Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.

Information criteria for efficient quantum state estimation

Abstract: Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state, or (iii) only the permutationally invariant part of the density matrix is determined. We add one more method in that same spirit: We allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in the above-mentioned cases, but is based on well-established statistical methods that go under the name of ``information criteria.'' We exploit here, in particular, the Akaike information criterion. We illustrate the method by simulating experiments on (noisy) Dicke states.

Maximum Fisher information in mixed state quantum systems

Abstract: We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of classical Fisher information, which has been found to constitute an upper bound for classical information itself [Braunstein and Caves (1994) Phys. Rev. Lett. 72 3439-3443]. It has then become of relevant interest among statisticians, who investigated the relations between classical and quantum information and derived a condition for equality in the particular case of two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys. A 33 4481-4490]. In this paper we show that this condition holds even in the more general setting of two-dimensional mixed state systems. We also derive the expression of the maximum Fisher information achievable and its relation with that attainable in pure states.

Quantum entanglement and Kaniadakis entropy

Abstract: A first use of Kaniadakis entropy in the context of quantum information is presented. First we show that (as all smooth and concave trace-form entropies) it exhibits some properties allowing it to be a possible candidate for a generalized quantum information theory. We then use it to determine the degree of entanglement. The influence of the parameter κ, that underpins Kaniadakis entropy, on the mutual information measure is then highlighted. It is shown that Kaniadakis entropy reduces the mutual information, which is always smaller than its usual von Neumann counterpart. Our results may contribute to the ongoing investigation involving generalized entropies in the context of quantum information.

Quantum States: Discrimination and Classical Information Transmission.A Review of Experimental Progress

Abstract: The purpose of this chapter is to review the experimental achievements made to date in two closely related areas of quantum information science. These are quantum state discrimination and classical information transmission using quantum states. In all experiments, the states were realised as quantum states of light. We begin by describing experimental implementations of two optimum discrimination strategies for a pair of nonorthogonal states. These are minimum error state discrimination and optimum unambiguous state discrimination. We then consider minimum error discrimination among certain, highly symmetrical sets of three and four states. The measurements involved were closely related to those required to attain the accessible information for such states. These measurements were also implemented. Subsequent accessible information experiments for up to seven quantum states are then described. The final experiment we discuss is an implementation of a novel, non-classical effect in quantum communications known as classical capacity superadditivity.

Information Rates Achievable with Algebraic Codes on Quantum Discrete Memoryless Channels

Abstract: The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, this work's bound is actually the highest possible rate at which symplectic stabilizer codes work reliably.