Publications (8)10.88 Total impact

Article: Theoretical constraints on implementations of arbitrary singlequbit gates under conservation laws
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ABSTRACT: We investigate theoretical limits on the precision of arbitrary singlequbit operations under conservation laws. When a singlequbit gate is implemented by the interaction between the qubit and the control system, the conservation laws on the total system may induce an inevitable imperfection on the qubit gate. We quantify this imperfection of singlequbit gates, employing the gate trace distance between the desired unitary map and a trace preserving completely positive map implemented with the interaction with the control qubits. We present the bounds of the gate accuracy for arbitrary qubit gates under conservation laws of additive quantities.  [Show abstract] [Hide abstract]
ABSTRACT: Recent investigations show that conservation laws limit the accuracy of gate operations in quantum computing. The inevitable error under the angular momentum conservation law has been evaluated so far for the CNOT, Hadamard, and NOT gates for spin 1/2 qubits, while the SWAP gate has no constraint. Here, we extend the above results to general singlequbit gates. We obtain an upper bound of the gate fidelity of arbitrary singlequbit gates implemented under arbitrary conservation laws, determined by the geometry of the conservation law and the gate operation on the Bloch sphere as well as the size of the ancilla.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the achievability problem of the CramérRao bound for multiparameter estimations. In general, it is not achievable due to the noncommutativity of optimal measurements for the corresponding parameters. However, we show that, under certain conditions, it can always be attained up to the leading order in the parameters as long as D⩽N−1, where D and N denote the number of parameters and the dimension of the system, respectively. After proving that, we discuss the achievability in the context of channel estimation for a general channel called a lownoise channel, which is very useful for investigating parameter estimation in the leading order. This allows us to find an ancillaassisted enhancement effect: if entangled input states with an ancilla system are utilized for the channel estimation together with collective measurements on those output states, the bound becomes achievable for D⩽N2−1. 
Article: Quantum precision limits for any implementation of single qubit gates under conservation laws
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ABSTRACT: A quantum gate is implemented by control interactions between qubits and their ancilla system. It has been shown that the control interactions have possibilities to induce the dynamical decoherence on the qubits if an additive conservation law is assumed in the interactions and the ancilla system is finite. This decoherece put the precision limit on the gate, which cannot be removed from the qubit by optimizing the interaction and the initialization of the ancilla system. In this paper, we give the outline of investigating the precision limit which is formulated by the lower bound of the gate infidelity, one minus the squared fidelity, for an arbitrary selfadjoint gate on a single qubit. We show rigorous lower bounds in terms of the variance of the conserved quantity and a simple geometrical relation between the conservation law to be assumed and the gates to be implemented. We also comment on another approach to provide the precision limit for an arbitrary single qubit gate under a conservation law.  [Show abstract] [Hide abstract]
ABSTRACT: In recent investigations, it has been found that conservation laws generally lead to precision limits on quantum computing. Lower bounds of the error probability have been obtained for various logic operations from the commutation relation between the noise operator and the conserved quantity or from the recently developed universal uncertainty principle for the noisedisturbance tradeoff in general measurements. However, the problem of obtaining the precision limit to realizing the quantum NOT gate has eluded a solution from these approaches. Here, we develop a new method for this problem based on analyzing the trace distance between the output state from the realization under consideration and the one from the ideal gate. Using the mathematical apparatus of orthogonal polynomials, we obtain a general lower bound on the error probability for the realization of the quantum NOT gate in terms of the number of qubits in the control system under the conservation of the total angular momentum of the computational qubit plus the the control system along the direction used to encode the computational basis. The lower bound turns out to be more stringent than one might expect from previous results. The new method is expected to lead to more accurate estimates for physical realizations of various types of quantum computations under conservation laws, and to contribute to related problems such as the accuracy of programmable quantum processors. Comment: 38 pages, 2 figures 
Conference Paper: LowNoise Channel Estimation
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ABSTRACT: The notion of lownoise channels was recently proposed and analyzed in detail in order to describe noiseprocesses driven by environment [M. Hotta, T. Karasawa and M. Ozawa, Phys. Rev. A72, 052334 (2005)]. An estimation theory of lownoise parameters of channels has also been developed. In this report, we address the lownoise parameter estimation problem for the $N$body extension of lownoise channels. We perturbatively calculate the Fisher information of the output states in order to evaluate the lowerbound of the meansquare error of the parameter estimation. We show that the maximum of the Fisher information over all input states can be attained by a factorized input state in the leading order of the lownoise parameter. Thus, to achieve optimal estimation, it is not necessary for there to be entanglement of the $N$ subsystems, as long as the true lownoise parameter is sufficiently small. Comment: 10 pages, 1 figure  [Show abstract] [Hide abstract]
ABSTRACT: In order to make a unified treatment for estimation problems of a very small noise or a very weak signal in a quantum process, we introduce the notion of a lownoise quantum channel with one noise parameter. It is known in several examples that prior entanglement together with nonlocal output measurement improves the performance of the channel estimation. In this paper, we study this ``ancillaassisted enhancement'' for estimation of the noise parameter in a general lownoise channel. For channels on two level systems we prove that the enhancement factor, the ratio of the Fisher information of the ancillaassisted estimation to that of the original one, is always upper bounded by 3/2. Some conditions for the attainability are also given with illustrative examples. Comment: 12 pages, Revtex
Publication Stats
44  Citations  
10.88  Total Impact Points  
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Institutions

2008

National Institute of Informatics
Edo, Tōkyō, Japan


20052007

Tohoku University
 Graduate School of Information Sciences
Sendai, Kagoshimaken, Japan
