1) Quantum theories may help explain emergent self-organization phenomena in life, brain, cognition, and consciousness that traditional mechanistic frameworks cannot. 2) Decoherence due to environmental interactions is a challenge for quantum theories of mind, but decoherence depends on specific contexts and some coherence mechanisms may cooperate. 3) Higher-order statistical analyses of mesoscopic and macroscopic observations may reveal signatures of underlying quantum phenomena in the brain even if simple average quantities do not.

1. QUANTUM THEORIES OF MIND-BRAIN :
WHAT FUTURE ?
ELIANO PESSA
Department of Psychology
University of Pavia, Italy

2. MOTIVATIONS UNDERLYING THE
ATTRACTIVENESS OF QUANTUM THEORIES
• Allow the occurrence of spontaneous (and
even large-scale) COHERENCE phenomena
without the resort to special design,
arrangement, boundary conditions, etc.
(Prototype : BOSE-EINSTEIN CONDENSATION)
• In suitable cases (Quantum Field Theory) offer
a framework for describing, understanding, and
forecasting PHASE TRANSITION phenomena

3. This implies that quantum theories can support
some form of TOP-DOWN CAUSATION
encompassing the pitfalls of the traditional
mechanistic and reductionist framework.
If we assume that all phenomena related to life,
brain, cognition, consciousness, etc. are based on
some forms of EMERGENT SELF-ORGANIZATION
then quantum theories are the best candidates for
an effective theorizing activity in these domains.

4. WHAT COULD WE MEAN BY SPEAKING
OF ‘QUANTUM THEORIES’ ?
TWO ALTERNATIVES :
• A set of known physical theories
(semiclassical, quantum mechanics, quantum
field theory) associated with a specific value of
Planck’s constant
• A general theoretical framework for describing
specific kinds of fluctuating systems (eventually
allowing different kinds of ‘effective’ Planck’s
constants)

5. The second alternative gained popularity in the
last times, owing to a number of circumstances :
• some kinds of ‘noisy’ field theories are
mathematically equivalent to QM or QFT,
provided we allow the introduction of suitable
‘effective’ Planck’s constants (see, e.g, Fogedby
et al.)
• a number of phenomena in psychology and
economics, like decision making and concept
formation, can be better described by models
mathematically equivalent to quantum ones, in
which, however, Planck’s constant has a value
different from the traditional one (see e.g. Aerts
et al., Busemeyer et al.)

6. THE BIG PROBLEM: DECOHERENCE
As it is well known, decoherence due to the
interaction with external environment can
destroy the coherence of quantum origin.
Two remarks :
• Decoherence is a problem only for quantum
computers. Biological systems need
decoherence in order to avoid becoming like
crystals
• Decoherence is a smaller problem in QFT
owing to the infinite number of degrees of
freedom and the infinite volume limit

7. THE ACTORS PLAYING THE
DECOHERENCE GAME
• The kind of environment and its symmetries
What models of environment?
THERMAL BATH (the simplest one)
SPIN CHAIN (endowed with symmetry)
ACTIVE MEDIA (feedback on the system)
• the NOISE
• the DISSIPATION
• the DISORDER

8. These actors interact in a very complex way
which makes the decoherence game strongly
dependent on the detailed nature of the
SPECIFIC CONTEXTS.
Some elementary examples can illustrate some
aspects of this game.
In order to understand them we can start from a
simple CLASSICAL (NEURAL) NETWORK and
transform it into a QUANTUM (NEURAL)
NETWORK.

9. A CLASSICAL NETWORK MODEL
• Neurons arranged in a plane network with toroidal topology
O O O O O O O O O O O
O O O O O O O O O O O
O O O O O O O O O O O
O O O O O O O O O O O
• Number of input lines for each neuron is always the same (4)
• Stochastic activation law
• Initial state randomly chosen

10. STOCHASTIC ACTIVATION LAW
This law has the form :
Prob(output = 1) = 1/(1 + exp[-S/T])
where S is the weighted sum of inputs minus the
threshold while T is a parameter, called
‘TEMPERATURE’
In practical cases biological neurons show a stochastic
discharge pattern

11. AN EXAMPLE OF EEG PRODUCED BY THIS
MODEL
Network of 30x30 neurons, threshold = 2, T = 1

12. The autocorrelation function of this EEG

13. THE PERIODOGRAM
THE POWER SPECTRUM

14. A QUANTUM NETWORK MODEL
Let us now compare the behavior of the previous
model with the one of a QUANTUM NETWORK MODEL
with the same structure and topology.
Here the momentarily state vector of each unit is given
by a linear combination of the two basic states “0” and
“1”. In general the coefficients ψ 0 and ψ 1 of this
combination are complex numbers which vary with
time. At every instant the probability of having an
output 1 is given by | ψ 1 |2 .

