Teleportation of qubit states through dissipative channels: Conditions for surpassing the no-cloning limit

We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the nonexistence of any other copy with better fidelity. The effect of the initially distributed maximally entangled state on the process is presented; the concurrence and the fully entangled fraction of the shared states are discussed. We intend to show that prior information on the dissipative channel and the range of qubit states to be teleported is helpful for the evaluation of the success of teleportation, where success is defined as surpassing the fidelity limit imposed by the fidelity of the 1-to-2 optimal cloning machine for the specific range of qubits.

Figure 1

Teleportation scenario 1, where both qubits of ${\widehat{\rho }}_{\mathrm{ent}}$ are affected by the channel, and scenario 2, where only one of the qubits is affected. A quantum channel is formed by the shared entangled state.

Figure 2

Comparison of concurrence (solid curves) and fully entangled fraction (dashed curves) for the ADC, when the initial entangled state is $\mid {\psi }^{\pm }⟩$ (i) and $\mid {\varphi }^{\pm }⟩$ (ii), as well as the PDC (iii) and the DC (iv) for scenarios 1 (curves a) and 2 (curves b). Note that for the PDC and DC results are independent of the initial entangled state.

Figure 3

(Color online) Optimal state-dependent fidelity in the presence of the ADC when the initial MES is $\mid {\psi }^{\pm }⟩$ (top) and $\mid {\varphi }^{\pm }⟩$ (bottom) and both qubits are affected by damping. Contours correspond to $F=2∕3$, $F=5∕6$ and the optimal PCCM fidelities when Alice’s measurement result is $\mid 01⟩⟨01\mid$ or $\mid 11⟩⟨11\mid$, solid curves, and when Alice’s measurement result is $\mid 10⟩⟨10\mid$ or $\mid 00⟩⟨00\mid$, dotted curves.

Figure 4

(Color online) Same as in Fig. 3 (top) for $\mid {\psi }^{\pm }⟩$ but for the case when only one of the qubits is affected by the ADC. For $\mid {\varphi }^{\pm }⟩$, the meaning of curves is reversed.

Figure 5

State-dependent fidelity in the presence of the PDC when the initial MES is any of the Bell states and only one of the qubits (dashed curves) and both qubits (solid curves) are affected by damping. Contours show $F=2∕3$, $F=5∕6$ and the optimal PCCM fidelities. Horizontal dashed lines correspond to the values of damping rate for $f_{\mathrm{ent}}=3∕4$ for scenarios 1 (lower) and 2 (upper).

Figure 6

State dependent teleportation fidelity when the qubit to be teleported is subjected to the ADC, a: $p=0.2$, b: $p=0.5$, and c: $p=0.9$. Horizontal dotted lines denote the limits between classical and quantum operations (lower) and the secure quantum teleportation (upper). The curve marked with circles corresponds to the optimal PCCM fidelity.

Figure 7

Average fidelity with noisy channels: a: PDC, b: ADC, and c: DC for scenarios 1 (left) and 2 (right). Horizontal dashed lines denote the limits between classical and quantum operations (lower) and the secure quantum teleportation (upper).