arXiv subjects

Chi-Sheng Niu

Publications and source records attributed to Chi-Sheng Niu.

5 recordsLinked to original sources

arXiv1999

Two qubit copying machine for economical quantum eavesdropping

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.

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arXiv1998

Optimal Copying of One Quantum Bit

A quantum copying machine producing two (in general non-identical) copies of an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied using a quality measure based on distinguishability of states, rather than fidelity. The problem of producing optimal copies is investigated with the help of a Bloch sphere representation, and shown to have a well-defined solution, including cases in which the two copies have unequal quality, or the quality depends upon the input state (is ``anisotropic'' in Bloch sphere language), or both. A simple quantum circuit yields the optimal copying machine. With a suitable choice of parameters it becomes an optimal eavesdropping machine for some versions of quantum cryptography, or reproduces the Buzek and Hillery result for isotropic copies.

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arXiv1997

Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit

It is shown that the optimum strategy of the eavesdropper, as described in the preceding paper, can be expressed in terms of a quantum circuit in a way which makes it obvious why certain parameters take on particular values, and why obtaining information in one basis gives rise to noise in the conjugate basis.

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arXiv1997

Optimal Eavesdropping in Quantum Cryptography. I

We consider the Bennett-Brassard cryptographic scheme, which uses two conjugate quantum bases. An eavesdropper who attempts to obtain information on qubits sent in one of the bases causes a disturbance to qubits sent in the other basis. We derive an upper bound to the accessible information in one basis, for a given error rate in the conjugate basis. Independently fixing the error rate in the conjugate bases, we show that both bounds can be attained simultaneously by an optimal eavesdropping probe, consisting of two qubits. The qubits' interaction and their subsequent measurement are described explicitly. These results are combined to give an expression for the optimal information an eavesdropper can obtain for a given average disturbance when her interaction and measurements are performed signal by signal. Finally, the relation between quantum cryptography and violations of Bell's inequalities is discussed.

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arXiv1995

Semiclassical Fourier Transform for Quantum Computation

Shor's algorithms for factorization and discrete logarithms on a quantum computer employ Fourier transforms preceding a final measurement. It is shown that such a Fourier transform can be carried out in a semi-classical way in which a ``classical'' (macroscopic) signal resulting from the measurement of one bit (embodied in a two-state quantum system) is employed to determine the type of measurement carried out on the next bit, and so forth. In this way the two-bit gates in the Fourier transform can all be replaced by a smaller number of one-bit gates controlled by classical signals. Success in simplifying the Fourier transform suggests that it may be worthwhile looking for other ways of using semi-classical methods in quantum computing.

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