<?xml version="1.0" encoding="utf-8"?> <feed xmlns="http://www.w3.org/2005/Atom"> <title type="text">Recent zbMATH articles in MSC 81P16</title> <id>https://zbmath.org/atom/cc/81P16</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/" /> <link href="https://zbmath.org/atom/cc/81P16" rel="self" /> <generator>Werkzeug</generator> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Coend optics for quantum combs</title> <id>https://zbmath.org/1545.18029</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.18029" /> <author> <name>"Hefford, James"</name> <uri>https://zbmath.org/authors/?q=ai:hefford.james</uri> </author> <author> <name>"Comfort, Cole"</name> <uri>https://zbmath.org/authors/?q=ai:comfort.cole</uri> </author> <content type="text">Summary: We compare two possible ways of defining a category of 1-combs, the first intensionally as coend optics and the second extensionally as a quotient by the operational behaviour of 1-combs on lower-order maps. We show that there is a full and bijective on objects functor quotienting the intensional definition to the extensional one and give some sufficient conditions for this functor to be an isomorphism of categories. We also show how the constructions for 1-combs can be extended to produce polycategories of \(n\)-combs with similar results about when these polycategories are equivalent. The extensional definition is of particular interest in the study of quantum combs and we hope this work might produce further interest in the usage of optics for modelling these structures in quantum theory. For the entire collection see [Zbl 1522.68037].</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Is the universe in a mixed state?</title> <id>https://zbmath.org/1545.81016</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81016" /> <author> <name>"Gao, Shan"</name> <uri>https://zbmath.org/authors/?q=ai:gao.shan</uri> </author> <content type="text">Summary: Quantum mechanics with a fundamental density matrix has been proposed and discussed recently. Moreover, it has been conjectured that the universe is not in a pure state but in a mixed state in this theory. In this paper, I argue that this mixed state conjecture has two main problems: the redundancy problem and the underdetermination problem, which are lacking in quantum mechanics with a definite initial wave function of the universe.</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Mutual conversions between Knill-Laflamme-Milburn and \(W\) states</title> <id>https://zbmath.org/1545.81025</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81025" /> <author> <name>"Shen, Cai-Peng"</name> <uri>https://zbmath.org/authors/?q=ai:shen.cai-peng</uri> </author> <author> <name>"Gao, Ya"</name> <uri>https://zbmath.org/authors/?q=ai:gao.ya</uri> </author> <author> <name>"Su, Shi-Lei"</name> <uri>https://zbmath.org/authors/?q=ai:su.shi-lei</uri> </author> <author> <name>"Mao, Yanchao"</name> <uri>https://zbmath.org/authors/?q=ai:mao.yanchao</uri> </author> <author> <name>"Liang, Erjun"</name> <uri>https://zbmath.org/authors/?q=ai:liang.erjun</uri> </author> <author> <name>"Chen, Shu"</name> <uri>https://zbmath.org/authors/?q=ai:chen.shu</uri> </author> <content type="text">Summary: Herein, two proposals are speculated to realize mutual conversions between Knill-Laflamme-Milburn (KLM) and \(W\) entangled states via X homodyne measurement (HM). By one of these proposals three-qubit mutual conversions can be realized between these two photonic polarization entangled states. The other can be generalized to convert an arbitrary-qubit KLM state to a \(W\) state adopting a control-NOT gate. With the increasing number of qubits, the utilization ratio of photons in the second proposal would be close to unity. Analyses of the three-qubit mutual conversions show that the proposal has a low error rate and high utilization ratio of photons. Moreover, the fidelity can also be very high even in consideration of decoherence. The P homodyne measurement is analyzed as well to improve the precision. The proposals, especially the second one, are expected to be helpful to reveal the relationship between these two robust multiple-qubit entanglements. {\copyright} 2018 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Multipartite quantum clock synchronization under the influence of Unruh thermal noise</title> <id>https://zbmath.org/1545.81028</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81028" /> <author> <name>"Zhang, Li"</name> <uri>https://zbmath.org/authors/?q=ai:zhang.li.13|zhang.li.9|zhang.li.14|zhang.li.91|zhang.li.7|zhang.li.5|zhang.li.1|zhang.li.40|zhang.li|zhang.li.27|zhang.li.6|zhang.li.32|zhang.li.20|zhang.li.11|zhang.li.35|zhang.li.10|zhang.li.15|zhang.li.43|zhang.li.8</uri> </author> <author> <name>"Jing, Jiliang"</name> <uri>https://zbmath.org/authors/?q=ai:jing.jiliang</uri> </author> <author> <name>"Fan, Heng"</name> <uri>https://zbmath.org/authors/?q=ai:fan.heng</uri> </author> <author> <name>"Wang, Jieci"</name> <uri>https://zbmath.org/authors/?q=ai:wang.jieci</uri> </author> <content type="text">Summary: A protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh-DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two-party system is always higher than in a multipartite system, while the optimal \(Z\)-type multipartite initial state always performs better than the \(W\)-type state. {\copyright} 2019 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Erratum to: ``Sufficient condition for a quantum state to be genuinely quantum non-Gaussian''</title> <id>https://zbmath.org/1545.81030</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81030" /> <author> <name>"Happ, L."</name> <uri>https://zbmath.org/authors/?q=ai:happ.leon</uri> </author> <author> <name>"Efremov, M. A."</name> <uri>https://zbmath.org/authors/?q=ai:efremov.m-a</uri> </author> <author> <name>"Nha, H."</name> <uri>https://zbmath.org/authors/?q=ai:nha.hyunchul</uri> </author> <author> <name>"Schleich, W. P."</name> <uri>https://zbmath.org/authors/?q=ai:schleich.wolfgang-p</uri> </author> <content type="text">Erratum to the authors' paper [ibid. 20, No. 2, Article ID 023046, 20 p. (2018; Zbl 1540.81017)].