2,150 research outputs found
Characterizing the geometrical edges of nonlocal two-qubit gates
Nonlocal two-qubit gates are geometrically represented by tetrahedron known
as Weyl chamber within which perfect entanglers form a polyhedron. We identify
that all edges of the Weyl chamber and polyhedron are formed by single
parametric gates. Nonlocal attributes of these edges are characterized using
entangling power and local invariants. In particular, SWAP (power)alpha family
of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only
perfect entangler. Finally, optimal constructions of controlled-NOT using
SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.Comment: 11 pages, 4 figures, Phys. Rev. A 79, 052339 (2009
On the Contractivity of Hilbert-Schmidt distance under open system dynamics
We show that the Hilbert-Schmidt distance, unlike the trace distance, between
quantum states is generally not monotonic for open quantum systems subject to
Lindblad semigroup dynamics. Sufficient conditions for contractivity of the
Hilbert-Schmidt norm in terms of the dissipation generators are given. Although
these conditions are not necessary, simulations suggest that non-contractivity
is the typical case, i.e., that systems for which the Hilbert-Schmidt distance
between quantum states is monotonically decreasing form only a small set of all
possible dissipative systems for N>2, in contrast to the case N=2 where the
Hilbert-Schmidt distance is always monotonically decreasing.Comment: Major revision. We would particularly like to thank D Perez-Garcia
for constructive feedbac
Thermal entanglement of spins in a nonuniform magnetic field
We study the effect of inhomogeneities in the magnetic field on the thermal
entanglement of a two spin system. We show that in the ferromagnetic case a
very small inhomogeneity is capable to produce large values of thermal
entanglement. This shows that the absence of entanglement in the ferromagnetic
Heisenberg system is highly unstable against inhomogeneoity of magnetic fields
which is inevitably present in any solid state realization of qubits.Comment: 14 pages, 7 figures, latex, Accepted for publication in Physical
Review
Entangling characterization of (SWAP)1/m and Controlled unitary gates
We study the entangling power and perfect entangler nature of (SWAP)1/m, for
m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only
perfect entangler in the family. On the other hand, a subset of CU which is
locally equivalent to CNOT is identified. It is shown that the subset, which is
a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio
Scalability of Shor's algorithm with a limited set of rotation gates
Typical circuit implementations of Shor's algorithm involve controlled
rotation gates of magnitude where is the binary length of the
integer N to be factored. Such gates cannot be implemented exactly using
existing fault-tolerant techniques. Approximating a given controlled
rotation gate to within currently requires both
a number of qubits and number of fault-tolerant gates that grows polynomially
with . In this paper we show that this additional growth in space and time
complexity would severely limit the applicability of Shor's algorithm to large
integers. Consequently, we study in detail the effect of using only controlled
rotation gates with less than or equal to some . It is found
that integers up to length can be factored
without significant performance penalty implying that the cumbersome techniques
of fault-tolerant computation only need to be used to create controlled
rotation gates of magnitude if integers thousands of bits long are
desired factored. Explicit fault-tolerant constructions of such gates are also
discussed.Comment: Substantially revised version, twice as long as original. Two tables
converted into one 8-part figure, new section added on the construction of
arbitrary single-qubit rotations using only the fault-tolerant gate set.
Substantial additional discussion and explanatory figures added throughout.
(8 pages, 6 figures
Joining the Conversation: Graduate Students’ Perceptions of Writing for Publication
The authors report on their qualitative study of eight students in a class on writing for publication and the nature of the writing process in academia. While the participants found value and purpose in writing and scholarly writing, they had great difficulty with criticism and using feedback in constructive ways
Optimized pulse sequences for suppressing unwanted transitions in quantum systems
We investigate the nature of the pulse sequence so that unwanted transitions
in quantum systems can be inhibited optimally. For this purpose we show that
the sequence of pulses proposed by Uhrig [Phys. Rev. Lett. \textbf{98}, 100504
(2007)] in the context of inhibition of environmental dephasing effects is
optimal. We derive exact results for inhibiting the transitions and confirm the
results numerically. We posit a very significant improvement by usage of the
Uhrig sequence over an equidistant sequence in decoupling a quantum system from
unwanted transitions. The physics of inhibition is the destructive interference
between transition amplitudes before and after each pulse.Comment: 5 figure
Orbits of quantum states and geometry of Bloch vectors for -level systems
Physical constraints such as positivity endow the set of quantum states with
a rich geometry if the system dimension is greater than two. To shed some light
on the complicated structure of the set of quantum states, we consider a
stratification with strata given by unitary orbit manifolds, which can be
identified with flag manifolds. The results are applied to study the geometry
of the coherence vector for n-level quantum systems. It is shown that the
unitary orbits can be naturally identified with spheres in R^{n^2-1} only for
n=2. In higher dimensions the coherence vector only defines a non-surjective
embedding into a closed ball. A detailed analysis of the three-level case is
presented. Finally, a refined stratification in terms of symplectic orbits is
considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version,
corrected eq.(3), to appear in J. Physics
Schmidt Analysis of Pure-State Entanglement
We examine the application of Schmidt-mode analysis to pure state
entanglement. Several examples permitting exact analytic calculation of Schmidt
eigenvalues and eigenfunctions are included, as well as evaluation of the
associated degree of entanglement.Comment: 5 pages, 3 figures, for C.M. Bowden memoria
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