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Register a new userOn Reduced Time Evolution for Initially Correlated Pure States
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A new method to deal with reduced dynamics of open systems by means of the Schrodinger equation is presented. It allows one to consider the reduced time evolution for correlated and uncorrelated initial conditions.
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We use the Koashi-Imoto decomposition of the degrees of freedom of joint system-environment initial states to investigate the reduced dynamics. We show that a subset of joint system-environment initial states guarantees completely positive reduced dynamics, if and only if the system privately owns all quantum degrees of freedom and can locally access the classical degrees of freedom, without disturbing all joint initial states in the given subset. Furthermore, we show that the quantum mutual information for such kinds of states must be independent of the quantum degrees of freedom.
The geometric measure of entanglement is the distance or angle between an entangled target state and the nearest unentangled state. Often one considers the geometric measure of entanglement for highly symmetric entangled states because it simplifies the calculations and allows for analytic solutions. Although some symmetry is required in order to deal with large numbers of qubits, we are able to loosen significantly the restrictions on the highly symmetric states considered previously, and consider several generalizations of the coefficients of both target and unentangled states. This allows us to compute the geometric entanglement measure for larger and more relevant classes of states.
We provide a unified graphical calculus for all Gaussian pure states, including graph transformation rules for all local and semi-local Gaussian unitary operations, as well as local quadrature measurements. We then use this graphical calculus to analyze continuous-variable (CV) cluster states, the essential resource for one-way quantum computing with CV systems. Current graphical approaches to CV cluster states are only valid in the unphysical limit of infinite squeezing, and the associated graph transformation rules only apply when the initial and final states are of this form. Our formalism applies to all Gaussian pure states and subsumes these rules in a natural way. In addition, the term CV graph state currently has several inequivalent definitions in use. Using this formalism we provide a single unifying definition that encompasses all of them. We provide many examples of how the formalism may be used in the context of CV cluster states: defining the closest CV cluster state to a given Gaussian pure state and quantifying the error in the approximation due to finite squeezing; analyzing the optimality of certain methods of generating CV cluster states; drawing connections between this new graphical formalism and bosonic Hamiltonians with Gaussian ground states, including those useful for CV one-way quantum computing; and deriving a graphical measure of bipartite entanglement for certain classes of CV cluster states. We mention other possible applications of this formalism and conclude with a brief note on fault tolerance in CV one-way quantum computing.
Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a rigorous mathematical justification, since existing approximations to thermal states and time evolution demand a bond dimension growing with system size. To address this problem, we construct PEPOs that approximate, for all local observables, $i)$ their thermal expectation values and $ii)$ their Heisenberg time evolution. The bond dimension required does not depend on system size, but only on the temperature or time. We also show how these can be used to approximate thermal correlation functions and expectation values in quantum quenches.
Entanglement swapping has played an important role in quantum information processing, and become one of the necessary core technologies in the future quantum network. In this paper, we study entanglement swapping for multi-particle pure states and maximally entangled states in qudit systems. We generalize the entanglement swapping of two pure states from the case where each quantum system contains two particles to the case of containing any number of particles, and consider the entanglement swapping between any number of systems. We also generalize the entanglement swapping chain of bipartite pure states to the one of multi-particle pure states. In addition, we consider the entanglement swapping chains for maximally entangled states.
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