Localized Closed Timelike Curves Can Perfectly Distinguish Quantum States

We show that qubits traveling along closed timelike curves are a resource that a party can exploit to distinguish perfectly any set of quantum states. As a result, an adversary with access to closed timelike curves can break any prepare-and-measure quantum key distribution protocol. Our result also implies that a party with access to closed timelike curves can violate the Holevo bound.

Figure 1

The above circuit can perfectly distinguish the nonorthogonal states $|0⟩$ and $|-⟩$. The first qubit in state $|\psi ⟩$ is the unknown qubit ($|0⟩$ or $|-⟩$) and the second qubit with density matrix ${\rho }_{\mathrm{CTC}}$ travels along a closed timelike curve. The double vertical bars on the bottom left and right indicate the past and future mouths of the wormhole for the CTC.

Figure 2

The above circuit can perfectly distinguish the BB84 states $|0⟩$, $|1⟩$, $|+⟩$, and $|-⟩$. The circuit uses the standard quantum circuit notation from Ref. 14 and we define the unitaries $U_{00}$, $U_{01}$, $U_{10}$, and $U_{11}$ in (3).