Closed Timelike Curves are relativistically valid objects allowing time travel to the past. Treating them as computational objects opens the door to a wide range of results which cannot be achieved using non relativistic quantum mechanics. Recently, research in classical and quantum computation has focused on effectively harnessing the power of these curves. In particular, Brun (Found. Phys. Lett., 2003) has shown that CTCs can be utilized to efficiently solve problems like factoring and QSAT (Quantified Satisfiability Problem). In this paper, we find a flaw in Brun's algorithm and propose a modified algorithm to circumvent the flaw.
Closed Timelike Curves (CTCs) are intriguing relativistic objects that allow for time travel to the past and can be used as computational resources. In Deutschian Closed Timelike Curves (D-CTCs), due to the monogamy of entanglement, non-local correlations between entangled states are destroyed. In contrast, for Postselected Closed Timelike Curves (P-CTCs), a second variant of CTCs, the non-local correlations are preserved. P-CTCs can be harnessed for the signaling of non-orthogonal states to the past without a disruption of causality. In this paper, we take up signaling to the past and show a method of sending four non-orthogonal states to the past using P-CTCs. After constructing our signaling protocol, we study the causality violations that our protocol results in and put forward two consistency relations to prevent them.
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