23 research outputs found
Operational interpretation of the vacuum and process matrices for identical particles
This work overviews the single-particle two-way communication protocol
recently introduced by del Santo and Daki\'c (dSD), and analyses it using the
process matrix formalism. We give a detailed account of the importance and the
operational meaning of the interaction of an agent with the vacuum -- in
particular its role in the process matrix description. This raises the issue of
counting such operations in an operational manner. Motivated by this analysis,
we extend the process matrix formalism to Fock space using the framework of
second quantisation, in order to characterise protocols with an indefinite
number of identical particles.Comment: 9 pages (double column), 3 figure
Ground state overlap and quantum phase transitions
We present a characterization of quantum phase transitions in terms of the
the overlap function between two ground states obtained for two different
values of external parameters. On the examples of the Dicke and XY models, we
show that the regions of criticality of a system are marked by the extremal
points of the overlap and functions closely related to it. Further, we discuss
the connections between this approach and the Anderson orthogonality
catastrophe as well as with the dynamical study of the Loschmidt echo for
critical systems.Comment: 5 pages. Version to be published, title change
Dynamical phase transitions at finite temperature from fidelity and interferometric Loschmidt echo induced metrics
We study finite-temperature Dynamical Quantum Phase Transitions (DQPTs) by
means of the fidelity and the interferometric Loschmidt Echo (LE) induced
metrics. We analyse the associated dynamical susceptibilities (Riemannian
metrics), and derive analytic expressions for the case of two-band
Hamiltonians. At zero temperature the two quantities are identical,
nevertheless, at finite temperatures they behave very differently. Using the
fidelity LE, the zero temperature DQPTs are gradually washed away with
temperature, while the interferometric counterpart exhibits finite-temperature
Phase Transitions (PTs). We analyse the physical differences between the two
finite-temperature LE generalisations, and argue that, while the
interferometric one is more sensitive and can therefore provide more
information when applied to genuine quantum (microscopic) systems, when
analysing many-body macroscopic systems, the fidelity-based counterpart is a
more suitable quantity to study. Finally, we apply the previous results to two
representative models of topological insulators in 1D and 2D.Comment: 20 pages, 8 figure
Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
We study the fidelity approach to quantum phase transitions (QPTs) and apply
it to general thermal phase transitions (PTs). We analyze two particular cases:
the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of
superconductivity. In both cases we show that the sudden drop of the mixed
state fidelity marks the line of the phase transition. We conduct a detailed
analysis of the general case of systems given by mutually commuting
Hamiltonians, where the non-analyticity of the fidelity is directly related to
the non-analyticity of the relevant response functions (susceptibility and heat
capacity), for the case of symmetry-breaking transitions. Further, on the case
of BCS theory of superconductivity, given by mutually non-commuting
Hamiltonians, we analyze the structure of the system's eigenvectors in the
vicinity of the line of the phase transition showing that their sudden change
is quantified by the emergence of a generically non-trivial Uhlmann mixed state
geometric phase.Comment: 18 pages, 8 figures. Version to be publishe
Quantum Kolmogorov complexity and quantum correlations in deterministic-control quantum Turing machines
This work presents a study of Kolmogorov complexity for general quantum
states from the perspective of deterministic-control quantum Turing Machines
(dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and
outputs, and define dcq-computable states as those that can be approximated by
a dcq-TM. Moreover, we introduce (conditional) Kolmogorov complexity of quantum
states and use it to study three particular aspects of the algorithmic
information contained in a quantum state: a comparison of the information in a
quantum state with that of its classical representation as an array of real
numbers, an exploration of the limits of quantum state copying in the context
of algorithmic complexity, and study of the complexity of correlations in
quantum systems, resulting in a correlation-aware definition for algorithmic
mutual information that satisfies symmetry of information property.Comment: 31 page
Quantum Kolmogorov complexity and quantum correlations in deterministic-control quantum Turing machines
This work presents a study of Kolmogorov complexity for general quantum states from the perspective of deterministic-control quantum Turing Machines (dcq-TM). We extend the dcq-TM model to incorporate mixed state inputs and outputs, and define dcq-computable states as those that can be approximated by a dcq-TM. Moreover, we introduce (conditional) Kolmogorov complexity of quantum states and use it to study three particular aspects of the algorithmic information contained in a quantum state: a comparison of the information in a quantum state with that of its classical representation as an array of real numbers, an exploration of the limits of quantum state copying in the context of algorithmic complexity, and study of the complexity of correlations in quantum systems, resulting in a correlation-aware definition for algorithmic mutual information that satisfies symmetry of information property