13 research outputs found
Monogamy, polygamy, and other properties of entanglement of purification
For bipartite pure and mixed quantum states, in addition to the quantum
mutual information, there is another measure of total correlation, namely, the
entanglement of purification. We study the monogamy, polygamy, and additivity
properties of the entanglement of purification for pure and mixed states. In
this paper, we show that, in contrast to the quantum mutual information which
is strictly monogamous for any tripartite pure states, the entanglement of
purification is polygamous for the same. This shows that there can be genuinely
two types of total correlation across any bipartite cross in a pure tripartite
state. Furthermore, we find the lower bound and actual values of the
entanglement of purification for different classes of tripartite and
higher-dimensional bipartite mixed states. Thereafter, we show that if
entanglement of purification is not additive on tensor product states, it is
actually subadditive. Using these results, we identify some states which are
additive on tensor products for entanglement of purification. The implications
of these findings on the quantum advantage of dense coding are briefly
discussed, whereby we show that for tripartite pure states, it is strictly
monogamous and if it is nonadditive, then it is superadditive on tensor product
states.Comment: 12 pages, 2 figures, Published versio
Remote Creation of Quantum Coherence via Indefinite Causal Order
Quantum coherence is a prime resource in quantum computing and quantum
communication. Quantum coherence of an arbitrary qubit state can be created at
a remote location using maximally entangled state, local operation and
classical communication. However, if there is a noisy channel acting on one
side of the shared resource, then, it is not possible to create perfect quantum
coherence remotely. Here, we present a method for the creation of quantum
coherence at a remote location via the use of entangled state and indefinite
causal order. We show this specifically for the superposition of two completely
depolarizing channels, two partially depolarizing channels and one completely
depolarizing channel along with a unitary operator. We find that when the
indefinite causal order of channels act on one-half of the entangled pair, then
the shared state looses entanglement, but can retain non-zero quantum discord.
This finding may have some interesting applications on its own where discord
can be consumed as a resource. Our results suggest that the indefinite causal
order along with a tiny amount of quantum discord can act as a resource in
creating non-zero quantum coherence in the absence of entanglement.Comment: 9 pages, 4 figures, Accepted in Quantum Information Processin
Footprints of quantum pigeons
We show that in the mathematical framework of the quantum theory the
classical pigeonhole principle can be violated more directly than previously
suggested, i.e., in a setting closer to the traditional statement of the
principle. We describe how the counterfactual reasoning of the paradox may be
operationally grounded in the analysis of the tiny footprints left in the
environment by the pigeons. After identifying the drawbacks of recent
experiments of the quantum pigeonhole effect, we argue that a definitive
experimental violation of the pigeonhole principle is still needed and propose
such an implementation using modern quantum computing hardware: a
superconducting circuit with transmon qubits
Footprints of Quantum Pigeons
We show that in the mathematical framework of the quantum theory, the classical pigeonhole principle can be violated more directly than previously suggested, i.e., in a setting closer to the traditional statement of the principle. We describe how the counterfactual reasoning of the paradox may be operationally grounded in the analysis of the tiny footprints left in the environment by the pigeons. After identifying the drawbacks of recent experiments of the quantum pigeonhole effect, we argue that a definitive experimental violation of the pigeonhole principle is still needed and propose such an implementation using modern quantum computing hardware: a superconducting circuit with transmon qubits
Failed attempt to escape from the quantum pigeon conundrum
A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of
a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS
113, 532 (2016)] is refuted. The quantum nature of the violation of the
pigeonhole principle with pre- and postselection is clarified.Comment: to be published in Physics Letters