47 research outputs found
Unifying approach to the quantification of bipartite correlations by Bures distance
The notion of distance defined on the set of states of a composite quantum
system can be used to quantify total, quantum and classical correlations in a
unifying way. We provide new closed formulae for classical and total
correlations of two-qubit Bell-diagonal states by considering the Bures
distance. Complementing the known corresponding expressions for entanglement
and more general quantum correlations, we thus complete the quantitative
hierarchy of Bures correlations for Bell-diagonal states. We then explicitly
calculate Bures correlations for two relevant families of states: Werner states
and rank-2 Bell-diagonal states, highlighting the subadditivity which holds for
total correlations with respect to the sum of classical and quantum ones when
using Bures distance. Finally, we analyse a dynamical model of two independent
qubits locally exposed to non-dissipative decoherence channels, where both
quantum and classical correlations measured by Bures distance exhibit freezing
phenomena, in analogy with other known quantifiers of correlations.Comment: 18 pages, 4 figures; published versio
Signatures of quantumness: identification, quantification and dynamical preservation
2014 - 2015The quanti cation of quantumness is necessary to assess how much a physical system
departs from a classical behaviour and thus gauge the quantum enhancement in opera-
tional tasks such as information processing and computation. For arbitrary multiparti-
cle systems, the quanti cation of quantumness typically involves nontrivial optimisation
problems, and may require demanding tomographical techniques. We have developed an
experimentally feasible approach to the evaluation of geometric measures of quantumness,
according to which the distance from the state of the system to a suitable set of classi-
cal states is considered. Our approach provides analytical results for particular classes
of mixed states of N qubits, and computable lower bounds to global, partial, and gen-
uine multiparticle entanglement, as well as to quantum coherence, for any general state.
For global and partial entanglement, as well as quantum coherence, useful bounds have
been obtained with minimum e ort, requiring local measurements in just three settings
for any N. For genuine entanglement, a number of measurements scaling linearly with N
is required. We have demonstrated the power of our approach to estimate and quantify
di erent types of multiparticle entanglement in a variety of N-qubit states useful for quan-
tum information processing and recently engineered in laboratories with quantum optics
and trapped ion setups... [edited by author]XIV n.s
Robustness of asymmetry and coherence of quantum states
Quantum states may exhibit asymmetry with respect to the action of a given group. Such an asymmetry of states can be considered as a resource in applications such as quantum metrology, and it is a concept that encompasses quantum coherence as a special case. We introduce explicitly and study the robustness of asymmetry, a quantifier of asymmetry of states that we prove to have many attractive properties, including efficient numerical computability via semidefinite programming, and an operational interpretation in a channel discrimination context. We also introduce the notion of asymmetry witnesses, whose measurement in a laboratory detects the presence of asymmetry. We prove that properly constrained asymmetry witnesses provide lower bounds to the robustness of asymmetry, which is shown to be a directly measurable quantity itself. We then focus our attention on coherence witnesses and the robustness of coherence, for which we prove a number of additional results; these include an analysis of its specific relevance in phase discrimination and quantum metrology, an analytical calculation of its value for a relevant class of quantum states, and tight bounds that relate it to another previously defined coherence monotone
Universal freezing of quantum correlations within the geometric approach
Quantum correlations in a composite system can be measured by resorting to a
geometric approach, according to which the distance from the state of the
system to a suitable set of classically correlated states is considered. Here
we show that all distance functions, which respect natural assumptions of
invariance under transposition, convexity, and contractivity under quantum
channels, give rise to geometric quantifiers of quantum correlations which
exhibit the peculiar freezing phenomenon, i.e., remain constant during the
evolution of a paradigmatic class of states of two qubits each independently
interacting with a non-dissipative decohering environment. Our results
demonstrate from first principles that freezing of geometric quantum
correlations is independent of the adopted distance and therefore universal.
