We present a general model for quantum channels with memory and show that it is sufficiently general to encompass all causal automata: any quantum process in which outputs up to some time @math do not depend on inputs at times @math can be decomposed into a concatenated memory channel. We then examine and present different physical setups in which channels with memory may be operated for the transfer of (private) classical and quantum information. These include setups in which either the receiver or a malicious third party have control of the initializing memory. We introduce classical and quantum channel capacities for these settings and give several examples to show that they may or may not coincide. Entropic upper bounds on the various channel capacities are given. For forgetful quantum channels, in which the effect of the initializing memory dies out as time increases, coding theorems are presented to show that these bounds may be saturated. Forgetful quantum channels are shown to be open and dense in the set of quantum memory channels.
@cite_30: We propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distantspin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then 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. We 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, our channel allows distillable entanglement to be shared over arbitrary distances.
@cite_28: Information capacities achievable in the multi-parallel-use scenarios are employed to characterize the quantum correlations in unmodulated spin chains. By studying the qubit amplitude damping channel, we calculate the quantum capacity Q, the entanglement assisted capacity C sub E , and the classical capacity C sub 1 of a spin chain with ferromagnetic Heisenberg interactions.
@cite_56: We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-(1 2) particles can be achieved in a timescale of the order of (0.33( Dirac_h 2 pi ) J)N sup 1.7 vertical bar ln P vertical bar. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.
@cite_23: We propose a class of qubit networks that admit the perfect state transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to @math -qubit spin networks of identical qubit couplings, we show that @math is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits, then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.
@cite_11: We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher-dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2 log sub 3 N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done by , Phys. Rev. Lett. 92, 187902 (2004)
Recently, an unmodulated spin chain has been proposed as a model for short distance quantum communication @cite_30 @cite_56 @cite_23 @cite_11 . In such a scheme, the state to be communicated over the channel is placed on one of the spins of the chain, propagates for a specific amount of time, and is then received at a distant spin of the chain (cf. Fig. ). When viewed as a model for quantum communication, it is generally assumed that a reset of the spin chain occurs after each signal @cite_28 , for example by applying an external magnetic field, resulting in a memoryless channel. However, a continuous operation without reset may lead to higher transmission rates, and corresponds to a quantum channel with memory.