332 research outputs found
Cloning a Qutrit
We investigate several classes of state-dependent quantum cloners for
three-level systems. These cloners optimally duplicate some of the four
maximally-conjugate bases with an equal fidelity, thereby extending the
phase-covariant qubit cloner to qutrits. Three distinct classes of qutrit
cloners can be distinguished, depending on two, three, or four
maximally-conjugate bases are cloned as well (the latter case simply
corresponds to the universal qutrit cloner). These results apply to symmetric
as well as asymmetric cloners, so that the balance between the fidelity of the
two clones can also be analyzed.Comment: 14 pages LaTex. To appear in the Journal of Modern Optics for the
special issue on "Quantum Information: Theory, Experiment and Perspectives".
Proceedings of the ESF Conference, Gdansk, July 10-18, 200
Continuous-variable entropic uncertainty relations
Uncertainty relations are central to quantum physics. While they were
originally formulated in terms of variances, they have later been successfully
expressed with entropies following the advent of Shannon information theory.
Here, we review recent results on entropic uncertainty relations involving
continuous variables, such as position and momentum . This includes the
generalization to arbitrary (not necessarily canonically-conjugate) variables
as well as entropic uncertainty relations that take - correlations into
account and admit all Gaussian pure states as minimum uncertainty states. We
emphasize that these continuous-variable uncertainty relations can be
conveniently reformulated in terms of entropy power, a central quantity in the
information-theoretic description of random signals, which makes a bridge with
variance-based uncertainty relations. In this review, we take the quantum
optics viewpoint and consider uncertainties on the amplitude and phase
quadratures of the electromagnetic field, which are isomorphic to and ,
but the formalism applies to all such variables (and linear combinations
thereof) regardless of their physical meaning. Then, in the second part of this
paper, we move on to new results and introduce a tighter entropic uncertainty
relation for two arbitrary vectors of intercommuting continuous variables that
take correlations into account. It is proven conditionally on reasonable
assumptions. Finally, we present some conjectures for new entropic uncertainty
relations involving more than two continuous variables.Comment: Review paper, 42 pages, 1 figure. We corrected some minor errors in
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Operational quantum theory without predefined time
The standard formulation of quantum theory assumes a predefined notion of
time. This is a major obstacle in the search for a quantum theory of gravity,
where the causal structure of space-time is expected to be dynamical and
fundamentally probabilistic in character. Here, we propose a generalized
formulation of quantum theory without predefined time or causal structure,
building upon a recently introduced operationally time-symmetric approach to
quantum theory. The key idea is a novel isomorphism between transformations and
states which depends on the symmetry transformation of time reversal. This
allows us to express the time-symmetric formulation in a time-neutral form with
a clear physical interpretation, and ultimately drop the assumption of time. In
the resultant generalized formulation, operations are associated with regions
that can be connected in networks with no directionality assumed for the
connections, generalizing the standard circuit framework and the process matrix
framework for operations without global causal order. The possible events in a
given region are described by positive semidefinite operators on a Hilbert
space at the boundary, while the connections between regions are described by
entangled states that encode a nontrivial symmetry and could be tested in
principle. We discuss how the causal structure of space-time could be
understood as emergent from properties of the operators on the boundaries of
compact space-time regions. The framework is compatible with indefinite causal
order, timelike loops, and other acausal structures.Comment: 15 pages, 7 figures, published version (this version covers the
second half of the original submission; the first half has been published
separately and is available at arXiv:1507.07745
Operational formulation of time reversal in quantum theory
The symmetry of quantum theory under time reversal has long been a subject of
controversy because the transition probabilities given by Born's rule do not
apply backward in time. Here, we resolve this problem within a rigorous
operational probabilistic framework. We argue that reconciling time reversal
with the probabilistic rules of the theory requires a notion of operation that
