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arXiv:2301.04443 · Entropy

Entangled States Are Harder to Transfer than Product States

Tony J. G. Apollaro, Salvatore Lorenzo, Francesco Plastina, Mirko Consiglio, Karol Życzkowski

Published Dec 27, 2022• 6 citations

Abstract

The distribution of entangled states is a key task of utmost importance for many quantum information processing protocols. A commonly adopted setup for distributing quantum states envisages the creation of the state in one location, which is then sent to (possibly different) distant receivers through some quantum channels. While it is undoubted and, perhaps, intuitively expected that the distribution of entangled quantum states is less efficient than that of product states, a thorough quantification of this inefficiency (namely, of the difference between the quantum-state transfer fidelity for entangled and factorized states) has not been performed. To this end, in this work, we consider n-independent amplitude-damping channels, acting in parallel, i.e., each, locally, on one part of an n-qubit state. We derive exact analytical results for the fidelity decrease, with respect to the case of product states, in the presence of entanglement in the initial state, for up to four qubits. Interestingly, we find that genuine multipartite entanglement has a more detrimental effect on the fidelity than two-qubit entanglement. Our results hint at the fact that, for larger n-qubit states, the difference in the average fidelity between product and entangled states increases with increasing single-qubit fidelity, thus making the latter a less trustworthy figure of merit.

DOI: 10.3390/e25010046

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We show that the entanglement of the two-qubit teleported state via a class of four-qubit entangled channel states can be increased by collective amplitude damping locally acting on one part of the channel state. Specifically, we compare the entanglement contained in the output state of teleportation before and after the action of the collective amplitude damping on the channel state, and show that for a wide range of input entangled two-qubit states, the local decoherence can result in an increase in the output entanglement. In this process, the average fidelity of the teleportation is also increased. Our result reveals that some quantum properties of the four-qubit channel state are definitely improved in the process of enhancing the fidelity by local noise.

A new analytical expression for the average quantum fidelity of a teleportation protocol for an arbitrary two-qubit state transmitted through an amplitude-damping noise environment has been established. This expression shows that the average fidelity depends not only on the purity measure and the bipartite entanglement measure of each parallel state forming the quantum channel, but also on the multipartite entanglement measure. This entanglement is generated between the qubits of each parallel state when they interact independently with the amplitude-damping environment. Based on this analytical relation, the physical mechanism for enhancing the teleportation protocol’s average quantum fidelity under two distinct amplitude-damping noise scenarios has been elucidated.

Abstract The transfer of quantum information between different locations is key to many quantum information processing tasks. Whereas, the transfer of a single qubit state has been extensively investigated, the transfer of a many-body system configuration has insofar remained elusive. We address the problem of transferring the state of n interacting qubits. Both the exponentially increasing Hilbert space dimension, and the presence of interactions significantly scale-up the complexity of achieving high-fidelity transfer. By employing tools from random matrix theory and using the formalism of quantum dynamical maps, we derive a general expression for the average and the variance of the fidelity of an arbitrary quantum state transfer protocol for n interacting qubits. Finally, by adopting a weak-coupling scheme in a spin chain, we obtain the explicit conditions for high-fidelity transfer of three and four interacting qubits.

Quantum entanglement is a central resource for quantum computation and state transfer, yet the usefulness of multipartite entanglement depends on how rapidly coherence and nonclassical correlations degrade as the register size and communication depth increase. This methodology paper develops a reproducible density-matrix simulation for studying entanglement and information transfer in multi-qubit systems. GHZ and W states containing 3, 4, 5, 6 and 8 qubits are generated and exposed to independent local depolarizing noise. State fidelity and bipartite negativity are used to quantify preservation of the prepared resource, while an entanglement-assisted multi-hop teleportation model measures the fidelity of transferred single-qubit information. The simulation shows a systematic decrease in state fidelity and negativity with increasing register size at a fixed local error probability. At a local depolarizing probability of 0.02, GHZ fidelity decreases from 0.941 for three qubits to 0.852 for eight qubits, whereas W-state fidelity decreases from 0.943 to 0.877. In a separate transfer experiment with an effective error probability of 0.10 per teleportation hop, average transfer fidelity decreases from 0.933 after one hop to 0.745 after five hops, while remaining above the classical benchmark of 2/3. These results illustrate how multipartite entanglement quality; noise accumulation and path depth jointly determine the reliability of information transfer in multi-qubit computing architectures.

The effect of noise on the transmission of quantum state has attached much interest recently. Here we investigate the effect of different types of quantum noise on deterministic exact remote preparation of an arbitrary single-qubit state. Four types of noise which usually encountered in application of quantum remote state preparation, including bit-flipping, phase-flipping, depolarizing and amplitude damping, are considered. The average fidelities of remote state preparation for any combinations of noise are calculated. It is shown that more fidelity can be achieved via less entanglement in single-qubit remote preparation when part or all of the entangled qubits are subjected to amplitude damping noise. It is shown that in several situations more noise may leading to more fidelity in remote state preparation. Moreover, we discuss the effect of noise on probabilistic remote state preparation.

In this work, we investigate controlled quantum teleportation in the presence of noisy channels acting on the three-qubit resource state. We employ a series of generalized noisy channels that bridge the dephasing channels and amplitude damping channels while encompassing extensive intermediate scenarios. We provide an in-depth analysis of the degradation of the maximal average fidelity and the optimal average fidelity in controlled quantum teleportation induced by such noisy channels by deriving the analytical expression and examining several special cases. The analytical expression shows that attaining the optimal average fidelity requires Charlie's cooperation in performing a measurement at suitably chosen angles, and is also related to the initial state and the channel parameters. Our analysis reveals that the optimal average fidelity does not always decrease monotonically with the evolution parameter, instead, it first decreases and then increases. This non-monotonic behavior depends on the entanglement of the initial resource state, as well as on the parameters of the channel traversed by the first qubit.