32 research outputs found
Time correlated quantum amplitude damping channel
We analyze the problem of sending classical information through qubit
channels where successive uses of the channel are correlated. This work extends
the analysis of C. Macchiavello and G. M. Palma to the case of a non-Pauli
channel - the amplitude damping channel. Using the channel description outlined
in S. Daffer, et al, we derive the correlated amplitude damping channel. We
obtain a similar result to C. Macchiavello and G. M. Palma, that is, that under
certain conditions on the degree of channel memory, the use of entangled input
signals may enhance the information transmission compared to the use of product
input signals.Comment: 9 pages, REVTex
Unital quantum operators on the Bloch ball and Bloch region
For one qubit systems, we present a short, elementary argument characterizing
unital quantum operators in terms of their action on Bloch vectors. We then
show how our approach generalizes to multi-qubit systems, obtaining
inequalities that govern when a ``diagonal'' superoperator on the Bloch region
is a quantum operator. These inequalities are the n-qubit analogue of the
Algoet-Fujiwara conditions. Our work is facilitated by an analysis of
operator-sum decompositions in which negative summands are allowed.Comment: Revised and corrected, to appear in Physical Review
Reconstruction of superoperators from incomplete measurements
We present strategies how to reconstruct (estimate) properties of a quantum
channel described by the map E based on incomplete measurements. In a
particular case of a qubit channel a complete reconstruction of the map E can
be performed via complete tomography of four output states E[rho_j ] that
originate from a set of four linearly independent test states j (j = 1, 2, 3,
4) at the input of the channel. We study the situation when less than four
linearly independent states are transmitted via the channel and measured at the
output. We present strategies how to reconstruct the channel when just one, two
or three states are transmitted via the channel. In particular, we show that if
just one state is transmitted via the channel then the best reconstruction can
be achieved when this state is a total mixture described by the density
operator rho = I/2. To improve the reconstruction procedure one has to send via
the channel more states. The best strategy is to complement the total mixture
with pure states that are mutually orthogonal in the sense of the Bloch-sphere
representation. We show that unitary transformations (channels) can be uniquely
reconstructed (determined) based on the information of how three properly
chosen input states are transformed under the action of the channel.Comment: 13 pages, 6 figure
A quantization procedure based on completely positive maps and Markov operators
We describe -limit sets of completely positive (CP) maps over
finite-dimensional spaces. In such sets and in its corresponding convex hulls,
CP maps present isometric behavior and the states contained in it commute with
each other. Motivated by these facts, we describe a quantization procedure
based on CP maps which are induced by Markov (transfer) operators. Classical
dynamics are described by an action over essentially bounded functions. A
non-expansive linear map, which depends on a choice of a probability measure,
is the centerpiece connecting phenomena over function and matrix spaces
Quantum Network Coding
Since quantum information is continuous, its handling is sometimes
surprisingly harder than the classical counterpart. A typical example is
cloning; making a copy of digital information is straightforward but it is not
possible exactly for quantum information. The question in this paper is whether
or not quantum network coding is possible. Its classical counterpart is another
good example to show that digital information flow can be done much more
efficiently than conventional (say, liquid) flow.
Our answer to the question is similar to the case of cloning, namely, it is
shown that quantum network coding is possible if approximation is allowed, by
using a simple network model called Butterfly. In this network, there are two
flow paths, s_1 to t_1 and s_2 to t_2, which shares a single bottleneck channel
of capacity one. In the classical case, we can send two bits simultaneously,
one for each path, in spite of the bottleneck. Our results for quantum network
coding include: (i) We can send any quantum state |psi_1> from s_1 to t_1 and
|psi_2> from s_2 to t_2 simultaneously with a fidelity strictly greater than
1/2. (ii) If one of |psi_1> and |psi_2> is classical, then the fidelity can be
improved to 2/3. (iii) Similar improvement is also possible if |psi_1> and
|psi_2> are restricted to only a finite number of (previously known) states.
(iv) Several impossibility results including the general upper bound of the
fidelity are also given.Comment: 27pages, 11figures. The 12page version will appear in 24th
International Symposium on Theoretical Aspects of Computer Science (STACS
2007
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
The H\"older Inequality for KMS States
We prove a H\"older inequality for KMS States, which generalises a well-known
trace-inequality. Our results are based on the theory of non-commutative
-spaces.Comment: 10 page
Proof of the ionization conjecture in a reduced Hartree-Fock model
The ionization conjecture for atomic models states that the ionization energy and maximal excess charge are bounded by constants independent of the nuclear charge. We prove this for the Hartree-Fock model without the exchange term.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46574/1/222_2005_Article_BF01245077.pd
Unique Solutions to Hartree-Fock Equations for Closed Shell Atoms
In this paper we study the problem of uniqueness of solutions to the Hartree
and Hartree-Fock equations of atoms. We show, for example, that the
Hartree-Fock ground state of a closed shell atom is unique provided the atomic
number is sufficiently large compared to the number of electrons. More
specifically, a two-electron atom with atomic number has a unique
Hartree-Fock ground state given by two orbitals with opposite spins and
identical spatial wave functions. This statement is wrong for some , which
exhibits a phase segregation.Comment: 18 page
Nuclearity and Thermal States in Conformal Field Theory
We introduce a new type of spectral density condition, that we call
L^2-nuclearity. One formulation concerns lowest weight unitary representations
of SL(2,R) and turns out to be equivalent to the existence of characters. A
second formulation concerns inclusions of local observable von Neumann algebras
in Quantum Field Theory. We show the two formulations to agree in chiral
Conformal QFT and, starting from the trace class condition for the semigroup
generated by the conformal Hamiltonian L_0, we infer and naturally estimate the
Buchholz-Wichmann nuclearity condition and the (distal) split property. As a
corollary, if L_0 is log-elliptic, the Buchholz-Junglas set up is realized and
so there exists a beta-KMS state for the translation dynamics on the net of
C*-algebras for every inverse temperature beta>0. We include further
discussions on higher dimensional spacetimes. In particular, we verify that
L^2-nuclearity is satisfied for the scalar, massless Klein-Gordon field.Comment: 37 pages, minor correction