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We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a receiver who has no knowledge of which MUB was chosen by the sender. These upper bounds imply a complementarity of information encoded via different MUBs and ultimately ensure the security in quantum key distribution protocols.
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We demonstrate that the concept of information offers a more complete description of complementarity than the traditional approach based on observables. We present the first experimental test of information complementarity for two-qubit pure states, achieving close agreement with theory; We also explore the distribution of information in a comprehensive range of mixed states. Our results highlight the strange and subtle properties of even the simplest quantum systems: for example, entanglement can be increased by reducing correlations between two subsystems.
With the progress of increasingly precise measurements on the neutrino mixing angles, phenomenological relations such as quark-lepton complementarity (QLC) among mixing angles of quarks and leptons and self-complementarity (SC) among lepton mixing angles have been observed. Using the latest global fit results of the quark and lepton mixing angles in the standard Chau-Keung scheme, we calculate the mixing angles and CP-violating phases in the other eight different schemes. We check the dependence of these mixing angles on the CP-violating phases in different phase schemes. The dependence of QLC and SC relations on the CP phase in the other eight schemes is recognized and then analyzed, suggesting that measurements on CP-violating phases of the lepton sector are crucial to the explicit forms of QLC and SC in different schemes.
Uncertainty relations and complementarity relations are core issues in quantum mechanics and quantum information theory. By use of the generalized Wigner-Yanase-Dyson (GWYD) skew information, we derive several uncertainty and complementarity relations with respect to mutually unbiased measurements (MUMs), and general symmetric informationally complete positive operator valued measurements (SIC-POVMs), respectively. Our results include some existing ones as particular cases. We also exemplify our results by providing a detailed example.
We derive complementarity relations for arbitrary quantum states of multiparty systems, of arbitrary number of parties and dimensions, between the purity of a part of the system and several correlation quantities, including entanglement and other quantum correlations as well as classical and total correlations, of that part with the remainder of the system. We subsequently use such a complementarity relation, between purity and quantum mutual information in the tripartite scenario, to provide a bound on the secret key rate for individual attacks on a quantum key distribution protocol.
We develop an information theoretic interpretation of the number-phase complementarity in atomic systems, where phase is treated as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as an upper bound on a sum of knowledge of these two observables for the case of two-level systems. A tighter bound characterizing the uncertainty relation is obtained numerically in terms of a weighted knowledge sum involving these variables. We point out that complementarity in these systems departs from mutual unbiasededness in two signalificant ways: first, the maximum knowledge of a POVM variable is less than log(dimension) bits; second, surprisingly, for higher dimensional systems, the unbiasedness may not be mutual but unidirectional in that phase remains unbiased with respect to number states, but not vice versa. Finally, we study the effect of non-dissipative and dissipative noise on these complementary variables for a single-qubit system.
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