202 research outputs found
Complementarity Relations Between Quantum Steering Criteria
Recently, a connection between quantum coherence and quantum steering was
established and criteria for quantum steering or in other words, nonlocal
advantage of quantum coherence (NAQC) were derived for two-qubit states. Here,
we derive a set of complementarity relations between the steering or NAQC
inequalities achieved by various criteria. We also extend the idea in the
multi-partite scenario, specifically, in the three-qubit scenario, which can
easily be generalized to the multi-partite scenario.Comment: 6 pages, 3 figure
Quantum Speed Limit For Mixed States Using Experimentally Realizable Metric
The minimal time required for a system to evolve between two different states
is an important notion for developing ultra-speed quantum computer and
communication channel. Here, we introduce a new metric for non-degenerate
density operator evolving along unitary orbit and show that this is
experimentally realizable operation dependent metric on quantum state space.
Using this metric, we obtain the geometric uncertainty relation that leads to a
new quantum speed limit. Furthermore, we argue that this gives a tighter bound
for the evolution time compared to any other bound. We also obtain a Levitin
kind of bound for mixed states. We propose how to measure this new distance and
speed limit in quantum interferometry. Finally, the lower bound for the
evolution time of a quantum system is studied for any completely positive trace
preserving map using this metric.Comment: Latex, 8+\epsilon pages, 1 Fig accepted in PL
Non-Local Advantage of Quantum Coherence
A bipartite state is said to be steerable if and only if it does not have a
single system description, i.e., the bipartite state cannot be explained by a
local hidden state model. Several steering inequalities have been derived using
different local uncertainty relations to verify the ability to control the
state of one subsystem by the other party. Here, we derive complementarity
relations between coherences measured on mutually unbiased bases using various
coherence measures such as the -norm, relative entropy and skew
information. Using these relations, we derive conditions under which non-local
advantage of quantum coherence can be achieved and the state is steerable. We
show that not all steerable states can achieve such advantage.Comment: 8 pages, protocol modified, To appear in PRA-Rapid Communication
Authentication protocol based on collective quantum steering
It is well known that certain quantum correlations like quantum steering
exhibit a monogamous relationship. In this paper, we exploit the asymmetric
nature of quantum steering and show that there exist states which exhibit a
polygamous correlation, known as collective correlation [He and Reid, Phys.
Rev. Lett. 111, 250403 (2013)], where the state of one party, Alice, can be
steered only by the joint effort of the other two parties, Bob and Charlie. As
an example, we explicitly single out a particular set of qubit states which
exhibit this polygamous relationship, known as collective steerability. We
provide a recipe to identify the complete set of such states. We also provide a
possible application of such states to an information theoretic task, termed as
quantum key authentication (QKA) protocol. QKA can also be used in conjunction
with other well known cryptography protocols to improve their security and we
provide one such example with quantum private comparison (QPC).Comment: 6 pages, 1 figure, comments appreciated :
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