221 research outputs found
Optimal Cloning of Pure States, Judging Single Clones
We consider quantum devices for turning a finite number N of d-level quantum
systems in the same unknown pure state \sigma into M>N systems of the same
kind, in an approximation of the M-fold tensor product of the state \sigma. In
a previous paper it was shown that this problem has a unique optimal solution,
when the quality of the output is judged by arbitrary measurements, involving
also the correlations between the clones. We show in this paper, that if the
quality judgement is based solely on measurements of single output clones,
there is again a unique optimal cloning device, which coincides with the one
found previously.Comment: 16 Pages, REVTe
Maximally entangled fermions
Fermions play an essential role in many areas of quantum physics and it is
desirable to understand the nature of entanglement within systems that consists
of fermions. Whereas the issue of separability for bipartite fermions has
extensively been studied in the present literature, this paper is concerned
with maximally entangled fermions. A complete characterization of maximally
entangled quasifree (gaussian) fermion states is given in terms of the
covariance matrix. This result can be seen as a step towards distillation
protocols for maximally entangled fermions.Comment: 13 pages, 1 figure, RevTex, minor errors are corrected, section
"Conclusions" is adde
Quantum information becomes classical when distributed to many users
Any physical transformation that equally distributes quantum information over
a large number M of users can be approximated by a classical broadcasting of
measurement outcomes. The accuracy of the approximation is at least of the
order 1/M. In particular, quantum cloning of pure and mixed states can be
approximated via quantum state estimation. As an example, for optimal qubit
cloning with 10 output copies, a single user has error probability p > 0.45 in
distinguishing classical from quantum output--a value close to the error
probability of the random guess.Comment: 4 pages, no figures, published versio
Superbroadcasting of mixed states
We derive the optimal universal broadcasting for mixed states of qubits. We
show that the nobroadcasting theorem cannot be generalized to more than a
single input copy. Moreover, for four or more input copies it is even possible
to purify the input states while broadcasting. We name such purifying
broadcasting superbroadcasting.Comment: 4 pages, 4 figures, to appear on Phys. Rev. Let
Optimal probabilistic cloning and purification of quantum states
We investigate the probabilistic cloning and purification of quantum states.
The performance of these probabilistic operations is quantified by the average
fidelity between the ideal and actual output states. We provide a simple
formula for the maximal achievable average fidelity and we explictly show how
to construct a probabilistic operation that achieves this fidelity. We
illustrate our method on several examples such as the phase covariant cloning
of qubits, cloning of coherent states, and purification of qubits transmitted
via depolarizing channel and amplitude damping channel. Our examples reveal
that the probabilistic cloner may yield higher fidelity than the best
deterministic cloner even when the states that should be cloned are linearly
dependent and are drawn from a continuous set.Comment: 9 pages, 2 figure
On Nonzero Kronecker Coefficients and their Consequences for Spectra
A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a
density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,
r^B, r^{AB}). How can we characterise such triples? It turns out that the
admissible spectral triples correspond to Young diagrams (mu, nu, lambda) with
nonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in
Comm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means
that the irreducible representation V_lambda is contained in the tensor product
of V_mu and V_nu. Here, we show that such triples form a finitely generated
semigroup, thereby resolving a conjecture of Klyachko. As a consequence we are
able to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a
complete information-theoretic proof of the correspondence between triples of
spectra and representations. Finally, we show that spectral triples form a
convex polytope.Comment: 13 page
Numerical simulations of mixed states quantum computation
We describe quantum-octave package of functions useful for simulations of
quantum algorithms and protocols. Presented package allows to perform
simulations with mixed states. We present numerical implementation of important
quantum mechanical operations - partial trace and partial transpose. Those
operations are used as building blocks of algorithms for analysis of
entanglement and quantum error correction codes. Simulation of Shor's algorithm
is presented as an example of package capabilities.Comment: 6 pages, 4 figures, presented at Foundations of Quantum Information,
16th-19th April 2004, Camerino, Ital
A generalization of Schur-Weyl duality with applications in quantum estimation
Schur-Weyl duality is a powerful tool in representation theory which has many
applications to quantum information theory. We provide a generalization of this
duality and demonstrate some of its applications. In particular, we use it to
develop a general framework for the study of a family of quantum estimation
problems wherein one is given n copies of an unknown quantum state according to
some prior and the goal is to estimate certain parameters of the given state.
In particular, we are interested to know whether collective measurements are
useful and if so to find an upper bound on the amount of entanglement which is
required to achieve the optimal estimation. In the case of pure states, we show
that commutativity of the set of observables that define the estimation problem
implies the sufficiency of unentangled measurements.Comment: The published version, Typos corrected, 40 pages, 2 figure
Universal and phase covariant superbroadcasting for mixed qubit states
We describe a general framework to study covariant symmetric broadcasting
maps for mixed qubit states. We explicitly derive the optimal N to M
superbroadcasting maps, achieving optimal purification of the single-site
output copy, in both the universal and the phase covariant cases. We also study
the bipartite entanglement properties of the superbroadcast states.Comment: 19 pages, 8 figures, strictly related to quant-ph/0506251 and
quant-ph/051015
Clean Positive Operator Valued Measures
In quantum mechanics the statistics of the outcomes of a measuring apparatus
is described by a positive operator valued measure (POVM). A quantum channel
transforms POVM's into POVM's, generally irreversibly, thus loosing some of the
information retrieved from the measurement. This poses the problem of which
POVM's are "undisturbed", namely they are not irreversibly connected to another
POVM. We will call such POVM clean. In a sense, the clean POVM's would be
"perfect", since they would not have any additional "extrinsical" noise. Quite
unexpectedly, it turns out that such cleanness property is largely unrelated to
the convex structure of POVM's, and there are clean POVM's that are not
extremal and vice-versa. In this paper we solve the cleannes classification
problem for number n of outcomes n<=d (d dimension of the Hilbert space), and
we provide a a set of either necessary or sufficient conditions for n>d, along
with an iff condition for the case of informationally complete POVM's for
n=d^2.Comment: Minor changes. amsart 21 pages. Accepted for publication on J. Math.
Phy
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