574 research outputs found
Self-testing multipartite entangled states through projections onto two systems
Finding ways to test the behaviour of quantum devices is a timely enterprise,
especially in the light of the rapid development of quantum technologies.
Device-independent self-testing is one desirable approach, as it makes minimal
assumptions on the devices being tested. In this work, we address the question
of which states can be self-tested. This has been answered recently in the
bipartite case [Nat. Comm. 8, 15485 (2017)], while it is largely unexplored in
the multipartite case, with only a few scattered results, using a variety of
different methods: maximal violation of a Bell inequality, numerical SWAP
method, stabilizer self-testing etc. In this work, we investigate a simple, and
potentially unifying, approach: combining projections onto two-qubit spaces
(projecting parties or degrees of freedom) and then using maximal violation of
the tilted CHSH inequalities. This allows to obtain self-testing of Dicke
states and partially entangled GHZ states with two measurements per party, and
also to recover self-testing of graph states (previously known only through
stabilizer methods). Finally, we give the first self-test of a class
multipartite qudit states: we generalize the self-testing of partially
entangled GHZ states by adapting techniques from [Nat. Comm. 8, 15485 (2017)],
and show that all multipartite states which admit a Schmidt decomposition can
be self-tested with few measurements.Comment: The title is changed and the presentation is slightly restructure
Characterizing Operations Preserving Separability Measures via Linear Preserver Problems
We use classical results from the theory of linear preserver problems to
characterize operators that send the set of pure states with Schmidt rank no
greater than k back into itself, extending known results characterizing
operators that send separable pure states to separable pure states. We also
provide a new proof of an analogous statement in the multipartite setting. We
use these results to develop a bipartite version of a classical result about
the structure of maps that preserve rank-1 operators and then characterize the
isometries for two families of norms that have recently been studied in quantum
information theory. We see in particular that for k at least 2 the operator
norms induced by states with Schmidt rank k are invariant only under local
unitaries, the swap operator and the transpose map. However, in the k = 1 case
there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3
simplified and clarifie
GHZ extraction yield for multipartite stabilizer states
Let be an arbitrary stabilizer state distributed between three
remote parties, such that each party holds several qubits. Let be a
stabilizer group of . We show that can be converted by local
unitaries into a collection of singlets, GHZ states, and local one-qubit
states. The numbers of singlets and GHZs are determined by dimensions of
certain subgroups of . For an arbitrary number of parties we find a
formula for the maximal number of -partite GHZ states that can be extracted
from by local unitaries. A connection with earlier introduced measures
of multipartite correlations is made. An example of an undecomposable
four-party stabilizer state with more than one qubit per party is given. These
results are derived from a general theoretical framework that allows one to
study interconversion of multipartite stabilizer states by local Clifford group
operators. As a simple application, we study three-party entanglement in
two-dimensional lattice models that can be exactly solved by the stabilizer
formalism.Comment: 12 pages, 1 figur
Multipartite entanglement in qubit systems
We introduce a potential of multipartite entanglement for a system of n
qubits, as the average over all balanced bipartitions of a bipartite
entanglement measure, the purity. We study in detail its expression and look
for its minimizers, the maximally multipartite entangled states. They have a
bipartite entanglement that does not depend on the bipartition and is maximal
for all possible bipartitions. We investigate their structure and consider
several examples for small n.Comment: 42 page
Tight bounds on the distinguishability of quantum states under separable measurements
One of the many interesting features of quantum nonlocality is that the
states of a multipartite quantum system cannot always be distinguished as well
by local measurements as they can when all quantum measurements are allowed. In
this work, we characterize the distinguishability of sets of multipartite
quantum states when restricted to separable measurements -- those which contain
the class of local measurements but nevertheless are free of entanglement
between the component systems. We consider two quantities: The separable
fidelity -- a truly quantum quantity -- which measures how well we can "clone"
the input state, and the classical probability of success, which simply gives
the optimal probability of identifying the state correctly.
We obtain lower and upper bounds on the separable fidelity and give several
examples in the bipartite and multipartite settings where these bounds are
optimal. Moreover the optimal values in these cases can be attained by local
measurements. We further show that for distinguishing orthogonal states under
separable measurements, a strategy that maximizes the probability of success is
also optimal for separable fidelity. We point out that the equality of fidelity
and success probability does not depend on an using optimal strategy, only on
the orthogonality of the states. To illustrate this, we present an example
where two sets (one consisting of orthogonal states, and the other
non-orthogonal states) are shown to have the same separable fidelity even
though the success probabilities are different.Comment: 19 pages; published versio
Minimum Entangling Power is Close to Its Maximum
Given a quantum gate acting on a bipartite quantum system, its maximum
(average, minimum) entangling power is the maximum (average, minimum)
entanglement generation with respect to certain entanglement measure when the
inputs are restricted to be product states. In this paper, we mainly focus on
the 'weakest' one, i.e., the minimum entangling power, among all these
entangling powers. We show that, by choosing von Neumann entropy of reduced
density operator or Schmidt rank as entanglement measure, even the 'weakest'
entangling power is generically very close to its maximal possible entanglement
generation. In other words, maximum, average and minimum entangling powers are
generically close. We then study minimum entangling power with respect to other
Lipschitiz-continuous entanglement measures and generalize our results to
multipartite quantum systems.
As a straightforward application, a random quantum gate will almost surely be
an intrinsically fault-tolerant entangling device that will always transform
every low-entangled state to near-maximally entangled state.Comment: 26 pages, subsection III.A.2 revised, authors list updated, comments
are welcom
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