Why the Jordan Product anticommutator noncommutativity got ignored: quantum nonlocality antigravity

[1309.4635] Defining quantumness via the Jordan product
arXiv
by P Facchi · 2013 · Cited by 15 — A central role will be assumed by the anticommutator of the observables, namely the Jordan product.
The Jordan formulation of Quantum Mechanics: a review1

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"when A is noncommutative, is not closed under the associative product:
(ab)∗ = ba does not = ab, (5)
Quantumness via Jordan product 3
for some a, b ∈ L. This requires the introduction of new algebraic structures. By
following the seminal ideas by Jordan [11], later developed in conjunction with Wigner
and von Neumann [12], we define the Jordan product [13] as the symmetrized product"

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nection between spacetime geometry and quantum entanglement....As we have seen, spacetime topology change leads in-
exorably to violation of causality, via either breakdown
of the Hausdorff condition or creation of traversable
wormholes. Using ER=EPR to translate this result to
quantum mechanics, we find that violation of the axioms
of the topology-conservation theorems is dual to viola-
tion of monogamy of entanglement (i.e., cloning) and the
existence of wormholes is dual to the existence of entan-
glement entropy....It is striking that on both the general relativistic and
quantum mechanical sides of the duality, violation of the
no-go theorem leads to problems for causality. The unex-
pected connection between cloning and topology change
offers support for the ER=EPR correspondence, which
provides a natural explanation for their relation.

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shown in [8], the noncommutativity of two states can be
witnessed by relying on the anti-commutator of the states,
for which an experimental verification scheme is in princi-
ple available. However, the experimental procedure turns
out to depend on a state-dependent iterative procedure.
For some states, a large number of copies are required in
order to characterize precisely their quantum properties.
In the following, we propose a witness for the global
quantum properties of a state, and provide a universal
quantum circuit for the experimental verification of such
characterization, that is independent of the input states.

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"The notions of classicality and quantumness should then be contrasted
on the basis of the different footings on which observables and states stand. A natural

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A matha also written as math, muth, mutth, mutt, or mut, is a Sanskrit word that means 'institute or college', and it also refers to a monastery in Hinduism

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1996, 76, 2818. [CrossRef] "This result extends the standard no-cloning theorem for pure states." The pure-state “no-cloning” theorem [2, 3] prohibits
broadcasting pure states, for the only way to broadcast a
pure state jcl is to put the two systems in the product state
jcl ≠ jcl, i.e., to clone jcl. ...We show that such
an evolution can lead to broadcasting if and only if r0
and r1 commute. This result strikes close to the heart of
the difference between the classical and quantum theories,
because it provides another physical distinction between
commuting and noncommuting states. We further show
that A is clonable if and only if r0 and r1 are identical
or orthogonal (r0r1 ≠ 0).
To see that the set A can be broadcast when the states
commute, we do not need to attach an auxiliary system.
Since orthogonal pure states can be cloned, broadcasting
can be obtained by cloning the simultaneous eigenstates
of r0 and r1."

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Hearing the shape of a quantum boundary condition
al., 4 who constructed an isospectral pair of two-dimensional polygons, depicted in
Fig. 1. In the case of two-dimensional domains with a smooth boundary, a positive
result can be recovered by requiring some additional symmetries, see e.g. the work
of S. Zelditch, 5 but the general problem is still unsolved. " 2022 We remark that although a twisted torus is topologically indistinguishable from
a non-twisted one, S1/Z2 being indeed homeomorphic to S1, a function defined on
the torus is generally modified by the twist. The action of the twist, as well as its
necessity, is highlighted in Fig. 3, where the twisted torus is compared with the
non-twisted one and also with the “doubled” torus ̃Σ ∼= D × S1.