360 research outputs found
Versatile Wideband Balanced Detector for Quantum Optical Homodyne Tomography
We present a comprehensive theory and an easy to follow method for the design
and construction of a wideband homodyne detector for time-domain quantum
measurements. We show how one can evaluate the performance of a detector in a
specific time-domain experiment based on electronic spectral characteristic of
that detector. We then present and characterize a high-performance detector
constructed using inexpensive, commercially available components such as
low-noise high-speed operational amplifiers and high-bandwidth photodiodes. Our
detector shows linear behavior up to a level of over 13 dB clearance between
shot noise and electronic noise, in the range from DC to 100 MHz. The detector
can be used for measuring quantum optical field quadratures both in the
continuous-wave and pulsed regimes with pulse repetition rates up to about 250
MHz.Comment: 11 pages, 8 figures, 1 tabl
All Inequalities for the Relative Entropy
The relative entropy of two n-party quantum states is an important quantity
exhibiting, for example, the extent to which the two states are different. The
relative entropy of the states formed by reducing two n-party to a smaller
number of parties is always less than or equal to the relative entropy of
the two original n-party states. This is the monotonicity of relative entropy.
Using techniques from convex geometry, we prove that monotonicity under
restrictions is the only general inequality satisfied by relative entropies. In
doing so we make a connection to secret sharing schemes with general access
structures.
A suprising outcome is that the structure of allowed relative entropy values
of subsets of multiparty states is much simpler than the structure of allowed
entropy values. And the structure of allowed relative entropy values (unlike
that of entropies) is the same for classical probability distributions and
quantum states.Comment: 15 pages, 3 embedded eps figure
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
Wehrl entropy, Lieb conjecture and entanglement monotones
We propose to quantify the entanglement of pure states of
bipartite quantum system by defining its Husimi distribution with respect to
coherent states. The Wehrl entropy is minimal if and only
if the pure state analyzed is separable. The excess of the Wehrl entropy is
shown to be equal to the subentropy of the mixed state obtained by partial
trace of the bipartite pure state. This quantity, as well as the generalized
(R{\'e}nyi) subentropies, are proved to be Schur--convex, so they are
entanglement monotones and may be used as alternative measures of entanglement
Continuity of the Maximum-Entropy Inference
We study the inverse problem of inferring the state of a finite-level quantum
system from expected values of a fixed set of observables, by maximizing a
continuous ranking function. We have proved earlier that the maximum-entropy
inference can be a discontinuous map from the convex set of expected values to
the convex set of states because the image contains states of reduced support,
while this map restricts to a smooth parametrization of a Gibbsian family of
fully supported states. Here we prove for arbitrary ranking functions that the
inference is continuous up to boundary points. This follows from a continuity
condition in terms of the openness of the restricted linear map from states to
their expected values. The openness condition shows also that ranking functions
with a discontinuous inference are typical. Moreover it shows that the
inference is continuous in the restriction to any polytope which implies that a
discontinuity belongs to the quantum domain of non-commutative observables and
that a geodesic closure of a Gibbsian family equals the set of maximum-entropy
states. We discuss eight descriptions of the set of maximum-entropy states with
proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur
Lattice gauge theory with baryons at strong coupling
We study the effective Hamiltonian for strong-coupling lattice QCD in the
case of non-zero baryon density. In leading order the effective Hamiltonian is
a generalized antiferromagnet. For naive fermions, the symmetry is U(4N_f) and
the spins belong to a representation that depends on the local baryon number.
Next-nearest-neighbor (nnn) terms in the Hamiltonian break the symmetry to
U(N_f) x U(N_f). We transform the quantum problem to a Euclidean sigma model
which we analyze in a 1/N_c expansion. In the vacuum sector we recover
spontaneous breaking of chiral symmetry for the nearest-neighbor and nnn
theories. For non-zero baryon density we study the nearest-neighbor theory
only, and show that the pattern of spontaneous symmetry breaking depends on the
baryon density.Comment: 31 pages, 5 EPS figures. Corrected Eq. (6.1
Multiplicativity of completely bounded p-norms implies a new additivity result
We prove additivity of the minimal conditional entropy associated with a
quantum channel Phi, represented by a completely positive (CP),
trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is
restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We
show that this follows from multiplicativity of the completely bounded norm of
Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten
p-norm on matrices; we also give an independent proof based on entropy
inequalities. Several related multiplicativity results are discussed and
proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map
and the corresponding completely bounded norm are achieved for positive
semi-definite matrices. Physical interpretations are considered, and a new
proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous
version deleted in view of the results in quant-ph/0601071 Other changes
mino
Relations for certain symmetric norms and anti-norms before and after partial trace
Changes of some unitarily invariant norms and anti-norms under the operation
of partial trace are examined. The norms considered form a two-parametric
family, including both the Ky Fan and Schatten norms as particular cases. The
obtained results concern operators acting on the tensor product of two
finite-dimensional Hilbert spaces. For any such operator, we obtain upper
bounds on norms of its partial trace in terms of the corresponding
dimensionality and norms of this operator. Similar inequalities, but in the
opposite direction, are obtained for certain anti-norms of positive matrices.
Through the Stinespring representation, the results are put in the context of
trace-preserving completely positive maps. We also derive inequalities between
the unified entropies of a composite quantum system and one of its subsystems,
where traced-out dimensionality is involved as well.Comment: 11 pages, no figures. A typo error in Eq. (5.15) is corrected. Minor
improvements. J. Stat. Phys. (in press
Symmetry and topology in antiferromagnetic spintronics
Antiferromagnetic spintronics focuses on investigating and using
antiferromagnets as active elements in spintronics structures. Last decade
advances in relativistic spintronics led to the discovery of the staggered,
current-induced field in antiferromagnets. The corresponding N\'{e}el
spin-orbit torque allowed for efficient electrical switching of
antiferromagnetic moments and, in combination with electrical readout, for the
demonstration of experimental antiferromagnetic memory devices. In parallel,
the anomalous Hall effect was predicted and subsequently observed in
antiferromagnets. A new field of spintronics based on antiferromagnets has
emerged. We will focus here on the introduction into the most significant
discoveries which shaped the field together with a more recent spin-off
focusing on combining antiferromagnetic spintronics with topological effects,
such as antiferromagnetic topological semimetals and insulators, and the
interplay of antiferromagnetism, topology, and superconductivity in
heterostructures.Comment: Book chapte
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