64 research outputs found
Measurement-induced criticality as a data-structure transition
We employ unsupervised learning tools to identify different phases and their
transition in quantum systems subject to the combined action of unitary
evolution and stochastic measurements. Specifically, we consider principal
component analysis and intrinsic dimension estimation to reveal a
measurement-induced structural transition in the data space. We test our
approach on a 1+1D stabilizer circuit and find the quantities of interest
furnish novel order parameters defined directly in the raw data space. Our
results provide a first use of unsupervised tools in dynamical quantum phase
transitions.Comment: 7 pages, 5 figure
Crimes against Environment in Albania and the European Union's Approach to the Protection of Environment through Criminal Law
The protection of environment is of particular importance for Albania in its integration process to the European Union (EU), which considers it to be one of the “essential objectives of the Community” as highlighted in the case-law of the European Court of Justice. Taking into consideration the requirements of the specific EU directives on the protection of environment through criminal law, one of the expected legal reforms in the approximation process will be the adaption of the Albanian substantive environmental criminal law to the requirements of the Environmental Crime Directives. The need for aligning the Albanian criminal law with these directives has been highlighted by the Commission in the 2014 Progress Report on Albania. This paper examines the Albanian substantive environmental criminal law and its application in practice in the last ten years, aiming to identify the main challenges it faces in the context of the required transposition of EU Environmental Crime Directives, while also making suggestions on how to better respond to these issues. For this purpose, the paper will also refer to the experience of other countries with the implementation process in this field, highlighting the main problems encountered and the impacts of the Environmental Crime Directives transposition
Controlling entanglement at absorbing state phase transitions in random circuits
Many-body unitary dynamics interspersed with repeated measurements display a
rich phenomenology hallmarked by measurement-induced phase transitions.
Employing feedback-control operations that steer the dynamics toward an
absorbing state, we study the entanglement entropy behavior at the absorbing
state phase transition. For short-range control operations, we observe a
transition between phases with distinct sub-extensive scalings of entanglement
entropy. In contrast, the system undergoes a transition between volume-law and
area-law phases for long-range feedback operations. The fluctuations of
entanglement entropy and of the order parameter of the absorbing state
transition are fully coupled for sufficiently strongly entangling feedback
operations. In that case, entanglement entropy inherits the universal dynamics
of the absorbing state transition. This is, however, not the case for arbitrary
control operations, and the two transitions are generally distinct. We
quantitatively support our results by introducing a framework based on
stabilizer circuits with classical flag labels. Our results shed new light on
the problem of observability of measurement-induced phase transitions.Comment: 4+6pp, comments welcome
Entanglement guided search for parent Hamiltonians
We introduce a method for the search of parent Hamiltonians of input
wave-functions based on the structure of their reduced density matrix. The two
key elements of our recipe are an ansatz on the relation between reduced
density matrix and parent Hamiltonian that is exact at the field theory level,
and a minimization procedure on the space of relative entropies, which is
particularly convenient due to its convexity. As examples, we show how our
method correctly reconstructs the parent Hamiltonian correspondent to several
non-trivial ground state wave functions, including conformal and
symmetry-protected-topological phases, and quantum critical points of
two-dimensional antiferromagnets described by strongly coupled field theories.
Our results show the entanglement structure of ground state wave-functions
considerably simplifies the search for parent Hamiltonians.Comment: 5 pages, 5 figures, supplementary materia
Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
We investigate the structure of many-body wave functions of 1D quantum
circuits with local measurements employing the participation entropies. The
leading term in system size dependence of participation entropy indicates a
model dependent multifractal scaling of the wave-functions at any non-zero
measurement rate. The sub-leading term contains universal information about
measurement-induced phase transitions and plays the role of an order parameter,
being constant non-zero in the error correcting phase and vanishing in the
quantum Zeno phase. We provide robust numerical evidence investigating a
variety of quantum many-body systems, and provide an analytical interpretation
of this behavior expressing the participation entropy in terms of partition
functions of classical statistical models in 2D.Comment: 4+16 pages, added new results on universality and extended
discussions, comments welcom
Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
We consider the dynamics of the non-Hermitian Su-Schrieffer-Heeger model
arising as the no-click limit of a continuously monitored free fermion chain
where particles and holes are measured on two sublattices. The model has
-symmetry, which we show to spontaneously break as a function of
the strength of measurement backaction, resulting in a spectral transition
where quasiparticles acquire a finite lifetime in patches of the Brillouin
zone. We compute the entanglement entropy's dynamics in the thermodynamic limit
and demonstrate an entanglement transition between volume-law and area-law
scaling, which we characterize analytically. Interestingly we show that the
entanglement transition and the -symmetry breaking do not
coincide, the former occurring when the entire decay spectrum of the
quasiparticle becomes gapped.Comment: version 2 , 4 figures, minor adjustments and clarifications in
section I
Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
Understanding how errors deteriorate the information encoded in a many-body
quantum system is a fundamental problem with practical implications for quantum
technologies. Here, we investigate a class of encoding-decoding random circuits
with coherent errors. The existence of a phase transition separating an
error-protecting phase at weak error strength from an error-vulnerable phase is
analytically demonstrated. We derive exact expressions showing that this
transition is accompanied by an area-to-volume law entanglement transition and
a localization transition in the computational basis. The emergence of
multifractal features in the considered system is highlighted.Comment: 4+9 pages, comments welcome
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