This finding paves the way to a deeper physical interpretation and future
practical exploitation of the phenomenon for noisy quantum technologies.Comment: 18 pages, 2 figures. To appear in Nature Scientific Report
Robustness of coherence: an operational and observable measure of quantum coherence
Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase discrimination task
Frozen quantum coherence
We analyze under which dynamical conditions the coherence of an open quantum system is totally unaffected by noise. For a single qubit, specific measures of coherence are found to freeze under different conditions, with no general agreement between them. Conversely, for an N-qubit system with even N, we identify universal conditions in terms of initial states and local incoherent channels such that all bona fide distance-based coherence monotones are left invariant during the entire evolution. This finding also provides an insightful physical interpretation for the freezing phenomenon of quantum correlations beyond entanglement. We further obtain analytical results for distance-based measures of coherence in two-qubit states with maximally mixed marginals
Converting multilevel nonclassicality into genuine multipartite entanglement
Characterizing genuine quantum resources and determining operational rules for their manipulation are crucial steps to appraise possibilities and limitations of quantum technologies. Two such key resources are nonclassicality, manifested as quantum superposition between reference states of a single system, and entanglement, capturing quantum correlations among two or more subsystems. Here we present a general formalism for the conversion of nonclassicality into multipartite entanglement, showing that a faithful reversible transformation between the two resources is always possible within a precise resource-theoretic framework. Specializing to quantum coherence between the levels of a quantum system as an instance of nonclassicality, we introduce explicit protocols for such a mapping. We further show that the conversion relates multilevel coherence and multipartite entanglement not only qualitatively, but also quantitatively, restricting the amount of entanglement achievable in the process and in particular yielding an equality between the two resources when quantified by fidelity-based geometric measures
Certification and Quantification of Multilevel Quantum Coherence
Quantum coherence, present whenever a quantum system exists in a
superposition of multiple classically distinct states, marks one of the
fundamental departures from classical physics. Quantum coherence has recently
been investigated rigorously within a resource-theoretic formalism. However,
the finer-grained notion of multilevel coherence, which explicitly takes into
account the number of superposed classical states, has remained relatively
unexplored. A comprehensive analysis of multi-level coherence, which acts as
the single-party analogue to multi-partite entanglement, is essential for
understanding natural quantum processes as well as for gauging the performance
of quantum technologies. Here we develop the theoretical and experimental
groundwork for characterizing and quantifying multilevel coherence. We prove
that non-trivial levels of purity are required for multilevel coherence, as
there is a ball of states around the maximally mixed state that do not exhibit
multilevel coherence in any basis. We provide a simple necessary and sufficient
analytical criterion to verify multilevel coherence, which leads to a complete
classification for three-level systems. We present the robustness of multilevel
coherence, a bona fide quantifier which we show to be numerically computable
via semidefinite programming and experimentally accessible via multilevel
coherence witnesses. We further verify and lower-bound the robustness of
multilevel coherence by performing a semi-device-independent phase
discrimination task, implemented experimentally with four-level probes in a
photonic setup. Our results contribute to understanding the operational
relevance of genuine multilevel coherence, also by demonstrating the key role
it plays in enhanced phase discrimination---a primitive for quantum
communication and metrology---and suggest new ways to reliably test the quantum
behaviour of physical systems.Comment: 20 pages, 6 figures. (v2) Title changed, presentation improved. (v3)
Expanded and updated with new results, including a necessary and sufficient
analytical criterion to detect multilevel coherence; one co-author adde
Role of non-Markovianity and backflow of information in the speed of quantum evolution
We consider a two-level open quantum system undergoing pure dephasing, dissipative, or multiply decohering dynamics and show that whenever the dynamics is non-Markovian, the initial speed of evolution is a monotonic function of the relevant physical parameter driving the transition between the Markovian and non-Markovian behavior of the dynamics. In particular, within the considered models, a speed increase can only be observed in the presence of backflow of information from the environment to the system