Universal entanglement concentration

We propose a new protocol of \textit{universal} entanglement concentration, which converts many copies of an \textit{unknown} pure state to an \textit{% exact} maximally entangled state. The yield of the protocol, which is outputted as a classical information, is probabilistic, and achives the entropy rate with high probability, just as non-universal entanglement concentration protocols do. Our protocol is optimal among all similar protocols in terms of wide varieties of measures either up to higher orders or non-asymptotically, depending on the choice of the measure. The key of the proof of optimality is the following fact, which is a consequence of the symmetry-based construction of the protocol: For any invariant measures, optimal protocols are found out in modifications of the protocol only in its classical output, or the claim on the product. We also observe that the classical part of the output of the protocol gives a natural estimate of the entropy of entanglement, and prove that that estimate achieves the better asymptotic performance than any other (potentially global) measurements.Comment: Revised a lot, especially proofs, though no change in theorems, lemmas itself. Very long, but essential part is from Sec.I to Sec IV-C. Some of the appendces are almost independent of the main bod

Generalized Jarzynski Equality under Nonequilibrium Feedback Control

The Jarzynski equality is generalized to situations in which nonequilibrium systems are subject to a feedback control. The new terms that arise as a consequence of the feedback describe the mutual information content obtained by measurement and the efficacy of the feedback control. Our results lead to a generalized fluctuation-dissipation theorem that reflects the readout information, and can be experimentally tested using small thermodynamic systems. We illustrate our general results by an introducing "information ratchet," which can transport a Brownian particle in one direction and extract a positive work from the particle

Optimal ratio between phase basis and bit basis in QKD

In the original BB84 protocol, the bit basis and the phase basis are used with equal probability. Lo et al (J. of Cryptology, 18, 133-165 (2005)) proposed to modify the ratio between the two bases by increasing the final key generation rate. However, the optimum ratio has not been derived. In this letter, in order to examine this problem, the ratio between the two bases is optimized for exponential constraints given Eve's information distinguishability and the final error probability

Practical Evaluation of Security for Quantum Key Distribution

Many papers proved the security of quantum key distribution (QKD) system, in the asymptotic framework. The degree of the security has not been discussed in the finite coding-length framework, sufficiently. However, to guarantee any implemented QKD system requires, it is needed to evaluate a protocol with a finite coding-length. For this purpose, we derive a tight upper bound of the eavesdropper's information. This bound is better than existing bounds. We also obtain the exponential rate of the eavesdropper's information. Further, we approximate our bound by using the normal distribution.Comment: The manuscript has been modfie

Hermitian conjugate measurement

We propose a new class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional information gain using the Hermitian conjugate of the measurement operator. We illustrate the general scheme by considering a quantum measurement consisting of spin systems with an experimentally feasible interaction and show that the reversing operation simultaneously increases both the fidelity to the original state and the information gain with such a high probability of success that their average values increase simultaneously.Comment: 26 pages, 4 figures; a paragraph is added in the introductio

Uncertainty Relation Revisited from Quantum Estimation Theory

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy Heisenberg's uncertainty relation, find the attainable bound, and provide a strategy to achieve it.Comment: manuscript including 4 pages and 2 figure

Faraday Rotation with Single Nuclear Spin Qubit in a High-Finesse Optical Cavity

When an off-resonant light field is coupled with atomic spins, its polarization can rotate depending on the direction of the spins via a Faraday rotation which has been used for monitoring and controlling the atomic spins. We observed Faraday rotation by an angle of more than 10 degrees for a single 1/2 nuclear spin of 171Yb atom in a high-finesse optical cavity. By employing the coupling between the single nuclear spin and a photon, we have also demonstrated that the spin can be projected or weakly measured through the projection of the transmitted single ancillary photon.Comment: 6 pages, 6 figure

Fluctuation Theorem with Information Exchange: Role of Correlations in Stochastic Thermodynamics

We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to the entropy production. The resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange. Our results apply not only to feedback-controlled processes but also to a much broader class of information exchanges, and provides a unified framework of nonequilibrium thermodynamics of measurement and feedback control.Comment: To appear in PR

The geometric measure of entanglement for a symmetric pure state with positive amplitudes

In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state'. We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.Comment: Similar results have been obtained independently and with different methods by T-C. Wei and S. Severini, see arXiv:0905.0012v