation and quantum communication channel of both free scalar and fermionic fields in de Sitter space, while the Planckian modification presented by the choice of a particular α-vacuum has been considered. We show the occurrence of degradation of quantum entanglement between field modes for an inertial observer in curved space, due to the radiation associated with its cosmological horizon. Comparing with standard Bunch–Davies choice, the possible Planckian physics causes some extra decrement on the quantum correlation, which may provide the means to detect quantum gravitational effects via quantum information methodology in future. Beyond single-mode approximation, we<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> construct proper Unruh modes admitting general α-vacua, and find a convergent feature of both bosonic and fermionic entanglements. In particular, we show that the convergent points of fermionic entanglement negativity are dependent on the choice of α. Moreover, an one-to-one correspondence between convergent points H{sub c} of negativity and zeros of quantum capacity of quantum channels in de Sitter space has been proved. - Highlights: • Quantum correlation and quantum channel in de Sitter space are studied. • Gibbons–Hawking effect causes entanglement degradation for static observer. • Planckian physics causes extra decrement on quantum correlation. • Convergent feature of negativity relies on the choice of alpha-vacua. • Link between negativity convergence and quantum channel capacity is given.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink">DOI: <a class="misc doi-link " href="https://doi.org/10.1016/J.AOP.2014.10.014" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="22403505" data-product-type="Journal Article" data-product-subtype="AC" >10.1016/J.AOP.2014.10.014</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item d-block d-inline-small"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook" style=""></span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter" style=""></span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play" style=""></span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/css/ostigov.fonts.191107.1502.css" rel="stylesheet"> <script src="/js/ostigov.191107.1502.js"></script><noscript></noscript> <script defer src="/js/ostigov.biblio.191107.1502.js"></script><noscript></noscript> <script defer src="/js/lity.js"></script><noscript></noscript> <script async type="text/javascript" src="/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- OSTI.GOV v.191107.1502 --> </html>