</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Probability distribution for the first Casimir operator \(C_1\) in the quantum Coulomb field</title> <id>https://zbmath.org/1545.81031</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81031" /> <author> <name>"Staruszkiewicz, Andrzej"</name> <uri>https://zbmath.org/authors/?q=ai:staruszkiewicz.andrzej</uri> </author> <content type="text">(no abstract)</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Entanglement of mixed states in K盲hler quantization</title> <id>https://zbmath.org/1545.81035</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81035" /> <author> <name>"Barron, Tatyana"</name> <uri>https://zbmath.org/authors/?q=ai:barron.tatyana</uri> </author> <author> <name>"Kazachek, Alexander"</name> <uri>https://zbmath.org/authors/?q=ai:kazachek.alexander</uri> </author> <content type="text">Summary: Let \(M\) is a product of two integral compact K盲hler manifolds. Fix a sufficiently large positive integer \(N\). With a submanifold \(\varLambda\) of \(M\) one can associate a specific mixed state, and entanglement of formation \(F_N(\varLambda)\) of this mixed state. We show that if \(\varLambda_1\) and \(\varLambda_2\) are two connected submanifolds of \(M\) such that \(\varLambda_1\cap \varLambda_2=\emptyset\), then \(F_N(\varLambda \cup \varLambda_2)\le F_N(\varLambda_1) +F_N(\varLambda_2)\). For the entire collection see [Zbl 1515.17004].</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Optimal port-based teleportation</title> <id>https://zbmath.org/1545.81045</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81045" /> <author> <name>"Mozrzymas, Marek"</name> <uri>https://zbmath.org/authors/?q=ai:mozrzymas.marek</uri> </author> <author> <name>"Studzi艅ski, Micha艂"</name> <uri>https://zbmath.org/authors/?q=ai:studzinski.michal</uri> </author> <author> <name>"Strelchuk, Sergii"</name> <uri>https://zbmath.org/authors/?q=ai:strelchuk.sergii</uri> </author> <author> <name>"Horodecki, Micha艂"</name> <uri>https://zbmath.org/authors/?q=ai:horodecki.michal</uri> </author> <content type="text">Summary: Deterministic port-based teleportation (dPBT) protocol is a scheme where a quantum state is guaranteed to be transferred to another system without unitary correction. We characterise the best achievable performance of the dPBT when both the resource state and the measurement is optimised. Surprisingly, the best possible fidelity for an arbitrary number of ports and dimension of the teleported state is given by the largest eigenvalue of a particular matrix -- Teleportation Matrix. It encodes the relationship between a certain set of Young diagrams and emerges as the optimal solution to the relevant semidefinite programme.</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Application of fermionic marginal constraints to hybrid quantum algorithms</title> <id>https://zbmath.org/1545.81054</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81054" /> <author> <name>"Rubin, Nicholas C."</name> <uri>https://zbmath.org/authors/?q=ai:rubin.nicholas-c</uri> </author> <author> <name>"Babbush, Ryan"</name> <uri>https://zbmath.org/authors/?q=ai:babbush.ryan</uri> </author> <author> <name>"McClean, Jarrod"</name> <uri>https://zbmath.org/authors/?q=ai:mcclean.jarrod-r</uri> </author> <content type="text">Summary: Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic \(n\)-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. As a general result, we demonstrate how these marginals concentrate to diagonal quantities when measured on random quantum states. We also show that one can use fermionic \(n\)-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. As a practical demonstration, we simulate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments.</content> </entry> <entry xml:base="https://zbmath.org/atom/cc/81P16"> <title type="text">Quantum mechanics on a \(p\)-adic Hilbert space: foundations and prospects</title> <id>https://zbmath.org/1545.81087</id> <updated>2024-11-22T16:52:57.400418Z</updated> <link href="https://zbmath.org/1545.81087" /> <author> <name>"Aniello, Paolo"</name> <uri>https://zbmath.org/authors/?q=ai:aniello.paolo</uri> </author> <author> <name>"Mancini, Stefano"</name> <uri>https://zbmath.org/authors/?q=ai:mancini.stefano</uri> </author> <author> <name>"Parisi, Vincenzo"</name> <uri>https://zbmath.org/authors/?q=ai:parisi.vincenzo</uri> </author> <content type="text">Summary: We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of \(p\)-adic numbers. In our approach, we are inspired by the idea -- first postulated in [\textit{I. V. Volovich}, Classical Quantum Gravity 4, No. 4, L83--L87 (1987; \url{doi:10.1088/0264-9381/4/4/003})] -- that space, below a suitably small scale, does not behave as a continuum and, accordingly, should be modeled as a totally disconnected metrizable topological space, ruled by a metric satisfying the strong triangle inequality. The first step of our construction is a suitable definition of a \(p\)-adic Hilbert space. Next, after introducing all necessary mathematical tools -- in particular, various classes of linear operators in a \(p\)-adic Hilbert space -- we consider an algebraic definition of physical states in \(p\)-adic quantum mechanics. The corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a \(p\)-adic counterpart of the POVMs associated with a standard quantum system over the complex numbers. Interestingly, it turns out that the typical convex geometry of the space of states of a standard quantum system is replaced, in the \(p\)-adic setting, with an \textit{affine} geometry; therefore, a symmetry transformation of a \(p\)-adic quantum system may be defined as a map preserving this affine geometry. We argue that, as a consequence, the group of all symmetry transformations of a \(p\)-adic quantum system has a richer structure with respect to the case of standard quantum mechanics over the complex numbers.</content> </entry> </feed>

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