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We clarify the controversy over the coherent-state (CS) versus the number-state (NS) pictures in quantum optics. The NS picture is equivalent to the CS picture, as long as the phases $\phi$ in the laser fields are randomly distributed, as M{\o}lmer argues [\pra {\bf 55}, 3195 (1997)]. However, the claim by Rudolph and Sanders [Phys. Rev. Lett. {\bf 87}, 077903 (2001)] has a few gaps. First, they make an assumption that is not necessarily true in the calculation of a density operator involved with a two-mode squeezed state. We show that there exists entanglement in the density operator without defying the assumption that phases are randomly distributed. Moreover, using a concept of picture-invariance, we argue that it is not that criteria for quantum teleportation are not satisfied. We discuss an analogy between the controversy on the CS versus NS pictures to that on the heliocentric versus geocentric pictures., Comment: 4 pages, RevTex

We prove a special case of Helstrom theorem by using no-signaling condition in the special theory of relativity that faster-than-light communication is impossible., Comment: Minor corrections (A reference added, discussion part deleted, typos in equations corrected), 2 pages, RevTex

The Ekert 91 quantum key distribution (QKD) protocol appears to be secure whatever devices legitimate users adopt for the protocol, as long as the devices give a result that violates Bell's inequality. However, this is not the case if they ignore non-detection events because Eve can make use of the detection-loophole, as Larrson showed. We show that even when legitimate users take into account non-detection events Eve can successfully eavesdrop if the QKD system has been appropriately designed by the manufacturer. A loophole utilized here is that of `free-choice' (or `real randomness'). Local QKD devices with pseudo-random sequence generator installed in them can apparently violate Bell's inequality., Comment: English corrected, 3 pages, RevTex

We discuss the `no-clicking' event, which is harmful for legitimate users in Bennett-Brassard 1984 quantum key distribution: We describe an attack where no-clicking events are utilized in the same way as double-clicking events are utilized in the quantum Trojan-pony attack. We discuss how to deal with the no-clicking events. We discuss how to estimate the security of the protocol against the proposed attack by using a formula involved with the fraction of adversarial removals of events., Comment: 4 pages, RevTex

We clarify the argument on the how (nonlocal) degenerate Bell measurement can be replaced by local measurements in the modified Lo-Chau quantum key distribution protocol. Discussing security criterion for users, we describe how eavesdropper's refined information on the final state is not helpful. We argue that current discussions on the equivalence of the Bell and the local measurements are not clear. We show how the problem of equivalence can be resolved using the fact that eavesdropper's refined information is not helpful for her., Comment: Minor corrections, 5 pages, RevTex

We propose a decoy-state 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 multi-photon pulses (decoy-states). Then they check the loss of the decoy-states. If the loss of the decoy-states is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate loss of signal multi-photon pulses based on that of decoy-states. This estimation can be done with an assumption that the two losses have similar values, that we justify., Comment: derivation made more detailed, 4 pages, RevTex

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 non-entanglement attacks. The security of the proposed scheme against entanglement attacks is shown heuristically., Comment: no essential correction, 4 pages, RevTex

We show that the entanglement of cost and entanglement of distillation can be vague when we consider a more general form of entanglement manipulation in which we collectively deal with not only states of our concern but also other states. We introduce the most general entanglement manipulation in which the formation and distillation can be simultaneously performed. We show that in a certain case entanglement manipulations are reversible with respect to the most general entanglement manipulation. This broadens our scope of vision on the irreversibility of entanglement manipulations., Comment: Typos and minor errors corrected, 3 pages, RevTex

We give a Shor-Preskill type security-proof to the 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, that 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., Comment: very minor correction, 5 pages, RevTex

We discuss long code problems in the Bennett-Brassard 1984 (BB84) quantum key distribution protocol and describe how they can be overcome by concatenation of the protocol. Observing that concatenated modified Lo-Chau protocol finally reduces to the concatenated BB84 protocol, we give the unconditional security of the concatenated BB84 protocol., Comment: 4 pages, RevTex

We propose entanglement measures with asymptotic weak-monotonicity. We show that a normalized form of entanglement measures with the asymptotic weak-monotonicity are lower (upper) bound for the entanglement of cost (distillation)., Comment: 3 pages, RevTex

We report that entangled pairs of quantum clocks (non-degenerate quantum bits) can be used as a specialized detector for precisely measuring difference of proper-times that each constituent quantum clock experiences. We describe why the proposed scheme would be more precise in the measurement of proper-time difference than a scheme of two-separate-quantum-clocks. We consider possibilities that the proposed scheme can be used in precision test of the relativity theory., Comment: no correction, 4 pages, RevTex

It has recently been suggested that various entanglement measures for bipartite mixed states do not in general give the same ordering even in the asymptotic cases [S. Virmani and M. B. Plenio, Phys. Lett. A {\bf 268}, 31 (2000)]. That is, for two certain mixed states, the order of the degree of entanglement depends on the measures. Therefore, incomparable pairs of mixed states which cannot be transformed to each other with unit efficiency by any combinations of local quantum operations and classical communications exist. We make an analogy of the relativity of the order of the degree of entanglement to the relativity of temporal orders in the special theory of relativity., Comment: no essential correction, 4 pages, 1 figure, RevTex

We give a (remote) quantum gambling scheme that makes use of the fact that quantum nonorthogonal states cannot be distinguished with certainty. In the proposed scheme, two participants Alice and Bob can be regarded as playing a game of making guesses on identities of quantum states that are in one of two given nonorthogonal states: if Bob makes a correct (an incorrect) guess on the identity of a quantum state that Alice has sent, he wins (loses). It is shown that the proposed scheme is secure against the nonentanglement attack. It can also be shown heuristically that the scheme is secure in the case of the entanglement attack., Comment: no essential correction, 4 pages, RevTex

We calculate eavesdropper's 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 eavesdropper's 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 party's information., Comment: no correction, 7 pages, 1 figure, RevTex

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., Comment: no correction, 3 pages, RevTex

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-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-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 which correct single-qubit-errors will work in most cases including the collective decoherence., Comment: no correction, 3 pages, RevTex