15. The dynamical evolution of this network is given by a
suitable HAMILTONIAN OPERATOR, whose diagonal
terms are constant, while non-diagonal terms contain
a contribution coming from the output produced by
neighboring neurons, minus a given threshold.
In turn, this output is computed in a probabilistic way
according to the probabilities of “0” and “1” states
existing in the previous instant.
In principle, the evolution of this network should be
characterized by some kind of long-range
correlations.
BUT IS THIS PREDICTION CORRECT ?

16. THE EEG OF THIS NETWORK …
The same conditions as in the classical case: 30x30
neurons, identical initial probabilities, threshold = 2,
diagonal terms = 1, non-diagonal terms = 0.5

17. …but the autocorrelation function differs in a
deep way from the classical case !
Evidence for long-range effects

18. EVEN PERIODOGRAM IS DIFFERENT
…AND POWER SPECTRUM

19. ANOTHER EXAMPLE
Average activity of a quantum neural network
of 10x10 neurons with threshold = 1, non-
diagonal elements of the Hamiltonian = 1,
second-order approximation.

20. WHAT HAPPENS IN PRESENCE OF
EXTERNAL NOISE ?
Average activity of the previous network in
presence of Gaussian input noise with mean=0
and standard deviation=5.

21. As a comparison between the two plots is
difficult, it is more convenient to compare the
two autocorrelation functions.
Without Noise With Noise
A difference appears but it is better to
compare the autocorrelation functions of
the average variances.

22. Without noise With Noise
Superposition of the two plots
Looking at the variance the effect of noise is
more evident !

23. A first lesson of the above simulations is that
the effects of the quantum or classical nature of
a network are difficult to detect when looking at
the macroscopic observation of simple average
quantities, such as mean activity.
They are best detected when looking at more
complex statistical quantities.
And, even at the level of biological neural
networks, the neurons seem to be more
sensitive to higher-order statistical features of
the neural assemblies in which they are
embedded.

24. CAN THE EFFECT OF NOISE BE
COUNTERACTED ?
Let us suppose, in this regard, that a noisy
quantum neural network be interacting with
another coherent system, like a spin bath or a
spin chain.
A simple way for implementing this situations
is to add within the previous quantum neural
network a spin-spin interaction between the
quantum neurons, of quantum nature.

25. Plot of average activity vs t of a noisy quantum
neuron with a moderate spin-spin
antiferromagnetic interaction between
neighboring spins.

26. Autocorrelation Autocorrelation
function of the function of average
average activity variance
As expected, the average variance better helps
to detect weak cues of the re-establishment of
some long-range order.

27. Another lesson is that taking into account
only the destroying influence of the
environment is not enough: if there is some
interaction with another coherent system, the
possibility of a RECOHERENCE or of
counteracting decoherence remains open.
Perhaps different coherence mechanisms can
cooperate, even if each one, taken in isolation,
is characterized by a very small decoherence
time.

28. THE MACROSCOPIC SIGNATURE OF
QUANTUM PHENOMENA
How can a quantum coherence present at the
microscopic level survive up to mesoscopic
and macroscopic level ?
The previous examples suggest that, by using
observations induced by a mean-field analysis,
the detection of quantum coherence becomes
very difficult.

29. However, the simulations show that, by
looking at higher-order statistical features of
mesoscopic and macroscopic quantities, it
should be possible to detect a ‘signature’ of
quantum phenomena at the microscopic level.
Another help comes from the existence of a
number of inequalities regarding the
macroscopic observations (Bell, Leggett-Garg)
that, when not satisfied, are cues revealing an
hidden quantum nature. In some cases these
effects have been experimentally detected.
However, they cannot give any information
about the lower-level quantum processes.

30. IS QUANTUM THEORY USEFUL FOR
PSYCHIATRISTS ?
So far, quantum theory appears to be useful to
describe mostly low-level phenomena. At the
higher levels it seems to be useful mostly as a
sort of framework for reasoning about
phenomena of holistic nature. Nobody
prevents, however, from thinking that, only
understood some principles underlying the
processes occurring within the wholistic
mind-brain system, quantum theory can be
used to design suitable forms of top-down
actions helping the human beings to reach a
better harmony with the environment.

31. The ultimate goal of these top-down
‘technologies’ would be the one of a world in
which human beings were able to live in a self-
sustaining harmony with the world, without any
intervention of drugs, physicians, hospitals,
and like.
The hope that this state of affairs can be
realized in the future is the basic push
underlying all applications of quantum theory
to the study of brain, cognition, and
consciousness.