719 research outputs found
Quantum Encodings in Spin Systems and Harmonic Oscillators
We show that higher-dimensional versions of qubits, or qudits, can be encoded
into spin systems and into harmonic oscillators, yielding important advantages
for quantum computation. Whereas qubit-based quantum computation is adequate
for analyses of quantum vs classical computation, in practice qubits are often
realized in higher-dimensional systems by truncating all but two levels,
thereby reducing the size of the precious Hilbert space. We develop natural
qudit gates for universal quantum computation, and exploit the entire
accessible Hilbert space. Mathematically, we give representations of the
generalized Pauli group for qudits in coupled spin systems and harmonic
oscillators, and include analyses of the qubit and the infinite-dimensional
limits.Comment: 4 pages, published versio
State-independent preparation uncertainty relations
The standard state-dependent Heisenberg-Robertson uncertainly-relation lower
bound fails to capture the quintessential incompatibility of observables as the
bound can be zero for some states. To remedy this problem, we establish a class
of tight (i.e., inequalities are saturated)variance-based sum-uncertainty
relations derived from the Lie algebraic properties of observables and show
that our lower bounds depend only on the irreducible representation assumed
carried by the Hilbert space of state of the system. We illustrate our result
for the cases of the Weyl-Heisenberg algebra, special unitary algebras up to
rank 4, and any semisimple compact algebra. We also prove the usefulness of our
results by extending a known variance-based entanglement detection criterion.Comment: 7 pages, 1 figur
Geometric Phase in SU(N) Interferometry
An interferometric scheme to study Abelian geometric phase shift over the
manifold SU(N)/SU(N-1) is presented.Comment: 14 pages, 1 figure, presented at the Doppler Institute-CRM meeting,
(Prague, Czech Republic, June 18-22 2000
Geometric Phase of Three-level Systems in Interferometry
We present the first scheme for producing and measuring an Abelian geometric
phase shift in a three-level system where states are invariant under a
non-Abelian group. In contrast to existing experiments and proposals for
experiments, based on U(1)-invariant states, our scheme geodesically evolves
U(2)-invariant states in a four-dimensional SU(3)/U(2) space and is physically
realized via a three-channel optical interferometer.Comment: 4 pages, 3 figure
Representations of the Weyl group and Wigner functions for SU(3)
Bases for SU(3) irreps are constructed on a space of three-particle tensor
products of two-dimensional harmonic oscillator wave functions. The Weyl group
is represented as the symmetric group of permutations of the particle
coordinates of these space. Wigner functions for SU(3) are expressed as
products of SU(2) Wigner functions and matrix elements of Weyl transformations.
The constructions make explicit use of dual reductive pairs which are shown to
be particularly relevant to problems in optics and quantum interferometry.Comment: : RevTex file, 11 pages with 2 figure
- …