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S. M. Finashin - One of the best experts on this subject based on the ideXlab platform.

  • On the Deformation Chirality of Real Cubic Fourfolds
    Compositio Mathematica, 2009
    Co-Authors: S. M. Finashin, Viatcheslav Kharlamov
    Abstract:

    According to our previous results, the conjugacy class of the involution induced by the Complex Conjugation in the homology of a real non-singular cubic fourfold determines the fourfold up to projective equivalence and deformation. Here, we show how to eliminate the projective equivalence and to obtain a pure deformation classification, that is how to respond to the chirality question: which cubics are not deformation equivalent to their image under a mirror reflection. We provide an arithmetical criterion of chirality, in terms of the eigen-sublattices of the Complex Conjugation involution in homology, and show how this criterion can be effectively applied taking as examples M -cubics (that is those for which the real locus has the richest topology) and (M − 1)-cubics (the next case with respect to Complexity of the real locus). It happens that there is one chiral class of M -cubics and three chiral classes of (M−1)-cubics, contrary to two achiral classes of M -cubics and three achiral classes of (M − 1)-cubics. L’univers est un ensemble dissymetrique, et je suis persuade que la vie, telle qu’elle manifeste a nous, est fonction de la dissymetrie de l’univers ou des consequences qu’elle entrâine.

  • ROKHLIN'S QUESTION AND QUOTIENTS OF REAL ALGEBRAIC SURFACES BY THE Complex Conjugation
    Journal of Mathematical Sciences, 2003
    Co-Authors: S. M. Finashin
    Abstract:

    Complex algebraic surfaces defined over ℝ are considered. Local and global topological properties of their quotients by the Complex Conjugation are discussed. Bibliography: 9 titles.

  • A Rokhlin Conjecture and Smooth Quotients by the Complex Conjugation of Singular Real Algebraic Surfaces
    arXiv: Geometric Topology, 1999
    Co-Authors: S. M. Finashin
    Abstract:

    The topology of the orbit space, $Y$, for the action of the Complex Conjugation on a Complex surface, $X$, defined over reals, is studied. I give a criterion for blow-up stable triviality of $Y$ (which implies vanishing of its Seiberg-Witten invariants). The main result concerns the double planes branched along the Complexification of reducible real curves with 2 non-singular components. In connection with it, I analize the real singularities of $X$ which become smooth in $Y$ (after taking quotient).

  • Differential topology of quotients of Complex surfaces by Complex Conjugation
    Journal of Mathematical Sciences, 1998
    Co-Authors: S. M. Finashin
    Abstract:

    The paper contains a brief survey of the author’s results on the diffeomorphism type of quotients of Complex surfaces by anti-holomorphic involutions. The conjecture of complete decomposability is discussed, which says that if such a quotient is simply connected, then it is completely decomposable, i.e., is diffeomorphic to the connected sum of several copies of the projective plane (possibly, with reversed orientation) and the quadric. Bibliography: 11 titles.

  • Decomposability of quotients by Complex Conjugation for rational and Enriques surfaces
    Topology and its Applications, 1997
    Co-Authors: S. M. Finashin
    Abstract:

    Abstract The quotients Y = X / conj by the Complex Conjugation conj: X → X for Complex rational and Enriques surfaces X defined over R are shown to be diffeomorphic to connected sums of CP 2 , whenever the Y are simply connected.

Xianggen Xia - One of the best experts on this subject based on the ideXlab platform.

  • a simple alamouti space time transmission scheme for asynchronous cooperative systems
    IEEE Signal Processing Letters, 2007
    Co-Authors: Xianggen Xia
    Abstract:

    In this letter, we propose a simple orthogonal frequency-division multiplexing (OFDM) scheme for an asynchronous cooperative system, where OFDM is implemented at the source node, and time-reversion and Complex Conjugation are implemented at the relay nodes. The cyclic prefix (CP) at the source node is used for combating the timing errors from the relay nodes. In this scheme, the received signals at the destination node have the Alamouti code structure on each subcarrier, and thus, it has the fast symbol-wise ML decoding. It should be emphasized that the relay nodes only need to implement the time-reversion, some sign changes from plus to minus, and/or the Complex Conjugation to the received signals, and no IDFT or DFT operation is needed. It is shown that this simple scheme achieves second-order diversity gain without the synchronization requirement at the relay nodes.

