78,094 research outputs found
Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2
Operator-Schmidt decompositions of the quantum Fourier transform on C^N1
tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be
completely degenerate when N1 is a factor of N2 and when N1>N2. The first known
special case, N1=N2=2^n, was computed by Nielsen in his study of the
communication cost of computing the quantum Fourier transform of a collection
of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,
University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More
generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in
their study of strength measures of quantum operations. [M.A. Nielsen et. al,
(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the
Schmidt decompositions presented here, it follows that in all cases the
communication cost of exact computation of the quantum Fourier transform is
maximal.Comment: 9 pages, LaTeX 2e; No changes in results. References and
acknowledgments added. Changes in presentation added to satisfy referees:
expanded introduction, inclusion of ommitted algebraic steps in the appendix,
addition of clarifying footnote
The trumping relation and the structure of the bipartite entangled states
The majorization relation has been shown to be useful in classifying which
transformations of jointly held quantum states are possible using local
operations and classical communication. In some cases, a direct transformation
between two states is not possible, but it becomes possible in the presence of
another state (known as a catalyst); this situation is described mathematically
by the trumping relation, an extension of majorization. The structure of the
trumping relation is not nearly as well understood as that of majorization. We
give an introduction to this subject and derive some new results. Most notably,
we show that the dimension of the required catalyst is in general unbounded;
there is no integer such that it suffices to consider catalysts of
dimension or less in determining which states can be catalyzed into a given
state. We also show that almost all bipartite entangled states are potentially
useful as catalysts.Comment: 7 pages, RevTe
Quantum states far from the energy eigenstates of any local Hamiltonian
What quantum states are possible energy eigenstates of a many-body
Hamiltonian? Suppose the Hamiltonian is non-trivial, i.e., not a multiple of
the identity, and L-local, in the sense of containing interaction terms
involving at most L bodies, for some fixed L. We construct quantum states \psi
which are ``far away'' from all the eigenstates E of any non-trivial L-local
Hamiltonian, in the sense that |\psi-E| is greater than some constant lower
bound, independent of the form of the Hamiltonian.Comment: 4 page
Continuity bounds for entanglement
This note quantifies the continuity properties of entanglement: how much does
entanglement vary if we change the entangled quantum state just a little? This
question is studied for the pure state entanglement of a bipartite system and
for the entanglement of formation of a bipartite system in a mixed state.Comment: 5 pages, submitted to Physical Review A Brief Reports. Minor typo in
equation (25) corrected in resubmissio
A simple formula for the average gate fidelity of a quantum dynamical operation
This note presents a simple formula for the average fidelity between a
unitary quantum gate and a general quantum operation on a qudit, generalizing
the formula for qubits found by Bowdrey et al [Phys. Lett. A 294, 258 (2002)].
This formula may be useful for experimental determination of average gate
fidelity. We also give a simplified proof of a formula due to Horodecki et al
[Phys. Rev. A 60, 1888 (1999)], connecting average gate fidelity to
entanglement fidelity.Comment: 3 pages, references and discussion of prior work update
Conditions for a Class of Entanglement Transformations
Suppose Alice and Bob jointly possess a pure state, |ψ〉. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |ψ〉 into another joint state |φ〉. This Letter gives necessary and sufficient conditions for this process of entanglement transformation to be possible. These conditions reveal a partial ordering on the entangled states and connect quantum entanglement to the algebraic theory of majorization. As a consequence, we find that there exist essentially different types of entanglement for bipartite quantum systems
Universal quantum computation using only projective measurement, quantum memory, and preparation of the 0 state
What resources are universal for quantum computation? In the standard model,
a quantum computer consists of a sequence of unitary gates acting coherently on
the qubits making up the computer. This paper shows that a very different model
involving only projective measurements, quantum memory, and the ability to
prepare the |0> state is also universal for quantum computation. In particular,
no coherent unitary dynamics are involved in the computation.Comment: 4 page
Optical quantum computation using cluster states
We propose an approach to optical quantum computation in which a
deterministic entangling quantum gate may be performed using, on average, a few
hundred coherently interacting optical elements (beamsplitters, phase shifters,
single photon sources, and photodetectors with feedforward). This scheme
combines ideas from the optical quantum computing proposal of Knill, Laflamme
and Milburn [Nature 409 (6816), 46 (2001)], and the abstract cluster-state
model of quantum computation proposed by Raussendorf and Briegel [Phys. Rev.
Lett. 86, 5188 (2001)].Comment: 4 page
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