Abstract
We present a closest separable state to cluster states, which in turn allows us to calculate the entanglement scaling using relative entropy of entanglement. We reproduce known results for pure cluster states and show how our method can be used in quantifying entanglement in noisy cluster states. Operational meaning is given to our method, which clearly demonstrates how these closest separable states can be constructed from two-qubit clusters in the case of pure states. We also discuss the issue of finding the critical temperature at which the cluster state becomes only classically correlated and the importance of this temperature to our method.
Highlights
Entanglement plays an important role in modern physics and is the subject of intense research for both its implications in our fundamental understanding of nature [1] and its practical usefulness in quantum information processing [2, 3]
We have demonstrated a systematic way of constructing a closest separable state to N -qubit cluster states
Our method reproduces known results for pure states and allows us to quantify entanglement for mixed cluster states
Summary
Entanglement plays an important role in modern physics and is the subject of intense research for both its implications in our fundamental understanding of nature [1] and its practical usefulness in quantum information processing [2, 3]. Measurement-based quantum computation (or one-way quantum computation) differs from the circuit model by using an initially prepared highly entangled resource state. This makes it easier to identify the role of entanglement in the information processing compared to the traditional circuit model. It has been shown both theoretically and experimentally in [9] that the quantum computational power of cluster states can be extended by replacing some projective measurements with generalized quantum measurements. Due to its clear role as a resource in one-way quantum computation, it is highly desirable to know the entanglement properties of cluster states. We show how bound entanglement complicates the procedure of finding the closest separable state for noisy cluster states
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