2,514 research outputs found
Background Independent Quantum Mechanics, Metric of Quantum States, and Gravity: A Comprehensive Perspective
This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.Comment: 25 Pages;journal reference added:Published in- Int. J. Theor. Phys.
46 (2007) 3216-3229. References revise
Resources required for exact remote state preparation
It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 69,
022310 (2004)] that it is possible to perform exactly faithful remote state
preparation using finite classical communication and any entangled state with
maximal Schmidt number. Here we give an explicit procedure for performing this
remote state preparation. We show that the classical communication required for
this scheme is close to optimal for remote state preparation schemes of this
type. In addition we prove that it is necessary that the resource state have
maximal Schmidt number.Comment: 7 pages, 1 figur
Probabilistic Super Dense Coding
We explore the possibility of performing super dense coding with
non-maximally entangled states as a resource. Using this we find that one can
send two classical bits in a probabilistic manner by sending a qubit. We
generalize our scheme to higher dimensions and show that one can communicate
2log_2 d classical bits by sending a d-dimensional quantum state with a certain
probability of success. The success probability in super dense coding is
related to the success probability of distinguishing non-orthogonal states. The
optimal average success probabilities are explicitly calculated. We consider
the possibility of sending 2 log_2 d classical bits with a shared resource of a
higher dimensional entangled state (D X D, D > d). It is found that more
entanglement does not necessarily lead to higher success probability. This also
answers the question as to why we need log_2 d ebits to send 2 log_2 d
classical bits in a deterministic fashion.Comment: Latex file, no figures, 11 pages, Discussion changed in Section
Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect
Geometric phase plays an important role in evolution of pure or mixed quantum
states. However, when a system undergoes decoherence the development of
geometric phase may be inhibited. Here, we show that when a quantum system
interacts with two competing environments there can be enhancement of geometric
phase. This effect is akin to Parrondo like effect on the geometric phase which
results from quantum frustration of decoherence. Our result suggests that the
mechanism of two competing decoherence can be useful in fault-tolerant
holonomic quantum computation.Comment: 5 pages, 3 figures, Published versio
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
Symmetry crossover and excitation thresholds at the neutral-ionic transition of the modified Hubbard model
Exact ground states, charge densities and excitation energies are found using
valence bond methods for N-site modified Hubbard models with uniform spacing.
At the neutral-ionic transition (NIT), the ground state has a symmetry
crossover in 4n, 4n+2 rings with periodic and antiperiodic boundary conditions,
respectively. The modified Hubbard model has a continuous NIT between a
diamagnetic band insulator on the paired side and a paramagnetic Mott insulator
on the covalent side. The singlet-triplet (ST), singlet-singlet (SS) and charge
gaps for finite N indicate that the ST and SS gaps close at the NIT with
increasing U and that the charge gap vanishes only there. Finite-N excitations
constrain all singularities to about 0.1t of the symmetry crossover. The NIT is
interpreted as a localized ground state (gs) with finite gaps on the paired
side and an extended gs with vanishing ST and SS gaps on the covalent side. The
charge gap and charge stiffness indicate a metallic gs at the transition that,
however, is unconditionally unstable to dimerization.Comment: 12 pages, including 8 figure
Minimum cbits for remote preperation and measurement of a qubit
We show that a qubit chosen from equatorial or polar great circles on a Bloch
spehere can be remotely prepared with one cbit from Alice to Bob if they share
one ebit of entanglement. Also we show that any single particle measurement on
an arbitrary qubit can be remotely simulated with one ebit of shared
entanglement and communication of one cbit.Comment: Latex, 7 pages, minor changes, references adde
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