Quantum Communication Through an Unmodulated Spin Chain

Quantum Communication Through an Unmodulated Spin Chain

13 Jun 2003 | Sougato Bose
This paper proposes a scheme for quantum communication using an unmodulated and unmeasured spin chain. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. The authors derive expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using their scheme. They apply this to the realizable case of an open-ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. They find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, the spin-chain channel allows distillable entanglement to be shared over arbitrarily large distances. Quantum state transfer is achieved by placing a spin encoding the state at one end of the chain and waiting for a specific amount of time to let this state propagate to the other end. This method avoids interfacing between different physical systems, making it an ideal connector between quantum computers and realizable systems. The authors consider both general graphs of spins and the realizable case of an open-ended chain. They show that the spin chain can act as an amplitude damping quantum channel, converting the input state to an output state with high fidelity. They also show that entanglement can be shared through the channel, which can be distilled into pure singlets and used for teleportation. The authors evaluate the performance of their protocol for various chain lengths and find that for N=2, 4, and 8, the fidelity is close to perfect. They also show that for very long chains, the entanglement sharable is of the order N^{-1/3}. They also consider a ring of 2N spins and show that the maximum entanglement is the same for both the line and the ring. They conclude that their scheme allows quantum communication between adjacent quantum computers without interfacing different physical systems. They also mention potential systems for realization, including Josephson junction arrays, excitons in quantum dots, and real 1D magnets. The authors conclude that their work provides a fundamental study of a condensed matter system from the viewpoint of quantum communications.This paper proposes a scheme for quantum communication using an unmodulated and unmeasured spin chain. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. The authors derive expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using their scheme. They apply this to the realizable case of an open-ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. They find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, the spin-chain channel allows distillable entanglement to be shared over arbitrarily large distances. Quantum state transfer is achieved by placing a spin encoding the state at one end of the chain and waiting for a specific amount of time to let this state propagate to the other end. This method avoids interfacing between different physical systems, making it an ideal connector between quantum computers and realizable systems. The authors consider both general graphs of spins and the realizable case of an open-ended chain. They show that the spin chain can act as an amplitude damping quantum channel, converting the input state to an output state with high fidelity. They also show that entanglement can be shared through the channel, which can be distilled into pure singlets and used for teleportation. The authors evaluate the performance of their protocol for various chain lengths and find that for N=2, 4, and 8, the fidelity is close to perfect. They also show that for very long chains, the entanglement sharable is of the order N^{-1/3}. They also consider a ring of 2N spins and show that the maximum entanglement is the same for both the line and the ring. They conclude that their scheme allows quantum communication between adjacent quantum computers without interfacing different physical systems. They also mention potential systems for realization, including Josephson junction arrays, excitons in quantum dots, and real 1D magnets. The authors conclude that their work provides a fundamental study of a condensed matter system from the viewpoint of quantum communications.
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