8,231 research outputs found
A complete family of separability criteria
We introduce a new family of separability criteria that are based on the
existence of extensions of a bipartite quantum state to a larger number
of parties satisfying certain symmetry properties. It can be easily shown that
all separable states have the required extensions, so the non-existence of such
an extension for a particular state implies that the state is entangled. One of
the main advantages of this approach is that searching for the extension can be
cast as a convex optimization problem known as a semidefinite program (SDP).
Whenever an extension does not exist, the dual optimization constructs an
explicit entanglement witness for the particular state. These separability
tests can be ordered in a hierarchical structure whose first step corresponds
to the well-known Positive Partial Transpose (Peres-Horodecki) criterion, and
each test in the hierarchy is at least as powerful as the preceding one. This
hierarchy is complete, in the sense that any entangled state is guaranteed to
fail a test at some finite point in the hierarchy, thus showing it is
entangled. The entanglement witnesses corresponding to each step of the
hierarchy have well-defined and very interesting algebraic properties that in
turn allow for a characterization of the interior of the set of positive maps.
Coupled with some recent results on the computational complexity of the
separability problem, which has been shown to be NP-hard, this hierarchy of
tests gives a complete and also computationally and theoretically appealing
characterization of mixed bipartite entangled states.Comment: 21 pages. Expanded introduction. References added, typos corrected.
Accepted for publication in Physical Review
Network Synthesis of Linear Dynamical Quantum Stochastic Systems
The purpose of this paper is to develop a synthesis theory for linear
dynamical quantum stochastic systems that are encountered in linear quantum
optics and in phenomenological models of linear quantum circuits. In
particular, such a theory will enable the systematic realization of
coherent/fully quantum linear stochastic controllers for quantum control,
amongst other potential applications. We show how general linear dynamical
quantum stochastic systems can be constructed by assembling an appropriate
interconnection of one degree of freedom open quantum harmonic oscillators and,
in the quantum optics setting, discuss how such a network of oscillators can be
approximately synthesized or implemented in a systematic way from some linear
and non-linear quantum optical elements. An example is also provided to
illustrate the theory.Comment: Revised and corrected version, published in SIAM Journal on Control
and Optimization, 200
A new bound of the ℒ2[0, T]-induced norm and applications to model reduction
We present a simple bound on the finite horizon ℒ2/[0, T]-induced norm of a linear time-invariant (LTI), not necessarily stable system which can be efficiently computed by calculating the ℋ∞ norm of a shifted version of the original operator. As an application, we show how to use this bound to perform model reduction of unstable systems over a finite horizon. The technique is illustrated with a non-trivial physical example relevant to the appearance of time-irreversible phenomena in statistical physics
Quantum Computation as Geometry
Quantum computers hold great promise, but it remains a challenge to find
efficient quantum circuits that solve interesting computational problems. We
show that finding optimal quantum circuits is essentially equivalent to finding
the shortest path between two points in a certain curved geometry. By recasting
the problem of finding quantum circuits as a geometric problem, we open up the
possibility of using the mathematical techniques of Riemannian geometry to
suggest new quantum algorithms, or to prove limitations on the power of quantum
computers.Comment: 13 Pages, 1 Figur
Detuned Mechanical Parametric Amplification as a Quantum Non-Demolition Measurement
Recently it has been demonstrated that the combination of weak-continuous
position detection with detuned parametric driving can lead to significant
steady-state mechanical squeezing, far beyond the 3 dB limit normally
associated with parametric driving. In this work, we show the close connection
between this detuned scheme and quantum non-demolition (QND) measurement of a
single mechanical quadrature. In particular, we show that applying an
experimentally realistic detuned parametric drive to a cavity optomechanical
system allows one to effectively realize a QND measurement despite being in the
bad-cavity limit. In the limit of strong squeezing, we show that this scheme
offers significant advantages over standard backaction evasion, not only by
allowing operation in the weak measurement and low efficiency regimes, but also
in terms of the purity of the mechanical state.Comment: 17 pages, 2 figure
Adaptive homodyne measurement of optical phase
We present an experimental demonstration of the power of real-time feedback
in quantum metrology, confirming a theoretical prediction by Wiseman regarding
the superior performance of an adaptive homodyne technique for single-shot
measurement of optical phase. For phase measurements performed on weak coherent
states with no prior knowledge of the signal phase, we show that the variance
of adaptive homodyne estimation approaches closer to the fundamental quantum
uncertainty limit than any previously demonstrated technique. Our results
underscore the importance of real-time feedback for reaching quantum
performance limits in coherent telecommunication, precision measurement and
information processing.Comment: RevTex4, color PDF figures (separate files), submitted to PR
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