Fundamental trade-off relation in probabilistic entanglement generation
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arXiv
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| Format: | Preprint |
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2021
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| author | Chen, Yuanbo Hasegawa, Yoshihiko |
| author_facet | Chen, Yuanbo Hasegawa, Yoshihiko |
| contents | We investigate the generation of entanglement between two non-interacting systems by synthesizing a new quantum process from the superposition of distinct processes characterized by local-only operations. Our analysis leads to the derivation of a universal trade-off relation, $P_{\text{succ}}(1+\mathcal{C})\le1$, that fundamentally bounds the success probability ($P_{\text{succ}}$) and the generated entanglement (concurrence $\mathcal{C}$). The derivation of this trade-off relation is inspired by indefinite causal order, but applies for a broader class of quantum processes. Next, we show that the mathematical structure of this bound predicts the existence of a "quasi-deterministic" mode of operation, a surprising phenomenon which we then confirm with concrete entanglement generation protocols, where a maximally entangled state is guaranteed to be produced. In this mode of operation, both outcomes of the post-selection measurement on the auxiliary control system result in a maximally entangled state of the target system. Furthermore, we demonstrate how this general principle can be realized using a quantum switch, which leverages an indefinite causal order as a physical resource, and explore the rich variety of dynamical behaviors governed by the universal trade-off. Our results establish a general principle for entanglement generation with superposition of quantum processes and introduce a novel way of controlling entanglement generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_03233 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fundamental trade-off relation in probabilistic entanglement generation Chen, Yuanbo Hasegawa, Yoshihiko Quantum Physics We investigate the generation of entanglement between two non-interacting systems by synthesizing a new quantum process from the superposition of distinct processes characterized by local-only operations. Our analysis leads to the derivation of a universal trade-off relation, $P_{\text{succ}}(1+\mathcal{C})\le1$, that fundamentally bounds the success probability ($P_{\text{succ}}$) and the generated entanglement (concurrence $\mathcal{C}$). The derivation of this trade-off relation is inspired by indefinite causal order, but applies for a broader class of quantum processes. Next, we show that the mathematical structure of this bound predicts the existence of a "quasi-deterministic" mode of operation, a surprising phenomenon which we then confirm with concrete entanglement generation protocols, where a maximally entangled state is guaranteed to be produced. In this mode of operation, both outcomes of the post-selection measurement on the auxiliary control system result in a maximally entangled state of the target system. Furthermore, we demonstrate how this general principle can be realized using a quantum switch, which leverages an indefinite causal order as a physical resource, and explore the rich variety of dynamical behaviors governed by the universal trade-off. Our results establish a general principle for entanglement generation with superposition of quantum processes and introduce a novel way of controlling entanglement generation. |
| title | Fundamental trade-off relation in probabilistic entanglement generation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2112.03233 |