835 research outputs found

    Linearly-independent quantum states can be cloned

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    A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $=∣Ψ1>,∣Ψ2>,...,∣Ψn>\$={ | \Psi _1> ,| \Psi_2> ,... ,| \Psi _n> } , whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states ∣Ψ1>,∣Ψ2>,...| \Psi_1>, | \Psi_2>,... and ∣Ψn>| \Psi_n> are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states ∣Ψ1>,∣Ψ2>,...| \Psi_1>, | \Psi _2>, ... and ∣Ψn>| \Psi_n> are linearly-independent, they do can be cloned by a unitary-reduction process.Comment: 9 pages, no figures, Late

    Reply to the comment "quant-ph/9710002"

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    In the comment, Zanardi and Rasetti argue that several claims in our recent letter (Phys. Rev. Lett. 79, 1953, 1997) are questionable. The reply shows these claims remain true.Comment: 2 pages, Late

    Fault Tolerant Quantum Random Number Generator Certified by Majorana Fermions

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    Braiding of Majorana fermions gives accurate topological quantum operations that are intrinsically robust to noise and imperfection, providing a natural method to realize fault-tolerant quantum information processing. Unfortunately, it is known that braiding of Majorana fermions is not sufficient for implementation of universal quantum computation. Here we show that topological manipulation of Majorana fermions provides the full set of operations required to generate random numbers by way of quantum mechanics and to certify its genuine randomness through violation of a multipartite Bell inequality. The result opens a new perspective to apply Majorana fermions for robust generation of certified random numbers, which has important applications in cryptography and other related areas.Comment: 4pages of the main text+5 pages of supplementary informatio

    Decoherence of quantum registers

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    We consider decoherence of quantum registers, which consist of the qubits sited approximately periodically in space. The sites of the qubits are permitted to have a small random variance. We derive the explicit conditions under which the qubits can be assumed decohering independently. In other circumstances, the qubits are decohered cooperatively. We describe two kinds of collective decoherence. In each case, a scheme is proposed for reducing the collective decoherence. The schemes operate by encoding the input states of the qubits into some ''subdecoherent'' states.Comment: 12 pages, no figures, Late

    Certification of Boson Sampling Devices with Coarse-Grained Measurements

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    A boson sampling device could efficiently sample from the output probability distribution of noninteracting bosons undergoing many-body interference. This problem is not only classically intractable, but its solution is also believed to be classically unverifiable. Hence, a major difficulty in experiment is to ensure a boson sampling device performs correctly. We present an experimental friendly scheme to extract useful and robust information from the quantum boson samplers based on coarse-grained measurements. The procedure can be applied to certify the equivalence of boson sampling devices while ruling out alternative fraudulent devices. We perform numerical simulations to demonstrate the feasibility of the method and consider the effects of realistic noise. Our approach is expected to be generally applicable to other many-body certification tasks beyond the boson sampling problem.Comment: 8 pages including Supplemental Materials, 7 figures, 3 table

    Two non-orthogonal states can be cloned by a unitary-reduction process

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    We show that, there are physical means for cloning two non-orthogonal pure states which are secretly chosen from a certain set % \$={ | \Psi_0 > , | \Psi_1 > }. The states are cloned through a unitary evolution together with a measurement. The cloning efficiency can not attain 100%. With some negative measurement results, the cloning fails.Comment: 9 pages, no figures, Late

    Reducing spatially correlated noise and decoherence with quantum error correcting codes

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    It is shown that the noise process in quantum computation can be described by spatially correlated decoherence and dissipation. We demonstrate that the conventional quantum error correcting codes correcting for single-qubit errors are applicable for reducing spatially correlated noise.Comment: 8 pages, late

    Pulse controlled noise suppressed quantum computation

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    To make arbitrarily accurate quantum computation possible, practical realization of quantum computers will require suppressing noise in quantum memory and gate operations to make it below a threshold value. A scheme based on realistic quantum computer models is described for suppressing noise in quantum computation without the cost of stringent quantum computing resources.Comment: 12 pages, late

    Cooperative loss and decoherence in quantum computation and commuication

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    Cooperative effects in the loss (the amplitude damping) and decoherence (the phase damping) of the qubits (two-state quantum systems) due to the inevitable coupling to the same environment are investigated. It is found that the qubits undergo the dissipation coherently in this case. In particular, for a special kind of input states (called the coherence-preserving states), whose form depends on the type of the coupling, loss and decoherence in quantum memory are much reduced. Based on this phenomenon, a scheme by encoding the general input states of the qubits into the corresponding coherence-preserving states is proposed for reducing the cooperative loss and decoherence in quantum computation or communication.Comment: 10 pages, no figures, Late

    Quantum Supremacy for Simulating A Translation-Invariant Ising Spin Model

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    We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.Comment: Phys. Rev. Lett.(2017, in press), "one-instance" is replaced by "single-instance-hardness", references added, "Simulation with variation Distance Errors" in Supplemental Material is rewritten in a clearer wa
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