1,094 research outputs found
The relations among two transversal submanifolds and global manifold
In Riemann geometry, the relations among two transversal submanifolds and
global manifold are discussed. By replacing the normal vector of a submanifold
with the tangent vector of another submanifold, the metric tensors, Christoffel
symbols and curvature tensors of the three manifolds are linked together. When
the inner product of the two tangent vectors vanishes, some corollaries of
these relations give the most important second fundamental form and
Gauss-Codazzi equation in the conventional submanifold theory. As a special
case, the global manifold is Euclidean is considered. It is pointed out that,
in order to obtain the nonzero energy-momentum tensor of matter field in a
submanifold, there must be the contributions of the above inner product and the
other submanifold. In general speaking, a submanifold is closely related to the
matter fields of the other submanifold through the above inner product. This
conclusion is in agreement with the Kaluza-Klein theory and it can be applied
to generalize the models of direct product of manifolds in string and D-brane
theories to the more general cases --- nondirect product manifolds.Comment: 18pages, LaTex, no figur
The Principle of Relativity, Kinematics and Algebraic Relations
Based on the principle of relativity and the postulate on universal invariant
constants (c,l), all possible kinematics can be set up with sub-symmetries of
the Umov-Weyl-Fock transformations for the inertial motions. Further, in the
combinatory approach, all these symmetries are intrinsically related to each
other, e.g. to the very important dS kinematics for the cosmic scale physics.Comment: 11 page
Running Coupling Constants of Fermions with Masses in Quantum Electro Dynamics and Quantum Chromo Dynamics
Based on a simple but effective regularization-renormalization method (RRM),
the running coupling constants (RCC) of fermions with masses in quantum
electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by
renormalization group equation (RGE). Starting at Q=0 ( being the momentum
transfer), the RCC in QED increases with the increase of whereas the RCCs
for different flavors of quarks with masses in QCD are different and they
increase with the decrease of to reach a maximum at low for each flavor
of quark and then decreases to zero at . The physical
explanation is given.Comment: Latex, 19 pages, 3 figure
Security of "Counterfactual Quantum Cryptography"
Recently, a "counterfactual" quantum key distribution scheme was proposed by
Tae-Gon Noh [1]. In this scheme, two legitimate distant peers may share secret
keys even when the information carriers are not traveled in the quantum
channel. We find that this protocol is equivalent to an entanglement
distillation protocol (EDP). According to this equivalence, a strict security
proof and the asymptotic key bit rate are both obtained when perfect single
photon source is applied and Trojan-horse attack can be detected. We also find
that the security of this scheme is deeply related with not only the bit error
rate but also the yields of photons. And our security proof may shed light on
security of other two-way protocols.Comment: 5 pages, 1 figur
Quantum simulation of Kibble-Zurek mechanism with a semiconductor electron charge qubit
The Kibble-Zurek mechanism provides a description of the topological
structure occurring in the symmetry breaking phase transitions, which may
manifest as the cosmological strings in the early universe or vortex lines in
the superfulid. A particularly intriguing analogy between Kibble-Zurek
mechanism and a text book quantum phenomenon, Landau-Zener transition has been
discovered, but is difficult to observe up to now. In recent years, there has
been broad interest in quantum simulations using different well-controlled
physical setups, in which full tunability allows access to unexplored parameter
regimes. Here we demonstrate a proof-of-principle quantum simulation of
Kibble-Zurek mechanism using a single electron charge qubit in double quantum
dot, set to behave as Landau-Zener dynamics. We measure the qubit states as a
function of driven pulse velocity and successfully reproduce Kibble-Zurek like
dependence of topological defect density on the quench rate. The high-level
controllability of semiconductor two-level system make it a platform to test
the key elements of topological defect formation process and shed a new insight
on the aspect of non-equilibrium phase transitions.Comment: 14 pages, 4 figure
Device and semi-device independent random numbers based on non-inequality paradox
In this work, we propose device independent true random numbers generation
protocols based on non-inequality paradoxes such as Hardy's and Cabello's
non-locality argument. The efficiency of generating randomness in our protocols
are far better than any other proposed protocols certified by CHSH inequality
or other non-locality test involving inequalities. Thus, highlighting
non-inequality paradox as an important resource for device independent quantum
information processing in particular generating true randomness. As a
byproduct, we find that the non-local bound of the Cabello's argument with
arbitrary dimension is the same as the one achieved in the qubits system. More
interestingly, we propose a new dimension witness paradox based on the
Cabello's argument, which can be used for constructing semi-device-independent
true random numbers generation protocol
More randomness from a prepare-and-measure scenario with independent devices
How to generate genuine quantum randomness from untrusted devices is an
important problem in quantum information processing. Inspired by previous work
on a self-testing quantum random number generator [T. Lunghi et al., Phys. Rev.
Lett. 114, 150501 (2015)], we present a method to generate quantum randomness
from a prepare-and-measure scenario with independent devices. In existing
protocols, the quantum randomness depends only on a witness value (e.g.,
Clauser-Horne-Shimony-Holt value), which is calculated with the observed
probabilities. Differently, here all the observed probabilities are directly
used to calculate the min-entropy in our method. Through numerical simulation,
we find that the min-entropy of our proposed scheme is higher than that in the
previous work when a typical untrusted Bennett-Brassard 1984 (BB84) setup is
used. Consequently, thanks to the proposed method, more genuine quantum random
numbers may be obtained than before.Comment: 8 pages, 3 figure
Security of modified Ping-Pong protocol in noisy and lossy channel
The "Ping-Pong" (PP) protocol is a two-way quantum key protocol based on
entanglement. In this protocol, Bob prepares one maximally entangled pair of
qubits, and sends one qubit to Alice. Then, Alice performs some necessary
operations on this qubit and sends it back to Bob. Although this protocol was
proposed in 2002, its security in the noisy and lossy channel has not been
proven. In this report, we add a simple and experimentally feasible
modification to the original PP protocol, and prove the security of this
modified PP protocol against collective attacks when the noisy and lossy
channel is taken into account. Simulation results show that our protocol is
practical.Comment: 7 pages, 2 figures, published in scientific report
A tunable hybrid qubit in a triple quantum dot
We experimentally demonstrate quantum coherent dynamics of a triple-dot-based
multi-electron hybrid qubit. Pulsed experiments show that this system can be
conveniently initialized, controlled, and measured electrically, and has good
coherence time as compared to gate time. Furthermore, the current
multi-electron hybrid qubit has an operation frequency that is tunable in a
wide range, from 2 to about 15 GHz. We provide qualitative understandings of
the experimental observations by mapping it onto a three-electron system, and
compare it with the double dot hybrid qubit and the all-exchange triple-dot
qubit.Comment: 16 pages, 4 figure
Symmetric reflection line resonator for semiconductor circuit quantum electrodynamics
We have designed and fabricated a half-wavelength reflection line resonator
(RLR) that consists of a pair of two coupled microstrip lines on a GaAs/AlGaAs
heterostructure. By changing the top gate voltage on a square of two
dimensional electron gas under the resonator, a large range of the quality
factors can be obtained. Energy loss in the two-dimensional electron gas can be
minimized, thus realizing a versatile resonator suitable for integration with
semiconductor quantum circuits.Comment: 9 pages, 3 figure
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