34 research outputs found
Relativistic BB84, relativistic errors, and how to correct them
The Bennett-Brassard cryptographic scheme (BB84) needs two bases, at least
one of them linearly polarized. The problem is that linear polarization
formulated in terms of helicities is not a relativistically covariant notion:
State which is linearly polarized in one reference frame becomes depolarized in
another one. We show that a relativistically moving receiver of information
should define linear polarization with respect to projection of
Pauli-Lubanski's vector in a principal null direction of the Lorentz
transformation which defines the motion, and not with respect to the helicity
basis. Such qubits do not depolarize.Comment: revtex
Stability of Circular Orbits in General Relativity: A Phase Space Analysis
Phase space method provides a novel way for deducing qualitative features of
nonlinear differential equations without actually solving them. The method is
applied here for analyzing stability of circular orbits of test particles in
various physically interesting environments. The approach is shown to work in a
revealing way in Schwarzschild spacetime. All relevant conclusions about
circular orbits in the Schwarzschild-de Sitter spacetime are shown to be
remarkably encoded in a single parameter. The analysis in the rotating Kerr
black hole readily exposes information as to how stability depends on the ratio
of source rotation to particle angular momentum. As a wider application, it is
exemplified how the analysis reveals useful information when applied to motion
in a refractive medium, for instance, that of optical black holes.Comment: 20 pages. Accepted for publication in Int. J. theor. Phy
Spin Fidelity for Three-qubit Greenberger-Horne-Zeilinger and W States Under Lorentz Transformations
Constructing the reduced density matrix for a system of three massive
spin particles described by a wave packet with Gaussian momentum
distribution and a spin part in the form of GHZ or W state, the fidelity for
the spin part of the system is investigated from the viewpoint of moving
observers in the jargon of special relativity. Using a numerical approach, it
turns out that by increasing the boost speed, the spin fidelity decreases and
reaches to a non-zero asymptotic value that depends on the momentum
distribution and the amount of momentum entanglement.Comment: 12pages, 2 figure
Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses
We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c
Quantum Communication in Rindler Spacetime
A state that an inertial observer in Minkowski space perceives to be the
vacuum will appear to an accelerating observer to be a thermal bath of
radiation. We study the impact of this Davies-Fulling-Unruh noise on
communication, particularly quantum communication from an inertial sender to an
accelerating observer and private communication between two inertial observers
in the presence of an accelerating eavesdropper. In both cases, we establish
compact, tractable formulas for the associated communication capacities
assuming encodings that allow a single excitation in one of a fixed number of
modes per use of the communications channel. Our contributions include a
rigorous presentation of the general theory of the private quantum capacity as
well as a detailed analysis of the structure of these channels, including their
group-theoretic properties and a proof that they are conjugate degradable.
Connections between the Unruh channel and optical amplifiers are also
discussed.Comment: v3: 44 pages, accepted in Communications in Mathematical Physic
Neutrino Interferometry In Curved Spacetime
Gravitational lensing introduces the possibility of multiple (macroscopic)
paths from an astrophysical neutrino source to a detector. Such a multiplicity
of paths can allow for quantum mechanical interference to take place that is
qualitatively different to neutrino oscillations in flat space. After an
illustrative example clarifying some under-appreciated subtleties of the phase
calculation, we derive the form of the quantum mechanical phase for a neutrino
mass eigenstate propagating non-radially through a Schwarzschild metric. We
subsequently determine the form of the interference pattern seen at a detector.
We show that the neutrino signal from a supernova could exhibit the
interference effects we discuss were it lensed by an object in a suitable mass
range. We finally conclude, however, that -- given current neutrino detector
technology -- the probability of such lensing occurring for a
(neutrino-detectable) supernova is tiny in the immediate future.Comment: 25 pages, 1 .eps figure. Updated version -- with simplified notation
-- accepted for publication in Phys.Rev.D. Extra author adde
Relativistic quantum clocks
The conflict between quantum theory and the theory of relativity is
exemplified in their treatment of time. We examine the ways in which their
conceptions differ, and describe a semiclassical clock model combining elements
of both theories. The results obtained with this clock model in flat spacetime
are reviewed, and the problem of generalizing the model to curved spacetime is
discussed, before briefly describing an experimental setup which could be used
to test of the model. Taking an operationalist view, where time is that which
is measured by a clock, we discuss the conclusions that can be drawn from these
results, and what clues they contain for a full quantum relativistic theory of
time.Comment: 12 pages, 4 figures. Invited contribution for the proceedings for
"Workshop on Time in Physics" Zurich 201
Dynamics of multipartite quantum correlations under decoherence
Quantum discord is an optimal resource for the quantification of classical
and non-classical correlations as compared to other related measures. Geometric
measure of quantum discord is another measure of quantum correlations.
Recently, the geometric quantum discord for multipartite states has been
introduced by Jianwei Xu [arxiv:quant/ph.1205.0330]. Motivated from the recent
study [Ann. Phys. 327 (2012) 851] for the bipartite systems, I have
investigated global quantum discord (QD) and geometric quantum discord (GQD)
under the influence of external environments for different multipartite states.
Werner-GHZ type three-qubit and six-qubit states are considered in inertial and
non-inertial settings. The dynamics of QD and GQD is investigated under
amplitude damping, phase damping, depolarizing and flipping channels. It is
seen that the quantum discord vanishes for p>0.75 in case of three-qubit GHZ
states and for p>0.5 for six qubit GHZ states. This implies that multipartite
states are more fragile to decoherence for higher values of N. Surprisingly, a
rapid sudden death of discord occurs in case of phase flip channel. However,
for bit flip channel, no sudden death happens for the six-qubit states. On the
other hand, depolarizing channel heavily influences the QD and GQD as compared
to the amplitude damping channel. It means that the depolarizing channel has
the most destructive influence on the discords for multipartite states. From
the perspective of accelerated observers, it is seen that effect of environment
on QD and GQD is much stronger than that of the acceleration of non-inertial
frames. The degradation of QD and GQD happens due to Unruh effect. Furthermore,
QD exhibits more robustness than GQD when the multipartite systems are exposed
to environment.Comment: 15 pages, 4 figures, 4 table
Entanglement or separability: The choice of how to factorize the algebra of a density matrix
We discuss the concept of how entanglement changes with respect to different
factorizations of the total algebra which describes the quantum states.
Depending on the considered factorization a quantum state appears either
entangled or separable. For pure states we always can switch unitarily between
separability and entanglement, however, for mixed states a minimal amount of
mixedness is needed. We discuss our general statements in detail for the
familiar case of qubits, the GHZ states, Werner states and Gisin states,
emphasizing their geometric features. As theorists we use and play with this
free choice of factorization, which is naturally fixed for an experimentalist.
For theorists it offers an extension of the interpretations and is adequate to
generalizations, as we point out in the examples of quantum teleportation and
entanglement swapping.Comment: 29 pages, 9 figures. Introduction, Conclusion and References have
been extended in v