65,794 research outputs found

    The trumping relation and the structure of the bipartite entangled states

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    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 kk such that it suffices to consider catalysts of dimension kk 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

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    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

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    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

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    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

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    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

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    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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