29,305 research outputs found
Quantum Channels and Representation Theory
In the study of d-dimensional quantum channels , an assumption
which is not very restrictive, and which has a natural physical interpretation,
is that the corresponding Kraus operators form a representation of a Lie
algebra. Physically, this is a symmetry algebra for the interaction
Hamiltonian. This paper begins a systematic study of channels defined by
representations; the famous Werner-Holevo channel is one element of this
infinite class. We show that the channel derived from the defining
representation of SU(n) is a depolarizing channel for all , but for most
other representations this is not the case. Since the Bloch sphere is not
appropriate here, we develop technology which is a generalization of Bloch's
technique. Our method works by representing the density matrix as a polynomial
in symmetrized products of Lie algebra generators, with coefficients that are
symmetric tensors. Using these tensor methods we prove eleven theorems, derive
many explicit formulas and show other interesting properties of quantum
channels in various dimensions, with various Lie symmetry algebras. We also
derive numerical estimates on the size of a generalized ``Bloch sphere'' for
certain channels. There remain many open questions which are indicated at
various points through the paper.Comment: 28 pages, 1 figur
Exchange-controlled single-electron-spin rotations in quantum dots
We show theoretically that arbitrary coherent rotations can be performed
quickly (with a gating time ~1 ns) and with high fidelity on the spin of a
single confined electron using control of exchange only, without the need for
spin-orbit coupling or ac fields. We expect that implementations of this scheme
would achieve gate error rates on the order of \eta ~ 10^{-3} in GaAs quantum
dots, within reach of several known error-correction protocolsComment: 4+ pages, 3 figures; v2: Streamlined presentation, final version
published in PRB (Rapid Comm.
True photo-counting statistics of multiple on-off detectors
We derive a closed photo-counting formula, including noise counts and a
finite quantum efficiency, for photon number resolving detectors based on
on-off detectors. It applies to detection schemes such as array detectors and
multiplexing setups. The result renders it possible to compare the
corresponding measured counting statistics with the true photon number
statistics of arbitrary quantum states. The photo-counting formula is applied
to the discrimination of photon numbers of Fock states, squeezed states, and
odd coherent states. It is illustrated for coherent states that our formula is
indispensable for the correct interpretation of quantum effects observed with
such devices.Comment: 7 pages, 4 figure
Operator-Schmidt decompositions and the Fourier transform, with applications to the operator-Schmidt numbers of unitaries
The operator-Schmidt decomposition is useful in quantum information theory
for quantifying the nonlocality of bipartite unitary operations. We construct a
family of unitary operators on C^n tensor C^n whose operator-Schmidt
decompositions are computed using the discrete Fourier transform. As a
corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number
S for every S in {1,...,9}. This corollary was unexpected, since it
contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003)
052301] based on intuition from a striking result in the two-qubit case. By the
results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901
quant-ph/0112124], who also considered the two-qubit case, our result implies
that there are nine equivalence classes of unitaries on C^3 tensor C^3 which
are probabilistically interconvertible by (stochastic) local operations and
classical communication. As another corollary, a prescription is produced for
constructing maximally-entangled operators from biunimodular functions.
Reversing tact, we state a generalized operator-Schmidt decomposition of the
quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 -->
C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by
Nielsen's bound) that the communication cost of the QFT remains maximal when a
net transfer of qudits is permitted. In an appendix, a canonical procedure is
given for removing basis-dependence for results and proofs depending on the
"magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair
of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and
quant-ph/9709029)].Comment: More formal version of my talk at the Simons Conference on Quantum
and Reversible Computation at Stony Brook May 31, 2003. The talk slides and
audio are available at
http://www.physics.sunysb.edu/itp/conf/simons-qcomputation.html. Fixed typos
and minor cosmetic
Distilling entanglement from arbitrary resources
We obtain the general formula for the optimal rate at which singlets can be
distilled from any given noisy and arbitrarily correlated entanglement
resource, by means of local operations and classical communication (LOCC). Our
formula, obtained by employing the quantum information spectrum method, reduces
to that derived by Devetak and Winter, in the special case of an i.i.d.
resource. The proofs rely on a one-shot version of the so-called "hashing
bound," which in turn provides bounds on the one-shot distillable entanglement
under general LOCC.Comment: 24 pages, article class, no figure. v2: references added, published
versio
A Simple Algorithm for Local Conversion of Pure States
We describe an algorithm for converting one bipartite quantum state into
another using only local operations and classical communication, which is much
simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436
(1999)]. Our algorithm uses only a single measurement by one of the parties,
followed by local unitary operations which are permutations in the local
Schmidt bases.Comment: 5 pages, LaTeX, reference adde
Implementation of the three-qubit phase-flip error correction code with superconducting qubits
We investigate the performance of a three qubit error correcting code in the
framework of superconducting qubit implementations. Such a code can recover a
quantum state perfectly in the case of dephasing errors but only in situations
where the dephasing rate is low. Numerical studies in previous work have
however shown that the code does increase the fidelity of the encoded state
even in the presence of high error probability, during both storage and
processing. In this work we give analytical expressions for the fidelity of
such a code. We consider two specific schemes for qubit-qubit interaction
realizable in superconducting systems; one -coupling and one
cavity mediated coupling. With these realizations in mind, and considering
errors during storing as well as processing, we calculate the maximum operation
time allowed in order to still benefit from the code. We show that this limit
can be reached with current technology.Comment: 10 pages, 8 figure
Physical Purification of Quantum States
We introduce the concept of a physical process that purifies a mixed quantum
state, taken from a set of states, and investigate the conditions under which
such a purification map exists. Here, a purification of a mixed quantum state
is a pure state in a higher-dimensional Hilbert space, the reduced density
matrix of which is identical to the original state. We characterize all sets of
mixed quantum states, for which perfect purification is possible. Surprisingly,
some sets of two non-commuting states are among them. Furthermore, we
investigate the possibility of performing an imperfect purification.Comment: 5 pages, 1 figure; published versio
Photon-assisted entanglement creation by minimum-error generalized quantum measurements in the strong coupling regime
We explore possibilities of entangling two distant material qubits with the
help of an optical radiation field in the regime of strong quantum
electrodynamical coupling with almost resonant interaction. For this purpose
the optimum generalized field measurements are determined which are capable of
preparing a two-qubit Bell state by postselection with minimum error. It is
demonstrated that in the strong-coupling regime some of the recently found
limitations of the non-resonant weak-coupling regime can be circumvented
successfully due to characteristic quantum electrodynamical quantum
interference effects. In particular, in the absence of photon loss it is
possible to postselect two-qubit Bell states with fidelities close to unity by
a proper choice of the relevant interaction time. Even in the presence of
photon loss this strong-coupling regime offers interesting perspectives for
creating spatially well-separated Bell pairs with high fidelities, high success
probabilities, and high repetition rates which are relevant for future
realizations of quantum repeaters.Comment: 14 pages, 12 figure
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