7,988 research outputs found
Quantum Phase Transitions in the Itinerant Ferromagnet ZrZn
We report a study of the ferromagnetism of ZrZn, the most promising
material to exhibit ferromagnetic quantum criticality, at low temperatures
as function of pressure . We find that the ordered ferromagnetic moment
disappears discontinuously at =16.5 kbar. Thus a tricritical point
separates a line of first order ferromagnetic transitions from second order
(continuous) transitions at higher temperature. We also identify two lines of
transitions of the magnetisation isotherms up to 12 T in the plane where
the derivative of the magnetization changes rapidly. These quantum phase
transitions (QPT) establish a high sensitivity to local minima in the free
energy in ZrZn, thus strongly suggesting that QPT in itinerant
ferromagnets are always first order
Entropic uncertainty relations and locking: tight bounds for mutually unbiased bases
We prove tight entropic uncertainty relations for a large number of mutually
unbiased measurements. In particular, we show that a bound derived from the
result by Maassen and Uffink for 2 such measurements can in fact be tight for
up to sqrt{d} measurements in mutually unbiased bases. We then show that using
more mutually unbiased bases does not always lead to a better locking effect.
We prove that the optimal bound for the accessible information using up to
sqrt{d} specific mutually unbiased bases is log d/2, which is the same as can
be achieved by using only two bases. Our result indicates that merely using
mutually unbiased bases is not sufficient to achieve a strong locking effect,
and we need to look for additional properties.Comment: 9 pages, RevTeX, v3: complete rewrite, new title, many new results,
v4: minor changes, published versio
Entropy and Entanglement in Quantum Ground States
We consider the relationship between correlations and entanglement in gapped
quantum systems, with application to matrix product state representations. We
prove that there exist gapped one-dimensional local Hamiltonians such that the
entropy is exponentially large in the correlation length, and we present strong
evidence supporting a conjecture that there exist such systems with arbitrarily
large entropy. However, we then show that, under an assumption on the density
of states which is believed to be satisfied by many physical systems such as
the fractional quantum Hall effect, that an efficient matrix product state
representation of the ground state exists in any dimension. Finally, we comment
on the implications for numerical simulation.Comment: 7 pages, no figure
Quantum states representing perfectly secure bits are always distillable
It is proven that recently introduced states with perfectly secure bits of
cryptographic key (private states representing secure bit) [K. Horodecki et
al., Phys. Rev. Lett. 94, 160502 (2005)] as well as its multipartite and higher
dimension generalizations always represent distillable entanglement. The
corresponding lower bounds on distillable entanglement are provided. We also
present a simple alternative proof that for any bipartite quantum state
entanglement cost is an upper bound on distillable cryptographic key in
bipartite scenario.Comment: RevTeX, 5 pages, published versio
Constructive counterexamples to additivity of minimum output R\'enyi entropy of quantum channels for all p>2
We present a constructive example of violation of additivity of minimum
output R\'enyi entropy for each p>2. The example is provided by antisymmetric
subspace of a suitable dimension. We discuss possibility of extension of the
result to go beyond p>2 and obtain additivity for p=0 for a class of
entanglement breaking channels.Comment: 4 pages; a reference adde
The asymptotic entanglement cost of preparing a quantum state
We give a detailed proof of the conjecture that the asymptotic entanglement
cost of preparing a bipartite state \rho is equal to the regularized
entanglement of formation of \rho.Comment: 7 pages, no figure
Random subspaces for encryption based on a private shared Cartesian frame
A private shared Cartesian frame is a novel form of private shared
correlation that allows for both private classical and quantum communication.
Cryptography using a private shared Cartesian frame has the remarkable property
that asymptotically, if perfect privacy is demanded, the private classical
capacity is three times the private quantum capacity. We demonstrate that if
the requirement for perfect privacy is relaxed, then it is possible to use the
properties of random subspaces to nearly triple the private quantum capacity,
almost closing the gap between the private classical and quantum capacities.Comment: 9 pages, published versio
Generalized remote state preparation: Trading cbits, qubits and ebits in quantum communication
We consider the problem of communicating quantum states by simultaneously
making use of a noiseless classical channel, a noiseless quantum channel and
shared entanglement. We specifically study the version of the problem in which
the sender is given knowledge of the state to be communicated. In this setting,
a trade-off arises between the three resources, some portions of which have
been investigated previously in the contexts of the quantum-classical trade-off
in data compression, remote state preparation and superdense coding of quantum
states, each of which amounts to allowing just two out of these three
resources. We present a formula for the triple resource trade-off that reduces
its calculation to evaluating the data compression trade-off formula. In the
process, we also construct protocols achieving all the optimal points. These
turn out to be achievable by trade-off coding and suitable time-sharing between
optimal protocols for cases involving two resources out of the three mentioned
above.Comment: 15 pages, 2 figures, 1 tabl
Matrix Element Distribution as a Signature of Entanglement Generation
We explore connections between an operator's matrix element distribution and
its entanglement generation. Operators with matrix element distributions
similar to those of random matrices generate states of high multi-partite
entanglement. This occurs even when other statistical properties of the
operators do not conincide with random matrices. Similarly, operators with some
statistical properties of random matrices may not exhibit random matrix element
distributions and will not produce states with high levels of multi-partite
entanglement. Finally, we show that operators with similar matrix element
distributions generate similar amounts of entanglement.Comment: 7 pages, 6 figures, to be published PRA, partially supersedes
quant-ph/0405053, expands quant-ph/050211
Intrinsic Gap of the nu=5/2 Fractional Quantum Hall State
The fractional quantum Hall effect is observed at low field, in a regime
where the cyclotron energy is smaller than the Coulomb interaction. The nu=5/2
excitation gap is measured to be 262+/-15 mK at ~2.6 T, in good agreement with
previous measurements performed on samples with similar mobility, but with
electronic density larger by a factor of two. The role of disorder on the
nu=5/2 gap is examined. Comparison between experiment and theory indicates that
a large discrepancy remains for the intrinsic gap extrapolated from the
infinite mobility (zero disorder) limit. In contrast, no such large discrepancy
is found for the nu=1/3 Laughlin state. The observation of the nu=5/2 state in
the low-field regime implies that inclusion of non-perturbative Landau level
mixing may be necessary to better understand the energetics of half-filled
fractional quantum hall liquids.Comment: 5 pages, 4 figures; typo corrected, comment expande
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