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Coherent information
About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.
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TL;DR: In this paper, an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigating its fundamental properties is proposed. But it is not a measure of quantum randomness, and it cannot be used to measure quantum correlations.
Abstract: The uncertainty of a mixed state has two quite different origins: classical mixing and quantum randomness. While the classical aspect (mixedness) is significantly quantified by the von Neumann entropy, it seems that we still do not have a well accepted measure of quantum uncertainty. In terms of the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurements, we will propose an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigate its fundamental properties. We illustrate how it arises naturally from a naive hidden-variable approach to entanglement and how it exhibits a simple relation to the notion of negativity, which is an entanglement monotone introduced quite recently. We further show that it has a dramatic nonextensive feature resembling the probability law relating operations of two events. This measure of quantum uncertainty provides an alternative quantity complementary to the von Neumann entropy for studying mixedness and quantum correlations.
72 citations
TL;DR: An alternative representation of quantum Fisher information for unitary parametrization processes, which can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative is discussed.
Abstract: Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator . Utilizing this representation, quantum Fisher information is only determined by and the initial state. Furthermore, can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of . For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
72 citations
TL;DR: In this article, an experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantum states based on the conditional entropy of the state with a Gaussian reference.
Abstract: Non-Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantum states based on the conditional entropy of the state with a Gaussian reference. Here we adopt such a criterion to characterize an important class of nonclassical states: single-photon-added coherent states. Our studies demonstrate the reliability and sensitivity of this measure and use it to quantify how detrimental is the role of experimental imperfections in our implementation.
72 citations
TL;DR: In this paper, it is shown that the difference of relative entropies between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy.
Abstract: The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative entropy. It is known that this inequality is only tight when there is a recovery map that exactly reverses the effects of the quantum channel on both states. In this paper, we strengthen this inequality by showing that the difference of relative entropies is bounded below by the measured relative entropy between the first state and a recovered state from its processed version. The recovery map is a convex combination of rotated Petz recovery maps and perfectly reverses the quantum channel on the second state. As a special case, we reproduce recent lower bounds on the conditional mutual information, such as the one proved by Fawzi and Renner. Our proof only relies on the elementary properties of pinching maps and the operator logarithm.
71 citations
TL;DR: This work extends the analysis of Macchiavello and Palma to the case of a non-Pauli channel-the amplitude damping channel, and obtains a result similar to that obtained, that is, under certain conditions on the degree of channel memory, the use of entangled input signals may enhance the information transmission compared to theUse of product input signals.
Abstract: We analyze the problem of sending classical information through qubit channels where successive uses of the channel are correlated. This work extends the analysis of Macchiavello and Palma to the case of a non-Pauli channel---the amplitude damping channel. Using the channel description outlined by Daffer et al., we derive the correlated amplitude damping channel. We obtain a result similar to that obtained by Macchiavello and Palma, that is, under certain conditions on the degree of channel memory, the use of entangled input signals may enhance the information transmission compared to the use of product input signals.
71 citations