ENTANGLEMENT OF GAUSSIAN STATES Gerardo Adesso

CHAPTER 8
Unlimited promiscuity of multipartite
Gaussian entanglement
The structure of multipartite entanglement of Gaussian states, as explored up to
now, opens interesting perspectives which are driving us towards the last part of this
Dissertation, namely the one concerning production and applications of multiparty
Gaussian entangled resources. This Chapter, based on Ref. [GA19], provides an
additional, exceptional motivation to select CV systems, and specifically Gaussian
states, as ideal candidates for physical realizations of current and perhaps revolutionary
quantum information and communication implementations. The findings
described here are also of importance from a fundamental point of view, for the
quantification and primarily the understanding of shared quantum correlations in
systems with infinitely large state space.
We have seen indeed in the previous Chapter that in the most basic multipartite
CV setting, namely that of three-mode Gaussian states, a partial “promiscuity”
of entanglement can be achieved. Permutation-invariant states exist which are the
simultaneous analogs of GHZ and W states of qubits, exhibiting unlimited tripartite
entanglement (with increasing squeezing) and nonzero, accordingly increasing
bipartite entanglement which nevertheless stays finite even for infinite squeezing
[GA10]. We will now show that in CV systems with more than three modes, entanglement
can be distributed in an infinitely promiscuous way.
8.1. Continuous variables versus qubits
From an operational perspective, qubits are the main logical units for standard
realizations of quantum information protocols [163]. Also CV Gaussian entangled
resources have been proven useful for all known implementations of quantum
information processing [40], including quantum computation [155], sometimes outperforming
more traditional qubit-based approaches as in the case of unconditional
teleportation [89]. It is therefore important to understand if special features of
entanglement appear in states of infinite Hilbert spaces, which are unparalleled in
the corresponding states of qubits. Such findings may lead to new ways of manipulating
quantum information in the CV setting. For instance, there exist infinitely
many inequivalent classes of bipartite entangled pure CV states, meaning that a
substantially richer structure is available for quantum correlations and it could be
potentially exploited for novel realizations of quantum information protocols [173].
Here, we address this motivation on a clearcut physical ground, aiming in particular
to show whether the unboundedness of the mean energy characterizing CV
states enables a qualitatively richer structure for distributed quantum correlations.
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