Won-Young Hwang

Quantum key distribution with high loss: toward global secure communication.

We propose a decoy-pulse method to overcome the photon-number-splitting attack for Bennett-Brassard 1984 quantum key distribution protocol in the presence of high loss: A legitimate user intentionally and randomly replaces signal pulses by multiphoton pulses (decoy pulses). Then they check the loss of the decoy pulses. If the loss of the decoy pulses is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate the loss of signal multiphoton pulses based on that of decoy pulses. This estimation can be done with an assumption that the two losses have similar values. We justify that assumption.

Quantum cryptography without public announcement of bases

Abstract We give a simple variation of the basic ideas of the BB84 quantum cryptographic scheme leading to a method of key expansion. A secure random sequence (the bases sequence) determines the encoding bases in a proposed scheme. Against incoherent attacks by Eve, using the bases sequence repeatedly is proven to be safe by quantum mechanical laws.

Shor-Preskill-type security proof for quantum key distribution without public announcement of bases

We give a Shor-Preskill-type security proof to quantum key distribution without public announcement of bases [W.Y. Hwang et al., Phys. Lett. A 244, 489 (1998)]. First, we modify the Lo-Chau protocol once more so that it finally reduces to the quantum key distribution without public announcement of bases. Then we show how we can estimate the error rate in the code bits based on that in the checked bits in the proposed protocol, which is the central point of the proof. We discuss the problem of imperfect sources and that of large deviation in the error rate distributions. We discuss when the bases sequence must be discarded.

Correlated errors in quantum-error corrections

We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubit-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubit-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes that correct single-qubit errors will work in most cases including the collective decoherence.

Minimum-error discrimination of qubit states: Methods, solutions, and properties

We show a geometric formulation for minimum-error discrimination of qubit states that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal a priori probabilities, we provide a systematic way of finding optimal discrimination and the complete solution in a closed form. This generally gives a bound to cases when prior probabilities are unequal. Then it is shown that the guessing probability does not depend on detailed relations among the given states, such as the angles between them, but on a property that can be assigned by the set of given states itself. This also shows how a set of quantum states can be modified such that the guessing probability remains the same. Optimal measurements are also characterized accordingly, and a general method of finding them is provided. DOI: 10.1103/PhysRevA.87.012334

Helstrom theorem from the no-signaling condition

We prove a special case of the Helstrom theorem by using the no-signaling condition in the special theory of relativity that faster-than-light communication is impossible.

Eavesdropper's optimal information in variations of Bennett–Brassard 1984 quantum key distribution in the coherent attacks

Abstract We calculate eavesdroppers optimal information on raw bits in Bennett–Brassard 1984 quantum key distribution (BB84 QKD) and six-state scheme in coherent attacks, using a formula by Lo and Chau (Science 283 (1999) 2050) with single photon assumption. We find that eavesdroppers optimal information in QKD without public announcement of bases (Phys. Lett. A 244 (1998) 489) is the same as that of a corresponding QKD with it in the coherent attack. We observe a sum-rule concerning each partys information.

Explicit solutions for negative-probability measures for all entangled states

Abstract We obtain explicit solutions for probability measures that reproduce quantum mechanical predictions for some spinmeasurement directions for all entangled states. The necessity of negative probability in this case is shown. This constitutes another proof of Gisins theorem that all entangled states are incompatible with any local hidden-variable models (all entangled states can violate Bells inequality). A degree of freedom that remains in the solution is noted.

Efficient schemes for reducing imperfect collective decoherences

We propose schemes that are efficient when each pair of qubits undergoes some imperfect collective decoherence with different baths. In the proposed scheme, each pair of qubits is first encoded in a decoherence-free subspace composed of two qubits. Leakage out of the encoding space generated by the imperfection is reduced by the quantum Zeno effect. Phase errors in the encoded bits generated by the imperfection are reduced by concatenation of the decoherence-free subspace with either a three-qubit quantum error correcting code that corrects only phase errors or a two-qubit quantum error detecting code that detects only phase errors, connected with the quantum Zeno effect again.

Quantum gambling using three nonorthogonal states

We provide a quantum gambling protocol using three (symmetric) nonorthogonal states. The bias of the proposed protocol is less than that of previous ones, making it more practical. We show that the proposed scheme is secure against nonentanglement attacks. The security of the proposed scheme against entanglement attacks is shown heuristically.