3,205 research outputs found
On extremal quantum states of composite systems with fixed marginals
We study the convex set of all bipartite quantum states with fixed marginal
states. The extremal states in this set have recently been characterized by
Parthasarathy [Ann. Henri Poincar\'e (to appear), quant-ph/0307182, [1]]. Here
we present an alternative necessary and sufficient condition for a state with
given marginals to be extremal. Our approach is based on a canonical duality
between bipartite states and a certain class of completely positive maps and
has the advantage that it is easier to check and to construct explicit examples
of extremal states. In dimension 2 x 2 we give a simple new proof for the fact
that all extremal states with maximally mixed marginals are precisely the
projectors onto maximally entangled wave functions. We also prove that in
higher dimension this does not hold and construct an explicit example of an
extremal state with maximally mixed marginals in dimension 3 x 3 that is not
maximally entangled. Generalizations of this result to higher dimensions are
also discussed.Comment: 6 pages, to appear in J.Math.Phy
On Tracial Operator Representations of Quantum Decoherence Functionals
A general `quantum history theory' can be characterised by the space of
histories and by the space of decoherence functionals. In this note we consider
the situation where the space of histories is given by the lattice of
projection operators on an infinite dimensional Hilbert space . We study
operator representations for decoherence functionals on this space of
histories. We first give necessary and sufficient conditions for a decoherence
functional being representable by a trace class operator on , an
infinite dimensional analogue of the Isham-Linden-Schreckenberg representation
for finite dimensions. Since this excludes many decoherence functionals of
physical interest, we then identify the large and physically important class of
decoherence functionals which can be represented, canonically, by bounded
operators on .Comment: 14 pages, LaTeX2
On the Consistent Effect Histories Approach to Quantum Mechanics
A formulation of the consistent histories approach to quantum mechanics in
terms of generalized observables (POV measures) and effect operators is
provided. The usual notion of `history' is generalized to the notion of `effect
history'. The space of effect histories carries the structure of a D-poset.
Recent results of J.D. Maitland Wright imply that every decoherence functional
defined for ordinary histories can be uniquely extended to a bi-additive
decoherence functional on the space of effect histories. Omnes' logical
interpretation is generalized to the present context. The result of this work
considerably generalizes and simplifies the earlier formulation of the
consistent effect histories approach to quantum mechanics communicated in a
previous work of this author.Comment: LaTeX 2.09 version replaced by LaTeX2e version, minor change
A new class of entanglement measures
We introduce new entanglement measures on the set of density operators on
tensor product Hilbert spaces. These measures are based on the greatest cross
norm on the tensor product of the sets of trace class operators on Hilbert
space. We show that they satisfy the basic requirements on entanglement
measures discussed in the literature, including convexity, invariance under
local unitary operations and non-increase under local quantum operations and
classical communication.Comment: Revised version accepted by J Math Phys, 12 pages, LaTeX, contains
Sections 1-5 & 7 of the previous version. The previous Section 6 is now in
quant-ph/0105104 and the previous Section 8 is superseded by quant-ph/010501
Cybersecurity Maturity in the Pacific Islands – Informing a Regional CERT Framework
Cybersecurity acts as a strong influence on national governments’ security, economic, physical and social interests. A common policy goal of governments is to protect their respective interests by supporting cybersecurity threat and attack response capabilities. Contemporary research addresses the use of multi-national CERT frameworks to improve national cybersecurity capability maturity and resilience, however little research has been conducted into the efficacy of such frameworks with Pacific Island nations. This research employs a qualitative interview technique to develop an inductive model for a regional Pacific Islands CERT framework. The research proposes a Pacific Islands regional model based on a network of affiliated national CERTs that operate independently and reflect their respective national interests, while collaborating on matters of shared interest, supported by regional partners providing targeted assistance to build national and regional cybersecurity capability maturity and resilience
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