3,533 research outputs found
Identification of Decoherence-Free Subspaces Without Quantum Process Tomography
Characterizing a quantum process is the critical first step towards applying
such a process in a quantum information protocol. Full process characterization
is known to be extremely resource-intensive, motivating the search for more
efficient ways to extract salient information about the process. An example is
the identification of "decoherence-free subspaces", in which computation or
communications may be carried out, immune to the principal sources of
decoherence in the system. Here we propose and demonstrate a protocol which
enables one to directly identify a DFS without carrying out a full
reconstruction. Our protocol offers an up-to-quadratic speedup over standard
process tomography. In this paper, we experimentally identify the DFS of a
two-qubit process with 32 measurements rather than the usual 256, characterize
the robustness and efficiency of the protocol, and discuss its extension to
higher-dimensional systems.Comment: 6 pages, 5 figure
On conjectures and problems of Ruzsa concerning difference graphs of S-units
Given a finite nonempty set of primes S, we build a graph with
vertex set by connecting x and y if the prime divisors of both the
numerator and denominator of x-y are from S. In this paper we resolve two
conjectures posed by Ruzsa concerning the possible sizes of induced
nondegenerate cycles of , and also a problem of Ruzsa concerning
the existence of subgraphs of which are not induced subgraphs.Comment: 15 page
Adaptive quantum state tomography improves accuracy quadratically
We introduce a simple protocol for adaptive quantum state tomography, which
reduces the worst-case infidelity between the estimate and the true state from
to . It uses a single adaptation step and just one
extra measurement setting. In a linear optical qubit experiment, we demonstrate
a full order of magnitude reduction in infidelity (from to ) for
a modest number of samples ().Comment: 8 pages, 7 figure
Pattern formation in quantum Turing machines
We investigate the iteration of a sequence of local and pair unitary
transformations, which can be interpreted to result from a Turing-head
(pseudo-spin ) rotating along a closed Turing-tape ( additional
pseudo-spins). The dynamical evolution of the Bloch-vector of , which can be
decomposed into primitive pure state Turing-head trajectories, gives
rise to fascinating geometrical patterns reflecting the entanglement between
head and tape. These machines thus provide intuitive examples for quantum
parallelism and, at the same time, means for local testing of quantum network
dynamics.Comment: Accepted for publication in Phys.Rev.A, 3 figures, REVTEX fil
Scalable Spatial Super-Resolution using Entangled Photons
N00N states -- maximally path-entangled states of N photons -- exhibit
spatial interference patterns sharper than any classical interference pattern.
This is known as super-resolution. However, even with perfectly efficient
number-resolving detectors, the detection efficiency of all previously
demonstrated methods to measure such interference decreases exponentially with
the number of photons in the N00N state, often leading to the conclusion that
N00N states are unsuitable for spatial measurements. Here, we create spatial
super-resolution fringes with two-, three-, and four-photon N00N states, and
demonstrate a scalable implementation of the so-called ``optical centroid
measurement'' which provides an in-principle perfect detection efficiency.
Moreover, we compare the N00N-state interference to the corresponding classical
super-resolution interference. Although both provide the same increase in
spatial frequency, the visibility of the classical fringes decreases
exponentially with the number of detected photons, while the visibility of our
experimentally measured N00N-state super-resolution fringes remains
approximately constant with N. Our implementation of the optical centroid
measurement is a scalable method to measure high photon-number quantum
interference, an essential step forward for quantum-enhanced measurements,
overcoming what was believed to be a fundamental challenge to quantum
metrology
Local Versus Global Thermal States: Correlations and the Existence of Local Temperatures
We consider a quantum system consisting of a regular chain of elementary
subsystems with nearest neighbor interactions and assume that the total system
is in a canonical state with temperature . We analyze under what condition
the state factors into a product of canonical density matrices with respect to
groups of subsystems each, and when these groups have the same temperature
. While in classical mechanics the validity of this procedure only depends
on the size of the groups , in quantum mechanics the minimum group size
also depends on the temperature ! As examples, we apply our
analysis to a harmonic chain and different types of Ising spin chains. We
discuss various features that show up due to the characteristics of the models
considered. For the harmonic chain, which successfully describes thermal
properties of insulating solids, our approach gives a first quantitative
estimate of the minimal length scale on which temperature can exist: This
length scale is found to be constant for temperatures above the Debye
temperature and proportional to below.Comment: 12 pages, 5 figures, discussion of results extended, accepted for
publication in Phys. Rev.
State Measurements with Short Laser Pulses and Lower-Efficiency Photon Detectors
It has been proposed by Cook (Phys. Scr. T 21, 49 (1988)) to use a short
probe laser pulse for state measurements of two-level systems. In previous work
we have investigated to what extent this proposal fulfills the projection
postulate if ideal photon detectors are considered. For detectors with overall
efficiency less than 1 complications arise for single systems, and for this
case we present a simple criterion for a laser pulse to act as a state
measurement and to cause an almost complete state reduction.Comment: 13 pages, LaTeX; submitted to J. mod. Op
The Lagrange and Markov spectra from the dynamical point of view
This text grew out of my lecture notes for a 4-hours minicourse delivered on
October 17 \& 19, 2016 during the research school "Applications of Ergodic
Theory in Number Theory" -- an activity related to the Jean-Molet Chair project
of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille,
France. The subject of this text is the same of my minicourse, namely, the
structure of the so-called Lagrange and Markov spectra (with an special
emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl
- …