PhysOrg.com) -- For more than 50 years, physicists have been intrigued by the concept of closed time-like curves (CTCs). Because a CTC returns to its starting point, it raises the possibility of traveling backward in time. More recently, physicists have theorized that CTC-assisted computers could enable ideal quantum state discrimination, and even make classical computers (with CTCs) equally as powerful as quantum computers. However, a new study argues that CTCs, if they exist, might actually provide much less computational benefit than previously thought.

A team of scientists consisting of Charles Bennett, Graeme Smith, and John Smolin from IBM, along with Debbie Leung from the University of Waterloo, argues that previous analyses of CTCs have fallen into the so-called "linearity trap," and have been based on physically irrelevant definitions that have led to incorrect conclusions about CTCs. The new study will be published in an upcoming issue of Physical Review Letters.
As the physicists explain, CTCs are difficult to think about because they make quantum evolution nonlinear, whereas standard quantum mechanics systems evolve linearly. (In linear systems, the evolution of a mixture of states is equal to the mixture of the evolutions of individual states; this is not the case in nonlinear systems.) It seems that much of the apparent power of CTCs has come from analyzing the evolution of pure quantum states, and extending these results linearly to find the evolution of mixed states. The physicists call this situation the "linearity trap," which occurs when nonlinear theories are extended linearly. In the case of CTC computations, Bennett and coauthors found that this problem was causing the output to be uncorrelated with the input, which isn't a very useful computation.

"The trouble with the earlier work is that it didn't take into account the physical processes by which the inputs to a computation are selected," Smith told PhysOrg.com. "In a nonlinear theory, the output of a computation depends not only on the input, but also on how it was selected. This is the strange thing about nonlinear theories, and easy to miss."

To overcome these problems, the scientists proposed that the inputs to the system should be selected by an independent referee at the start of the computation, rather than being built deterministically into the structure of the computer. In order to ensure that the proper input is selected, the physicists proposed the "Principle of Universal Inclusion." The principle states that the evolution of a nonlinearly evolving system may depend on parts of the universe with which it does not interact, ensuring that scientists do not ignore the parts of the universe that need to be used to select the inputs. The physicists hope that these criteria will lead to choosing the correct input, and then to generating the correct corresponding output, rather than simply evolving the system linearly based on incorrect inputs.

As the scientists note, one of the motivating factors for their investigation is the previous finding that CTCs can distinguish between two nonorthogonal pure states, which is impossible in standard quantum mechanics. Further, the previous results seemed to imply that CTCs could be used to distinguish between two identical states, which should be impossible no matter how you look at it. To investigate this problem, the scientists considered what would happen if they prepared and evolved quantum states according to a specific physical process. They found that two output states can be distinguished even without using a CTC, eliminating any advantage the CTC may have offered.