8,628 research outputs found
Modulated phases in magnetic models frustrated by long-range interactions
We study an Ising model in one dimension with short range ferromagnetic and
long range (power law) antiferromagnetic interactions. We show that the zero
temperature phase diagram in a (longitudinal) field H involves a sequence of up
and down domains whose size varies continuously with H, between -H_c and H_c
which represent the edge of the ferromagnetic up and down phases. The
implications of long range interaction in many body systems are discussed.Comment: 5 pages, 3 figure
Quantum information processing with single photons and atomic ensembles in microwave coplanar waveguide resonators
We show that pairs of atoms optically excited to the Rydberg states can
strongly interact with each other via effective long-range dipole-dipole or van
der Waals interactions mediated by their non-resonant coupling to a common
microwave field mode of a superconducting coplanar waveguide cavity. These
cavity mediated interactions can be employed to generate single photons and to
realize in a scalable configuration a universal phase gate between pairs of
single photon pulses propagating or stored in atomic ensembles in the regime of
electromagnetically induced transparency
Dialogical Breakdown and Covid-19: Solidarity and Disagreement in a Shared World
This article considers the limitations, but also the insights, of Gadamerian hermeneutics for understanding and responding to the crisis precipitated by the Covid-19 pandemic. Our point of departure is the experience of deep disagreements amid the pandemic, and our primary example is ongoing debates in the United States about wearing masks. We argue that, during this dire situation, interpersonal mutual understanding is insufficient for resolving such bitter disputes. Rather, following Gadamer’s account of our dialogical experience with an artwork, we suggest that our encounter with the virus gives rise to new ways of seeing and experiencing ourselves and the world. Further, we draw on Gadamer’s account of the fusion of horizons to show how even competing perspectives on wearing masks arise within a shared space of meaning created by the virus. These insights provide hope for an improved model of political dialogue in the world of Covid-19
Probing the qudit depolarizing channel
For the quantum depolarizing channel with any finite dimension, we compare
three schemes for channel identification: unentangled probes, probes maximally
entangled with an external ancilla, and maximally entangled probe pairs. This
comparison includes cases where the ancilla is itself depolarizing and where
the probe is circulated back through the channel before measurement. Compared
on the basis of (quantum Fisher) information gained per channel use, we find
broadly that entanglement with an ancilla dominates the other two schemes, but
only if entanglement is cheap relative to the cost per channel use and only if
the external ancilla is well shielded from depolarization. We arrive at these
results by a relatively simple analytical means. A separate, more complicated
analysis for partially entangled probes shows for the qudit depolarizing
channel that any amount of probe entanglement is advantageous and that the
greatest advantage comes with maximal entanglement
Minimum orbit dimension for local unitary action on n-qubit pure states
The group of local unitary transformations partitions the space of n-qubit
quantum states into orbits, each of which is a differentiable manifold of some
dimension. We prove that all orbits of the n-qubit quantum state space have
dimension greater than or equal to 3n/2 for n even and greater than or equal to
(3n + 1)/2 for n odd. This lower bound on orbit dimension is sharp, since
n-qubit states composed of products of singlets achieve these lowest orbit
dimensions.Comment: 19 page
Statistical comparison of ensemble implementations of Grover's search algorithm to classical sequential searches
We compare pseudopure state ensemble implementations, quantified by their
initial polarization and ensemble size, of Grover's search algorithm to
probabilistic classical sequential search algorithms in terms of their success
and failure probabilities. We propose a criterion for quantifying the resources
used by the ensemble implementation via the aggregate number of oracle
invocations across the entire ensemble and use this as a basis for comparison
with classical search algorithms. We determine bounds for a critical
polarization such that the ensemble algorithm succeeds with a greater
probability than the probabilistic classical sequential search. Our results
indicate that the critical polarization scales as N^(-1/4) where N is the
database size and that for typical room temperature solution state NMR, the
polarization is such that the ensemble implementation of Grover's algorithm
would be advantageous for N > 10^2
Discrimination of unitary transformations in the Deutsch-Jozsa algorithm
We describe a general framework for regarding oracle-assisted quantum
algorithms as tools for discriminating between unitary transformations. We
apply this to the Deutsch-Jozsa problem and derive all possible quantum
algorithms which solve the problem with certainty using oracle unitaries in a
particular form. We also use this to show that any quantum algorithm that
solves the Deutsch-Jozsa problem starting with a quantum system in a particular
class of initial, thermal equilibrium-based states of the type encountered in
solution state NMR can only succeed with greater probability than a classical
algorithm when the problem size exceeds Comment: 7 pages, 1 figur
Fermionic Linear Optics Revisited
We provide an alternative view of the efficient classical simulatibility of
fermionic linear optics in terms of Slater determinants. We investigate the
generic effects of two-mode measurements on the Slater number of fermionic
states. We argue that most such measurements are not capable (in conjunction
with fermion linear optics) of an efficient exact implementation of universal
quantum computation. Our arguments do not apply to the two-mode parity
measurement, for which exact quantum computation becomes possible, see
quant-ph/0401066.Comment: 16 pages, submitted to the special issue of Foundation of Physics in
honor of Asher Peres' 70th birthda
Causal and localizable quantum operations
We examine constraints on quantum operations imposed by relativistic
causality. A bipartite superoperator is said to be localizable if it can be
implemented by two parties (Alice and Bob) who share entanglement but do not
communicate; it is causal if the superoperator does not convey information from
Alice to Bob or from Bob to Alice. We characterize the general structure of
causal complete measurement superoperators, and exhibit examples that are
causal but not localizable. We construct another class of causal bipartite
superoperators that are not localizable by invoking bounds on the strength of
correlations among the parts of a quantum system. A bipartite superoperator is
said to be semilocalizable if it can be implemented with one-way quantum
communication from Alice to Bob, and it is semicausal if it conveys no
information from Bob to Alice. We show that all semicausal complete measurement
superoperators are semilocalizable, and we establish a general criterion for
semicausality. In the multipartite case, we observe that a measurement
superoperator that projects onto the eigenspaces of a stabilizer code is
localizable.Comment: 23 pages, 7 figures, REVTeX, minor changes and references adde
Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output
We compare the failure probabilities of ensemble implementations of quantum
algorithms which use pseudo-pure initial states, quantified by their
polarization, to those of competing classical probabilistic algorithms.
Specifically we consider a class algorithms which require only one bit to
output the solution to problems. For large ensemble sizes, we present a general
scheme to determine a critical polarization beneath which the quantum algorithm
fails with greater probability than its classical competitor. We apply this to
the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.Comment: 11 pages, 3 figure
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