538 research outputs found
Genuine quantum correlations in quantum many-body systems: a review of recent progress
Quantum information theory has considerably helped in the understanding of
quantum many-body systems. The role of quantum correlations and in particular,
bipartite entanglement, has become crucial to characterise, classify and
simulate quantum many body systems. Furthermore, the scaling of entanglement
has inspired modifications to numerical techniques for the simulation of
many-body systems leading to the, now established, area of tensor networks.
However, the notions and methods brought by quantum information do not end with
bipartite entanglement. There are other forms of correlations embedded in the
ground, excited and thermal states of quantum many-body systems that also need
to be explored and might be utilised as potential resources for quantum
technologies. The aim of this work is to review the most recent developments
regarding correlations in quantum many-body systems focussing on multipartite
entanglement, quantum nonlocality, quantum discord, mutual information but also
other non classical measures of correlations based on quantum coherence.
Moreover, we also discuss applications of quantum metrology in quantum
many-body systems.Comment: Review. Close to published version. Comments are welcome! Please
write an email to g.dechiara[(at)]qub.ac.u
No second law of entanglement manipulation after all
We prove that the theory of entanglement manipulation is asymptotically
irreversible under all non-entangling operations, showing from first principles
that reversible entanglement transformations require the generation of
entanglement in the process. Entanglement is thus shown to be the first example
of a quantum resource that does not become reversible under the maximal set of
free operations, that is, under all resource non-generating maps. Our result
stands in stark contrast with the reversibility of quantum and classical
thermodynamics, and implies that no direct counterpart to the second law of
thermodynamics can be established for entanglement -- in other words, there
exists no unique measure of entanglement governing all axiomatically possible
state-to-state transformations. This completes the solution of a long-standing
open problem [Problem 20 in arXiv:quant-ph/0504166]. We strengthen the result
further to show that reversible entanglement manipulation requires the creation
of exponentially large amounts of entanglement according to monotones such as
the negativity. Our findings can also be extended to the setting of
point-to-point quantum communication, where we show that there exist channels
whose parallel simulation entanglement cost exceeds their quantum capacity,
even under the most general quantum processes that preserve
entanglement-breaking channels. The main technical tool we introduce is the
tempered logarithmic negativity, a single-letter lower bound on the
entanglement cost that can be efficiently computed via a semi-definite program.Comment: 16+30 pages, 3 figures. v2: minor clarification
Complementary Quantum Correlations among Multipartite Systems
We study the monogamy and polygamy relations related to quantum correlations
for multipartite quantum systems. General monogamy relations are presented for
the th power of quantum
correlation, and general polygamy relations are given for the th
power of quantum correlation. These
monogamy and polygamy inequalities are complementary to the existing ones with
different parameter regions of and . Applying these results to
specific quantum correlations, the corresponding new classes of monogamy and
polygamy relations are obtained, which include the existing ones as special
cases. Detailed examples are given
- …