56 research outputs found
Quantum non-malleability and authentication
In encryption, non-malleability is a highly desirable property: it ensures
that adversaries cannot manipulate the plaintext by acting on the ciphertext.
Ambainis, Bouda and Winter gave a definition of non-malleability for the
encryption of quantum data. In this work, we show that this definition is too
weak, as it allows adversaries to "inject" plaintexts of their choice into the
ciphertext. We give a new definition of quantum non-malleability which resolves
this problem. Our definition is expressed in terms of entropic quantities,
considers stronger adversaries, and does not assume secrecy. Rather, we prove
that quantum non-malleability implies secrecy; this is in stark contrast to the
classical setting, where the two properties are completely independent. For
unitary schemes, our notion of non-malleability is equivalent to encryption
with a two-design (and hence also to the definition of Ambainis et al.). Our
techniques also yield new results regarding the closely-related task of quantum
authentication. We show that "total authentication" (a notion recently proposed
by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant
improvement over the eight-design construction of Garg et al. We also show
that, under a mild adaptation of the rejection procedure, both total
authentication and our notion of non-malleability yield quantum authentication
as defined by Dupuis, Nielsen and Salvail.Comment: 20+13 pages, one figure. v2: published version plus extra material.
v3: references added and update
Ancilla models for quantum operations: For what unitaries does the ancilla state have to be physical?
Any evolution described by a completely positive trace-preserving linear map
can be imagined as arising from the interaction of the evolving system with an
initially uncorrelated ancilla. The interaction is given by a joint unitary
operator, acting on the system and the ancilla. Here we study the properties
such a unitary operator must have in order to force the choice of a physical-
that is, positive-state for the ancilla if the end result is to be a
physical-that is, completely positive-evolution of the system.Comment: Quantum Information Processing, (2012
Physical realizations of quantum operations
Quantum operations (QO) describe any state change allowed in quantum
mechanics, such as the evolution of an open system or the state change due to a
measurement. We address the problem of which unitary transformations and which
observables can be used to achieve a QO with generally different input and
output Hilbert spaces. We classify all unitary extensions of a QO, and give
explicit realizations in terms of free-evolution direct-sum dilations and
interacting tensor-product dilations. In terms of Hilbert space dimensionality
the free-evolution dilations minimize the physical resources needed to realize
the QO, and for this case we provide bounds for the dimension of the ancilla
space versus the rank of the QO. The interacting dilations, on the other hand,
correspond to the customary ancilla-system interaction realization, and for
these we derive a majorization relation which selects the allowed unitary
interactions between system and ancilla.Comment: 8 pages, no figures. Accepted for publication on Phys. Rev.
Cloning of spin-coherent states
We consider optimal cloning of the spin coherent states in Hilbert spaces of
different dimensionality d. We give explicit form of optimal cloning
transformation for spin coherent states in the three-dimensional space,
analytical results for the fidelity of the optimal cloning in d=3 and d=4 as
well as numerical results for higher dimensions. In the low-dimensional case we
construct the corresponding completely positive maps and exhibit their
structure with the help of Jamiolkowski isomorphism. This allows us to
formulate some conjectures about the form of optimal coherent cloning CP maps
in arbitrary dimension.Comment: LateX, 9 pages, 1 figur
The entanglement of purification
We introduce a measure of both quantum as well as classical correlations in a
quantum state, the entanglement of purification. We show that the (regularized)
entanglement of purification is equal to the entanglement cost of creating a
state asymptotically from maximally entangled states, with negligible
communication. We prove that the classical mutual information and the quantum
mutual information divided by two are lower bounds for the regularized
entanglement of purification. We present numerical results of the entanglement
of purification for Werner states in .Comment: 12 pages RevTex, 1 figure, to appear in JMP special issue on quantum
information. v3 contains additional references, motivation, and a small
change in the figur
Optimization of entanglement witnesses
An entanglement witness (EW) is an operator that allows to detect entangled
states. We give necessary and sufficient conditions for such operators to be
optimal, i.e. to detect entangled states in an optimal way. We show how to
optimize general EW, and then we particularize our results to the
non-decomposable ones; the latter are those that can detect positive partial
transpose entangled states (PPTES). We also present a method to systematically
construct and optimize this last class of operators based on the existence of
``edge'' PPTES, i.e. states that violate the range separability criterion
[Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also
permits the systematic construction of non-decomposable positive maps (PM). Our
results lead to a novel sufficient condition for entanglement in terms of
non-decomposable EW and PM. Finally, we illustrate our results by constructing
optimal EW acting on H=\C^2\otimes \C^4. The corresponding PM constitute the
first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal
hermitian conjugate codomain.Comment: 18 pages, two figures, minor change
Test for entanglement using physically observable witness operators and positive maps
Motivated by the Peres-Horodecki criterion and the realignment criterion we
develop a more powerful method to identify entangled states for any bipartite
system through a universal construction of the witness operator. The method
also gives a new family of positive but non-completely positive maps of
arbitrary high dimensions which provide a much better test than the witness
operators themselves. Moreover, we find there are two types of positive maps
that can detect 2xN and 4xN bound entangled states. Since entanglement
witnesses are physical observables and may be measured locally our construction
could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl
A Factorization Law for Entanglement Decay
We present a simple and general factorization law for quantum systems shared
by two parties, which describes the time evolution of entanglement upon passage
of either component through an arbitrary noisy channel. The robustness of
entanglement-based quantum information processing protocols is thus easily and
fully characterized by a single quantity.Comment: 4 pages, 5 figure
Characterising a universal cloning machine by maximum-likelihood estimation
We apply a general method for the estimation of completely positive maps to
the 1-to-2 universal covariant cloning machine. The method is based on the
maximum-likelihood principle, and makes use of random input states, along with
random projective measurements on the output clones. The downhill simplex
algorithm is applied for the maximisation of the likelihood functional.Comment: 5 pages, 2 figure
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