1,396 research outputs found
General impossible operations in quantum information
We prove a general limitation in quantum information that unifies the
impossibility principles such as no-cloning and no-anticloning. Further, we
show that for an unknown qubit one cannot design a universal Hadamard gate for
creating equal superposition of the original and its complement state.
Surprisingly, we find that Hadamard transformations exist for an unknown qubit
chosen either from the polar or equatorial great circles. Also, we show that
for an unknown qubit one cannot design a universal unitary gate for creating
unequal superpositions of the original and its complement state. We discuss why
it is impossible to design a controlled-NOT gate for two unknown qubits and
discuss the implications of these limitations.Comment: 15 pages, no figures, Discussion about personal quantum computer
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Probing Grand Unification Through Neutrino Oscillations, Leptogenesis, and Proton Decay
Evidence in favor of supersymmetric grand unification including that based on
the observed family multiplet-structure, gauge coupling unification, neutrino
oscillations, baryogenesis, and certain intriguing features of quark-lepton
masses and mixings is noted. It is argued that attempts to understand (a) the
tiny neutrino masses (especially Delta m^2 (nu_2 -nu_3)), (b) the baryon
asymmetry of the universe (which seems to need leptogenesis), and (c) the
observed features of fermion masses such as the ratio m_b/m_tau, the smallness
of V_cb and the maximality of theta_{nu_mu-nu_tau}, seem to select out the
route to higher unification based on an effective string-unified G(224) =
SU(2)_L x SU(2)_R x SU(4)^c or SO(10)-symmetry, operative in 4D, as opposed to
other alternatives.
A predictive framework based on an effective SO(10) or G(224) symmetry
possessing supersymmetry is presented that successfully describes the masses
and mixings of all fermions including neutrinos. It also accounts for the
observed baryon asymmetry of the universe by utilizing the process of
leptogenesis, which is natural to this framework. It is argued that a
conservative upper limit on the proton lifetime within this
SO(10)/G(224)-framework, which is so far most successful, is given by (1/3-2) x
10^34 years. This in turn strongly suggests that an improvement in the current
sensitivity by a factor of five to ten (compared to SuperK) ought to reveal
proton decay. Implications of this prediction for the next-generation nucleon
decay and neutrino-detector are noted.Comment: 40 page, 3 figures. Conference proceedings from Erice School (Sept
2002), Neutrino Conference (Stony Brook, 2002), PASCOS Conference (Mumbai,
2003) Version 2: New references and some clarifications adde
Universal quantum Controlled-NOT gate
An investigation of an optimal universal unitary Controlled-NOT gate that
performs a specific operation on two unknown states of qubits taken from a
great circle of the Bloch sphere is presented. The deep analogy between the
optimal universal C-NOT gate and the `equatorial' quantum cloning machine (QCM)
is shown. In addition, possible applications of the universal C-NOT gate are
briefly discussed.Comment: 18 reference
Geometric Phases for Mixed States during Cyclic Evolutions
The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.Comment: 9 pages, 1 figur
Quantum Communication and Computing With Atomic Ensembles Using Light-Shift Imbalance Induced Blockade
Recently, we have shown that for conditions under which the so-called
light-shift imbalance induced blockade (LSIIB) occurs, the collective
excitation of an ensemble of a multi-level atom can be treated as a closed two
level system. In this paper, we describe how such a system can be used as a
quantum bit (qubit) for quantum communication and quantum computing.
Specifically, we show how to realize a C-NOT gate using the collective qubit
and an easily accessible ring cavity, via an extension of the so-called
Pellizzari scheme. We also describe how multiple, small-scale quantum computers
realized using these qubits can be linked effectively for implementing a
quantum internet. We describe the details of the energy levels and transitions
in 87Rb atom that could be used for implementing these schemes.Comment: 16 pages, 9 figures. Accepted in Phys. Rev.
Subfactors and 1+1-dimensional TQFTs
We construct a certain "cobordism category" D whose morphisms are suitably decorated cobordism classes between similarly decorated closed oriented 1-manifolds, and show that there is essentially a bijection between (1+1-dimensional) unitary topological quantum field theories (TQFTs) defined on D , on the one hand, and Jones' subfactor planar algebras, on the other
Baryon and Lepton Number Violation with Scalar Bilinears
We consider all possible scalar bilinears, which couple to two fermions of
the standard model. The various baryon and lepton number violating couplings
allowed by these exotic scalars are studied. We then discuss which ones are
constrained by limits on proton decay (to a lepton and a meson as well as to
three leptons), neutron-antineutron oscillations, and neutrinoless double beta
decay.Comment: 11 pages latex fil
Dark matter from SU(4) model
The left-right symmetric Pati-Salam model of the unification of quarks and
leptons is based on SU(4) and SU(2)xSU(2) groups. These groups are naturally
extended to include the classification of families of quarks and leptons. We
assume that the family group (the group which unites the families) is also the
SU(4) group. The properties of the 4-th generation of fermions are the same as
that of the ordinary-matter fermions in first three generations except for the
family charge of the SU(4)_F group: F=(1/3,1/3,1/3,-1), where F=1/3 for
fermions of ordinary matter and F=-1 for the 4-th generation. The difference in
F does not allow the mixing between ordinary and fourth-generation fermions.
Because of the conservation of the F charge, the creation of baryons and
leptons in the process of electroweak baryogenesis must be accompanied by the
creation of fermions of the 4-th generation. As a result the excess n_B of
baryons over antibaryons leads to the excess n_{\nu 4}=N-\bar N=n_B of
neutrinos over antineutrinos in the 4-th generation. This massive
fourth-generation neutrino may form the non-baryonic dark matter. In principle
their mass density n_{\nu 4}m_N in the Universe can give the main contribution
to the dark matter, since the lower bound on neutrino mass m_N from the data on
decay of the Z-bosons is m_N > m_Z/2. The straightforward prediction of this
model leads to the amount of cold dark matter relative to baryons, which is an
order of magnitude bigger than allowed by observations. This inconsistency may
be avoided by non-conservation of the F-charge.Comment: 9 pages, 2 figures, version accepted in JETP Letters, corrected after
referee reports, references are adde
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