61,211 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 $k$ such that it suffices to consider catalysts of
dimension $k$ 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

### 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

### Conditions for a Class of Entanglement Transformations

Suppose Alice and Bob jointly possess a pure state, |Ïˆã€‰. Using local operations on their respective systems and classical communication it may be possible for Alice and Bob to transform |Ïˆã€‰ into another joint state |Ï†ã€‰. 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

### 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

### Quantum parallelism of the controlled-NOT operation: an experimental criterion for the evaluation of device performance

It is shown that a quantum controlled-NOT gate simultaneously performs the
logical functions of three distinct conditional local operations. Each of these
local operations can be verified by measuring a corresponding truth table of
four local inputs and four local outputs. The quantum parallelism of the gate
can then be observed directly in a set of three simple experimental tests, each
of which has a clear intuitive interpretation in terms of classical logical
operations. Specifically, quantum parallelism is achieved if the average
fidelity of the three classical operations exceeds 2/3. It is thus possible to
evaluate the essential quantum parallelism of an experimental controlled-NOT
gate by testing only three characteristic classical operations performed by the
gate.Comment: 6 pages, no figures, added references and discussio

### Toward a more economical cluster state quantum computation

We assess the effects of an intrinsic model for imperfections in cluster
states by introducing {\it noisy cluster states} and characterizing their role
in the one-way model for quantum computation. The action of individual
dephasing channels on cluster qubits is also studied. We show that the effect
of non-idealities is limited by using small clusters, which requires compact
schemes for computation. In light of this, we address an experimentally
realizable four-qubit linear cluster which simulates a controlled-{\sf NOT}
({\sf CNOT}).Comment: 4 pages, 2 figures, RevTeX4; proposal for experimental setup include

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