8 research outputs found
Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras
The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled
by two parameters and . The aim of the present work is to investigate
the lowest weight representations of CGA with for any integer value of
. First we focus on the reducibility of the Verma modules. We give a
formula for the Shapovalov determinant and it follows that the Verma module is
irreducible if and the lowest weight is nonvanishing. We prove that
the Verma modules contain many singular vectors, i.e., they are reducible when
. Using the singular vectors, hierarchies of partial differential
equations defined on the group manifold are derived. The differential equations
are invariant under the kinematical transformation generated by CGA. Finally we
construct irreducible lowest weight modules obtained from the reducible Verma
modules
Accessible and inaccessible quantum coherence in relativistic quantum systems
The quantum coherence of a multipartite system is investigated when some of
the parties are moving with constant acceleration. Due to relativistic motion
the quantum coherence is divided into two parts as accessible and inaccessible
coherence. First we investigate tripartite systems, considering both GHZ and
W-states. We find that the quantum coherence of these states does not vanish in
the limit of infinite acceleration, rather asymptoting to a non-zero value.
These results hold for both single- and two-qubit relativistic motion. In the
GHZ and W states the coherence is distributed as correlations between the
qubits and is known as global coherence. But quantum coherence can also exist
due to the superposition within a qubit, the local coherence. To study the
properties of local coherence we investigate separable state. The GHZ state,
W-state and separable states contain only one type of coherence. Next we
consider the and star states in which both local and global
coherences coexist. We find that under relativistic motion both local and
global coherence show similar qualitative behaviour. Finally we derive analytic
expressions for the quantum coherence of -partite GHZ and W states where
qubits are subject to relativistic motion. We find that the quantum
coherence of a multipartite GHZ state falls exponentially with the number of
accelerated qubits, whereas for multipartite W-states the quantum coherence
decreases only polynomially. We conclude that W-states are more robust to Unruh
decoherence and discuss some potential applications in satellite-based quantum
communication and black hole physics.Comment: 18 page
Relativistic corrections to photonic entangled states for the space-based quantum network
In recent years there has been a great deal of focus on a globe-spanning quantum network, including linked satellites for applications ranging from quantum key distribution to distributed sensors and clocks. In many of these schemes, relativistic transformations may have deleterious effects on the purity of the distributed entangled pairs. In this paper, we make a comparison of several entanglement distribution schemes in the context of special relativity. We consider three types of entangled photon states: polarization, single photon, and Laguerre-Gauss mode entangled states. All three types of entangled states suffer relativistic corrections, albeit in different ways. These relativistic effects become important in the context of applications such as quantum clock synchronization, where high fidelity entanglement distribution is required