  • A Simple Alamouti Space–Time Transmission Scheme for Asynchronous Cooperative Systems
    IEEE Signal Processing Letters, 2007
    Co-Authors: Xianggen Xia
    Abstract:

    In this letter, we propose a simple orthogonal frequency-division multiplexing (OFDM) scheme for an asynchronous cooperative system, where OFDM is implemented at the source node, and time-reversion and Complex Conjugation are implemented at the relay nodes. The cyclic prefix (CP) at the source node is used for combating the timing errors from the relay nodes. In this scheme, the received signals at the destination node have the Alamouti code structure on each subcarrier, and thus, it has the fast symbol-wise ML decoding. It should be emphasized that the relay nodes only need to implement the time-reversion, some sign changes from plus to minus, and/or the Complex Conjugation to the received signals, and no IDFT or DFT operation is needed. It is shown that this simple scheme achieves second-order diversity gain without the synchronization requirement at the relay nodes.

Mio Murao - One of the best experts on this subject based on the ideXlab platform.

  • Probabilistic exact universal quantum circuits for transforming unitary operations
    Physical Review A, 2019
    Co-Authors: Marco Túlio Quintino, Akihito Soeda, Qingxiuxiong Dong, Atsushi Shimbo, Mio Murao
    Abstract:

    This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input operation into a unitary output operation in a probabilistic heralded manner. Three classes of protocols are considered, parallel circuits, where the input operations can be performed simultaneously, adaptive circuits, where sequential uses of the input operations are allowed, and general protocols, where the use of the input operations may be performed without a definite causal order. For these three classes, we develop a systematic semidefinite programming approach that finds a circuit which obtains the desired transformation with the maximal success probability. We then analyze in detail three particular transformations: unitary transposition, unitary Complex Conjugation, and unitary inversion. For unitary transposition and unitary inverse, we prove that for any fixed dimension $d$, adaptive circuits have an exponential improvement in terms of uses $k$ when compared to parallel ones. For unitary Complex Conjugation and unitary inversion we prove that if the number of uses $k$ is strictly smaller than $d\ensuremath{-}1$, the probability of success is necessarily zero. We also discuss the advantage of indefinite causal order protocols over causal ones and introduce the concept of delayed input-state quantum circuits.

  • Complex Conjugation supermap of unitary quantum maps and its universal implementation protocol
    Physical Review Research, 2019
    Co-Authors: Jisho Miyazaki, Akihito Soeda, Mio Murao
    Abstract:

    A Complex Conjugation of unitary quantum map is a second-order map (supermap) that maps a unitary operator $U$ to its Complex conjugate $U^*$. First, we present a deterministic quantum protocol that universally implements the Complex Conjugation supermap when we are given a blackbox quantum circuit, guaranteed to implement some unitary operation, whose only known description is its dimension. We then discuss the Complex Conjugation supermap in the context of entanglement theory and derive a Conjugation-based expression of the $G$-concurrence. Finally, we present a physical process involving identical fermions from which the Complex Conjugation protocol is derived as a simulation of the process using qudits.

  • Universal Complex Conjugation of quantum states and unitaries: implementation algorithm and implications
    arXiv: Quantum Physics, 2017
    Co-Authors: Jisho Miyazaki, Akihito Soeda, Mio Murao
    Abstract:

    Not all mathematical funcitions used to define physical quantities are guaranteed to be implementable; Complex Conjugation is one such. We show that universal state Conjugation, i.e., Complex Conjugation of unknown quantum states, is not implementable, even with nonzero failure probability admitted and finitely many state clones supplied. Complex Conjugation can also be defined on unitaries, for which we present a deterministic, universal quantum algorithm with a blackbox quantum gate as the input unitary. Multiple uses of the oracle is shown to be necessary for unitary dimensions larger than 2. An operator used to define this algorithm is exploited to generalize the two-qubit concurrence for pure states. The generalized concurrence is based on Complex Conjugation of states, much like the original concurrence. It is shown to be equivalent to the $G$-concurrence, a previously known generalization of the original concurrence, derived from a separate mathematical observation and a member of a family of concurrence monotones. We show that our approach also reproduces all these concurrence monotones. Finally, the unitary Conjugation algorithm is interpreted in terms of particles and holes and their mode transformation.

Nicolas Perrin - One of the best experts on this subject based on the ideXlab platform.

Sun Zhong-yu - One of the best experts on this subject based on the ideXlab platform.