39,015 research outputs found
Quantum discord and related measures of quantum correlations in XY chains
We examine the quantum correlations of spin pairs in the ground state of
finite XY chains in a transverse field, by evaluating the quantum discord as
well as other related entropic measures of quantum correlations. A brief review
of the latter, based on generalized entropic forms, is also included. It is
shown that parity effects are of crucial importance for describing the behavior
of these measures below the critical field. It is also shown that these
measures reach full range in the immediate vicinity of the factorizing field,
where they become independent of separation and coupling range. Analytical and
numerical results for the quantum discord, the geometric discord and other
measures in spin chains with nearest neighbor coupling and in fully connected
spin arrays are also provided.Comment: accepted in Int. J. Mod. Phys. B, special issue "Classical Vs Quantum
correlations in composite systems" edited by L. Amico, S. Bose, V. Korepin
and V. Vedra
Generalized information theoretic measure to discern the quantumness of correlations
A novel measure, quantumness of correlations is introduced here for bipartite
states, by incorporating the required measurement scheme crucial in defining
any such quantity. Quantumness coincides with the previously proposed measures
in special cases and it vanishes for separable states - a feature not captured
by the measures proposed earlier. It is found that an optimal generalized
measurement on one of the parts leaves the overall state in its closest
separable form, which shares the same marginal for the other part, implying
that quantumness is non-zero for all entangled bipartite states and it serves
as an upper bound to the relative entropy of entanglement.Comment: 5 pages, no figures, Revtex, Minor changes; Accepted for publication
in Physical Review Letter
Probabilistic Quantum Control Via Indirect Measurement
The most basic scenario of quantum control involves the organized
manipulation of pure dynamical states of the system by means of unitary
transformations. Recently, Vilela Mendes and Mank'o have shown that the
conditions for controllability on the state space become less restrictive if
unitary control operations may be supplemented by projective measurement. The
present work builds on this idea, introducing the additional element of
indirect measurement to achieve a kind of remote control. The target system
that is to be remotely controlled is first entangled with another identical
system, called the control system. The control system is then subjected to
unitary transformations plus projective measurement. As anticipated by
Schrodinger, such control via entanglement is necessarily probabilistic in
nature. On the other hand, under appropriate conditions the remote-control
scenario offers the special advantages of robustness against decoherence and a
greater repertoire of unitary transformations. Simulations carried out for a
two-level system demonstrate that, with optimization of control parameters, a
substantial gain in the population of reachable states can be realized.Comment: 9 pages, 2 figures; typos added, reference added, reference remove
Frustration, interaction strength and ground-state entanglement in complex quantum systems
Entanglement in the ground state of a many-body quantum system may arise when
the local terms in the system Hamiltonian fail to commute with the interaction
terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy
between ground-state entanglement and the phenomenon of frustration in spin
systems. In particular, we prove that the amount of ground-state entanglement
is bounded above by a measure of the extent to which interactions frustrate the
local terms in the Hamiltonian. As a corollary, we show that the amount of
ground-state entanglement is bounded above by a ratio between parameters
characterizing the strength of interactions in the system, and the local energy
scale. Finally, we prove a qualitatively similar result for other energy
eigenstates of the system.Comment: 11 pages, 3 figure
Fault-tolerant quantum computation with cluster states
The one-way quantum computing model introduced by Raussendorf and Briegel
[Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to
quantum compute using only a fixed entangled resource known as a cluster state,
and adaptive single-qubit measurements. This model is the basis for several
practical proposals for quantum computation, including a promising proposal for
optical quantum computation based on cluster states [M. A. Nielsen,
arXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant
open question is whether such proposals are scalable in the presence of
physically realistic noise. In this paper we prove two threshold theorems which
show that scalable fault-tolerant quantum computation may be achieved in
implementations based on cluster states, provided the noise in the
implementations is below some constant threshold value. Our first threshold
theorem applies to a class of implementations in which entangling gates are
applied deterministically, but with a small amount of noise. We expect this
threshold to be applicable in a wide variety of physical systems. Our second
threshold theorem is specifically adapted to proposals such as the optical
cluster-state proposal, in which non-deterministic entangling gates are used. A
critical technical component of our proofs is two powerful theorems which
relate the properties of noisy unitary operations restricted to act on a
subspace of state space to extensions of those operations acting on the entire
state space.Comment: 31 pages, 54 figure
Witnessing quantum discord in 2 x N systems
Bipartite states with vanishing quantum discord are necessarily separable and
hence positive partial transpose (PPT). We show that 2 x N states satisfy
additional property: the positivity of their partial transposition is
recognized with respect to the canonical factorization of the original density
operator. We call such states SPPT (for strong PPT). Therefore, we provide a
natural witness for a quantum discord: if a 2 x N state is not SPPT it must
contain nonclassical correlations measured by quantum discord. It is an analog
of the celebrated Peres-Horodecki criterion: if a state is not PPT it must be
entangled.Comment: 5 page
Dimension minimization of a quantum automaton
A new model of a Quantum Automaton (QA), working with qubits is proposed. The
quantum states of the automaton can be pure or mixed and are represented by
density operators. This is the appropriated approach to deal with measurements
and dechorence. The linearity of a QA and of the partial trace super-operator,
combined with the properties of invariant subspaces under unitary
transformations, are used to minimize the dimension of the automaton and,
consequently, the number of its working qubits. The results here developed are
valid wether the state set of the QA is finite or not. There are two main
results in this paper: 1) We show that the dimension reduction is possible
whenever the unitary transformations, associated to each letter of the input
alphabet, obey a set of conditions. 2) We develop an algorithm to find out the
equivalent minimal QA and prove that its complexity is polynomial in its
dimension and in the size of the input alphabet.Comment: 26 page
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