ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

CHAPTER 9
Two-mode Gaussian states in the lab
One of the strength points of the CV quantum information science with Gaussian
states, alongwith the mathematical structure which enables an accurate description
of their informational properties (see Chapter 2), has surely to be traced back
to the astonishing progress obtained on the experimental side for what concerns
preparation, processing and characterization of entangled Gaussian resources, and
their successful implementation for the most diverse communication and computation
tasks. We have already stressed, for instance, that one of the main byproducts
of our study on bipartite entanglement versus purity, presented in Sec. 4.3, is that
of having provided a direct, reliable way to estimate entanglement of arbitrary
unknown two-mode Gaussian states in terms of experimentally accessible measurements
of purity [GA2] (see Sec. 4.4.1).
This Chapter mainly originates from our collaboration to an experiment which
illustrates the state-of-the-art in the engineering and processing of two-mode Gaussian
states, via an original optical set-up based on a type-II optical parametric oscillator
(OPO) with adjustable mode coupling [GA8]. Experimental results allow a
direct verification of many theoretical predictions and provide a sharp insight into
the general properties of two-mode Gaussian states, elucidated in Chapter 4, and
the manipulation of the entanglement resource. We will discuss this experiment in
Sec. 9.2.
As a disclaimer, we remark that the main focus of this Dissertation is of a
theoretical nature, as our primary aim has been up to now to develop strong
mathematical tools to define and characterize entanglement of Gaussian states.
Therefore, many experimental details, largely available elsewhere (see, as a guide,
Refs. [40, 207, 203, 174, 138]) will be surely lacking here. However, and thanks to
the close contact with the “reality” of experiments achieved during the preparation
of Ref. [GA8], we have in parallel devoted a special attention towards the practical
production of CV entanglement on one side, and its interpretation in connection
with operational settings on the other.
These two aspects of our work are respectively treated in this, and in the next
Part of this Dissertation.
Let us first briefly comment on the latter, namely the investigation of the usefulness
of entangled Gaussian states for the most common implementations of CV
quantum information and communication protocols [40]. This side of our research
enriches the mathematical analysis and clarifies the physical understanding of our
results: an example is provided by the full equivalence between (bipartite and multipartite)
entanglement and optimal success of (two-party and multi-party) CV
quantum teleportation experiments with (two-mode and multimode) symmetric,
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