permits realizations via both pre- and post-selection. We develop the
generalized formulation of quantum theory that stems from this approach and
give a precise definition of time-reversal symmetry, emphasizing a previously
overlooked distinction between states and effects. We prove an analogue of
Wigner's theorem, which characterizes all allowed symmetry transformations in
this operationally time-symmetric quantum theory. Remarkably, we find larger
classes of symmetry transformations than those assumed before. This suggests a
possible direction for search of extensions of known physics.Comment: 17 pages, 5 figure
Exploring pure quantum states with maximally mixed reductions
We investigate multipartite entanglement for composite quantum systems in a
pure state. Using the generalized Bloch representation for n-qubit states, we
express the condition that all k-qubit reductions of the whole system are
maximally mixed, reflecting maximum bipartite entanglement across all k vs. n-k
bipartitions. As a special case, we examine the class of balanced pure states,
which are constructed from a subset of the Pauli group P_n that is isomorphic
to Z_2^n. This makes a connection with the theory of quantum error-correcting
codes and provides bounds on the largest allowed k for fixed n. In particular,
the ratio k/n can be lower and upper bounded in the asymptotic regime, implying
that there must exist multipartite entangled states with at least k=0.189 n
when . We also analyze symmetric states as another natural class
of states with high multipartite entanglement and prove that, surprisingly,
they cannot have all maximally mixed k-qubit reductions with k>1. Thus,
measured through bipartite entanglement across all bipartitions, symmetric
states cannot exhibit large entanglement. However, we show that the permutation
symmetry only constrains some components of the generalized Bloch vector, so
that very specific patterns in this vector may be allowed even though k>1 is
forbidden. This is illustrated numerically for a few symmetric states that
maximize geometric entanglement, revealing some interesting structures.Comment: 10 pages, 2 figure
Adiabatic quantum search algorithm for structured problems
The study of quantum computation has been motivated by the hope of finding
efficient quantum algorithms for solving classically hard problems. In this
context, quantum algorithms by local adiabatic evolution have been shown to
solve an unstructured search problem with a quadratic speed-up over a classical
search, just as Grover's algorithm. In this paper, we study how the structure
of the search problem may be exploited to further improve the efficiency of
these quantum adiabatic algorithms. We show that by nesting a partial search
over a reduced set of variables into a global search, it is possible to devise
quantum adiabatic algorithms with a complexity that, although still
exponential, grows with a reduced order in the problem size.Comment: 7 pages, 0 figur
A No-Go Theorem for Gaussian Quantum Error Correction
It is proven that Gaussian operations are of no use for protecting Gaussian
states against Gaussian errors in quantum communication protocols.
Specifically, we introduce a new quantity characterizing any single-mode
Gaussian channel, called entanglement degradation, and show that it cannot
decrease via Gaussian encoding and decoding operations only. The strength of
this no-go theorem is illustrated with some examples of Gaussian channels.Comment: 4 pages, 2 figures, REVTeX
Asymmetric quantum cloning machines in any dimension
A family of asymmetric cloning machines for -dimensional quantum states is
introduced. These machines produce two imperfect copies of a single state that
emerge from two distinct Heisenberg channels. The tradeoff between the quality
of these copies is shown to result from a complementarity akin to Heisenberg
uncertainty principle. A no-cloning inequality is derived for isotropic
cloners: if and are the depolarizing fractions associated with
the two copies, the domain in -space located
inside a particular ellipse representing close-to-perfect cloning is forbidden.
More generally, a no-cloning uncertainty relation is discussed, quantifying the
impossibility of copying imposed by quantum mechanics. Finally, an asymmetric
Pauli cloning machine is defined that makes two approximate copies of a quantum
bit, while the input-to-output operation underlying each copy is a (distinct)
Pauli channel. The class of symmetric Pauli cloning machines is shown to
provide an upper bound on the quantum capacity of the Pauli channel of
probabilities , and .Comment: 18 pages RevTeX, 3 Postscript figures; new discussion on no-cloning
uncertainty relations, several corrections, added reference
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