58 research outputs found
Bipartite unitary gates and billiard dynamics in the Weyl chamber
Long time behavior of a unitary quantum gate , acting sequentially on two
subsystems of dimension each, is investigated. We derive an expression
describing an arbitrary iteration of a two-qubit gate making use of a link to
the dynamics of a free particle in a billiard. Due to ergodicity of such a
dynamics an average along a trajectory stemming from a generic two-qubit
gate in the canonical form tends for a large to the average over an
ensemble of random unitary gates distributed according to the flat measure in
the Weyl chamber - the minimal set containing points from all orbits of
locally equivalent gates. Furthermore, we show that for a large dimension
the mean entanglement entropy averaged along a generic trajectory coincides
with the average over the ensemble of random unitary matrices distributed
according to the Haar measure on
Insights into Quantum Contextuality and Bell Nonclassicality: A Study on Random Pure Two-Qubit Systems
We explore the relationship between Kochen-Specker quantum contextuality and
Bell-nonclassicality for ensembles of two-qubit pure states. We present a
comparative analysis showing that the violation of a noncontextuality
inequality on a given quantum state reverberates on the Bell-nonclassicality of
the considered state. In particular, we use suitable inequalities that are
experimentally testable to detect quantum contextuality and nonlocality for
systems in a Hilbert space of dimension . While contextuality can be
assessed on different degrees of freedom of the same particle, the violation of
local realism requires parties spatially separated.Comment: Submitted to Int. J. Theor. Phys. as part of the Collection IQSA22 -
Quantum Structures for Interdisciplinary Application
Microscopic description for the emergence of collective dissipation in extended quantum systems
Practical implementations of quantum technology are limited by unavoidable
effects of decoherence and dissipation. With achieved experimental control for
individual atoms and photons, more complex platforms composed by several units
can be assembled enabling distinctive forms of dissipation and decoherence, in
independent heat baths or collectively into a common bath, with dramatic
consequences for the preservation of quantum coherence. The cross-over between
these two regimes has been widely attributed in the literature to the system
units being farther apart than the bath's correlation length. Starting from a
microscopic model of a structured environment (a crystal) sensed by two bosonic
probes, here we show the failure of such conceptual relation, and identify the
exact physical mechanism underlying this cross-over, displaying a sharp
contrast between dephasing and dissipative baths. Depending on the frequency of
the system and, crucially, on its orientation with respect to the crystal axes,
collective dissipation becomes possible for very large distances between
probes, opening new avenues to deal with decoherence in phononic baths
Information theoretical perspective on the method of Entanglement Witnesses
We frame entanglement detection as a problem of random variable inference to
introduce a quantitative method to measure and understand whether entanglement
witnesses lead to an efficient procedure for that task. Hence we quantify how
many bits of information a family of entanglement witnesses can infer about the
entanglement of a given quantum state sample. The bits are computed in terms of
the mutual information and we unveil there exists hidden information not
\emph{efficiently} processed. We show that there is more information in the
expected value of the entanglement witnesses, i.e. than in the sign of . This suggests that an
entanglement witness can provide more information about the entanglement if for
our decision boundary we compute a different functional of its expectation
value, rather than
Drawbacks of the use of fidelity to assess quantum resources
Fidelity is a figure of merit widely employed in quantum technology in order
to quantify similarity between quantum states and, in turn, to assess quantum
resources or reconstruction techniques. Fidelities higher than, say, 0.9 or
0.99, are usually considered as a piece of evidence to say that two states are
very close in the Hilbert space. On the other hand, on the basis of several
examples for qubits and continuous variable systems, we show that such high
fidelities may be achieved by pairs of states with considerably different
physical properties, including separable and entangled states or classical and
nonclassical ones. We conclude that fidelity as a tool to assess quantum
resources should be employed with caution, possibly combined with additional
constraints restricting the pool of achievable states, or only as a mere
summary of a full tomographic reconstruction.Comment: 6 pages, 6 figure
About the use of fidelity in continuous variable systems
We present examples of continuous variable (CV) states having high fidelity
to a given target, say or , and still showing striking
differences in their physical properties, including classical and quantum
states within the set, separable and entangled ones, or nearly Gaussian and
strongly non-Gaussian ones. We also show that the phenomenon persists also when
one imposes additional constraints on the energy or the squeezing fraction of
the states, thus generally questioning the use of fidelity to assess properties
of CV systems.Comment: 8 pages; 4 figure
On detecting violation of local realism with photon-number resolving weak-field homodyne measurements
Non-existence of a local hidden variables (LHV) model for a phenomenon
benchmarks its use in device-independent quantum protocols. Nowadays
photon-number resolving weak-field homodyne measurements allow realization of
emblematic gedanken experiments. Alas, claims that we can have no LHV models
for such experiments on (a) excitation of a pair of spatial modes by a single
photon, and (b) two spatial modes in a weakly squeezed vacuum state, involving
constant local oscillator strengths, are unfounded. For (a) an exact LHV model
resolves the dispute on the "non-locality of a single photon" in its original
formulation. It is measurements with local oscillators on or off that do not
have LHV models.Comment: 5 + 5 pages, 1 figure. Results partially overlap with
arXiv:2102.03254. Comments are welcom
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