201 research outputs found
A nonlinear Ramsey interferometer operating beyond the Heisenberg limit
We show that a dynamically evolving two-mode Bose-Einstein condensate (TBEC)
with an adiabatic, time-varying Raman coupling maps exactly onto a nonlinear
Ramsey interferometer that includes a nonlinear medium. Assuming a realistic
quantum state for the TBEC, namely the SU(2) coherent spin state, we find that
the measurement uncertainty of the ``path-difference'' phase shift scales as
the standard quantum limit (1/N^{1/2}) where N is the number of atoms, while
that for the interatomic scattering strength scales as 1/N^{7/5}, overcoming
the Heisenberg limit of 1/N.Comment: 4 figures. Submitted for publicatio
Clock synchronization using maximal multipartite entanglement
We propose a multi party quantum clock synchronization protocol that makes
optimal use of the maximal multipartite entanglement of GHZ-type states. To
realize the protocol, different versions of maximally entangled eigenstates of
collective energy are generated by local transformations that distinguish
between different groupings of the parties. The maximal sensitivity of the
entangled states to time differences between the local clocks can then be
accessed if all parties share the results of their local time dependent
measurements. The efficiency of the protocol is evaluated in terms of the
statistical errors in the estimation of time differences and the performance of
the protocol is compared to alternative protocols previously proposed
Necessary Condition for the Quantum Adiabatic Approximation
A gapped quantum system that is adiabatically perturbed remains approximately
in its eigenstate after the evolution. We prove that, for constant gap, general
quantum processes that approximately prepare the final eigenstate require a
minimum time proportional to the ratio of the length of the eigenstate path to
the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We
also give a necessary condition for the adiabatic approximation that depends on
local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur
Spectral Gap Amplification
A large number of problems in science can be solved by preparing a specific
eigenstate of some Hamiltonian H. The generic cost of quantum algorithms for
these problems is determined by the inverse spectral gap of H for that
eigenstate and the cost of evolving with H for some fixed time. The goal of
spectral gap amplification is to construct a Hamiltonian H' with the same
eigenstate as H but a bigger spectral gap, requiring that constant-time
evolutions with H' and H are implemented with nearly the same cost. We show
that a quadratic spectral gap amplification is possible when H satisfies a
frustration-free property and give H' for these cases. This results in quantum
speedups for optimization problems. It also yields improved constructions for
adiabatic simulations of quantum circuits and for the preparation of projected
entangled pair states (PEPS), which play an important role in quantum many-body
physics. Defining a suitable black-box model, we establish that the quadratic
amplification is optimal for frustration-free Hamiltonians and that no spectral
gap amplification is possible, in general, if the frustration-free property is
removed. A corollary is that finding a similarity transformation between a
stoquastic Hamiltonian and the corresponding stochastic matrix is hard in the
black-box model, setting limits to the power of some classical methods that
simulate quantum adiabatic evolutions.Comment: 14 pages. New version has an improved section on adiabatic
simulations of quantum circuit
Generalized Coherent States as Preferred States of Open Quantum Systems
We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras, stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated
Quantum Adiabatic Markovian Master Equations
We develop from first principles Markovian master equations suited for
studying the time evolution of a system evolving adiabatically while coupled
weakly to a thermal bath. We derive two sets of equations in the adiabatic
limit, one using the rotating wave (secular) approximation that results in a
master equation in Lindblad form, the other without the rotating wave
approximation but not in Lindblad form. The two equations make markedly
different predictions depending on whether or not the Lamb shift is included.
Our analysis keeps track of the various time- and energy-scales associated with
the various approximations we make, and thus allows for a systematic inclusion
of higher order corrections, in particular beyond the adiabatic limit. We use
our formalism to study the evolution of an Ising spin chain in a transverse
field and coupled to a thermal bosonic bath, for which we identify four
distinct evolution phases. While we do not expect this to be a generic feature,
in one of these phases dissipation acts to increase the fidelity of the system
state relative to the adiabatic ground state.Comment: 31 pages, 9 figures. v2: Generalized Markov approximation bound.
Included a section on thermal equilibration. v3: Added text that appears in
NJP version. Generalized Lindblad ME to include degenerate subspaces. v3.
Corrections made to Appendix E and F. We thank Kabuki Takada and Hidetoshi
Nishimori for pointing out the errors. v4: Corrected a typo in Eqt. B
Interaction-based quantum metrology showing scaling beyond the Heisenberg limit
Quantum metrology studies the use of entanglement and other quantum resources
to improve precision measurement. An interferometer using N independent
particles to measure a parameter X can achieve at best the "standard quantum
limit" (SQL) of sensitivity {\delta}X \propto N^{-1/2}. The same interferometer
using N entangled particles can achieve in principle the "Heisenberg limit"
{\delta}X \propto N^{-1}, using exotic states. Recent theoretical work argues
that interactions among particles may be a valuable resource for quantum
metrology, allowing scaling beyond the Heisenberg limit. Specifically, a
k-particle interaction will produce sensitivity {\delta}X \propto N^{-k} with
appropriate entangled states and {\delta}X \propto N^{-(k-1/2)} even without
entanglement. Here we demonstrate this "super-Heisenberg" scaling in a
nonlinear, non-destructive measurement of the magnetisation of an atomic
ensemble. We use fast optical nonlinearities to generate a pairwise
photon-photon interaction (k = 2) while preserving quantum-noise-limited
performance, to produce {\delta}X \propto N^{-3/2}. We observe super-Heisenberg
scaling over two orders of magnitude in N, limited at large N by higher-order
nonlinear effects, in good agreement with theory. For a measurement of limited
duration, super-Heisenberg scaling allows the nonlinear measurement to overtake
in sensitivity a comparable linear measurement with the same number of photons.
In other scenarios, however, higher-order nonlinearities prevent this crossover
from occurring, reflecting the subtle relationship of scaling to sensitivity in
nonlinear systems. This work shows that inter-particle interactions can improve
sensitivity in a quantum-limited measurement, and introduces a fundamentally
new resource for quantum metrology
Generalized Coherent States as Preferred States of Open Quantum Systems
We investigate the connection between quasi-classical (pointer) states and
generalized coherent states (GCSs) within an algebraic approach to Markovian
quantum systems (including bosons, spins, and fermions). We establish
conditions for the GCS set to become most robust by relating the rate of purity
loss to an invariant measure of uncertainty derived from quantum Fisher
information. We find that, for damped bosonic modes, the stability of canonical
coherent states is confirmed in a variety of scenarios, while for systems
described by (compact) Lie algebras stringent symmetry constraints must be
obeyed for the GCS set to be preferred. The relationship between GCSs,
minimum-uncertainty states, and decoherence-free subspaces is also elucidated.Comment: 5 pages, no figures; Significantly improved presentation, new
derivation of invariant uncertainty measure via quantum Fisher information
added
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