Experiment to illustrate the P-CTC predictions of the grandfather paradox. a) Diagram of the quantum circuit. Using a CNOT gate sandwiched between optional Z and X gates, it is possible to prepare all of the maximally entangled Bell states. The Bell state measurement is implemented using a CNOT and a Hadamard. Each of the probe qubits is coupled to the forward qubit via a CNOT gate. b) Diagram of experimental apparatus. The polarization and path degrees of freedom of single photons from a quantum dot are entangled via a calcite polarization-dependent beam displacer (BD1), implementing the CNOT. Half-wave plates (HWP) before and after BD1 implement the optional Z and X gates. The state | +i is created by setting the angle of both HWPs to zero. To complete the teleportation circuit, the post-selection onto | +i is carried out by first recombining the path degrees of freedom on a polarizing beamsplitter (performing a CNOT gate between path and polarization) and then passing the photons through a calcite polarizer set to 45 degrees and detecting them on a cooled CCD. A rotatable HWP acts as a quantum gun, implementing the unitary [formula]. Removable calcite beam displacers (BD2 and BD3) couple the polarization qubit to two probe qubits encoded in additional spatial degrees of freedom. When the beam displacers are inserted in the setup, four spots on the CCD correspond to the probe states 11, 10, 01, and 00.
Closed timelike curves (CTCs) are trajectories in spacetime that effectively travel backwards in time: a test particle following a CTC can interact with its former self in the past. A widely accepted quantum theory of CTCs was proposed by Deutsch. Here we analyze an alternative quantum formulation of CTCs based on teleportation and postselection, and show that it is inequivalent to Deutsch’s. The predictions or retrodictions of our theory can be simulated experimentally: we report the results of an experiment illustrating how in our particular theory the “grandfather paradox” is resolved.
A team of researchers has proposed a new theory of CTCs that can resolve the grandfather paradox, and they also perform an experiment showing how such a scheme works. The researchers, led by Seth Lloyd from MIT, along with scientists from the Scuola Normale Superiore in Pisa, Italy; the University of Pavia in Pavia, Italy; the Tokyo Institute of Technology; and the University of Toronto.
In the new theory, CTCs are required to behave like ideal quantum channels of the sort involved in teleportation. In this theory, self-consistent CTCs (those that don’t result in paradoxes) are postselected, and are called “P-CTCs.” As the scientists explain, this theory differs from the widely accepted quantum theory of CTCs proposed by physicist David Deutsch, in which a time traveler maintains self-consistency by traveling back into a different past than the one she remembers. In the P-CTC formulation, time travelers must travel to the past they remember.
Although postselecting CTCs may seem complicated, it can actually be investigated experimentally in laboratory simulations. By sending a “living” qubit (i.e., a bit in the state 1) a few billionths of a second back in time to try to “kill” its former self (i.e., flip to the state 0), the scientists show that only photons that don’t kill themselves can make the journey.
“P-CTCs work by projecting out part of the quantum state,” Lloyd said. “Another way of thinking about closed timelike curves is the following. In normal physics (i.e., without closed timelike curves), one specifies the state of a system in the past, and the laws of physics then tell how that state evolves in the future. In the presence of CTCs, this prescription breaks down: the state in the past plus the laws of physics no longer suffice to specify the state in the future. In addition, one has to supply final conditions as well as initial conditions. In our case, these final conditions specify the state when it enters the closed timelike curve in the future. These final conditions are what project out part of the quantum state as described above.
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