Tokishiro Karasawa

Publications (4)0 Total impact

• Source

  Available from: J. Gea-Banacloche

  Article: Gate fidelity of arbitrary single-qubit gates constrained by conservation laws

  Tokishiro Karasawa, Julio Gea-Banacloche, Masanao Ozawa
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  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 single-qubit gates. We obtain an upper bound of the gate fidelity of arbitrary single-qubit 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.
  10/2008;
• Source

  Available from: ArXiv

  Article: Channel Estimation Theory of Low-Noise Multiple Parameters:Attainablity Problem of the Cram{\'e}r-Rao Bounds

  Masahiro Hotta, Tokishiro Karasawa
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  ABSTRACT: For decoherence processes induced by weak interactions with the environment, a general quantum channel with one noise parameter has been formulated. This channel is called low-noise channel and very useful for investigating the parameter estimation in the leading order. In this paper, we formulate the low-noise channel with multiple unknown parameters in order to address the simultaneous achievability of the Cram{\'e}r-Rao bound for the parameters estimation. In general, the simultaneous achievement of the Cram{\'e}r-Rao bound for multi-parameter estimations suffers from non-commutativity of optimal measurements for respective parameters. However, with certain exceptions, we show that the Cram{\'e}r-Rao bound for output states of dissipative low-noise channels can be always attained in the first order of the parameters as long as D \leq N-1, where D and N denote the number of the parameters and the dimension of the system, respectively. This condition is replaced by D \leq N^{2}-1 if it is allowed to set the entanglement with ancilla systems in its input state and to perform the non-local measurement on the composite system. Comment: 22 pages
  03/2008;
• Source

  Available from: ArXiv

  Article: Conservation-Law-Induced Quantum Limits for Physical Realizations of the Quantum NOT Gate

  Tokishiro Karasawa, Masanao Ozawa
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  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 noise-disturbance trade-off 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
  05/2007;
• Source

  Available from: arxiv.org

  Article: Ancilla-Assisted Enhancement of Channel Estimation for Low-Noise Parameters

  Masahiro Hotta, Tokishiro Karasawa, Masanao Ozawa
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  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 low-noise 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 ``ancilla-assisted enhancement'' for estimation of the noise parameter in a general low-noise channel. For channels on two level systems we prove that the enhancement factor, the ratio of the Fisher information of the ancilla-assisted 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
  07/2005;