Quantum superposition of causal-structure as a universal resource for local implementation of nonlocal quantum operations

• URL: http://arxiv.org/abs/2209.12925v1
• Date: Mon, 26 Sep 2022 18:01:20 GMT
• Title: Quantum superposition of causal-structure as a universal resource for local implementation of nonlocal quantum operations
• Authors: Pratik Ghosal, Arkaprabha Ghosal, Debarshi Das and Ananda G. Maity
• Abstract summary: indefinite causal structure can be used as an independent universal resource for local implementation of any quantum operation on spatially distributed quantum systems. We show that exploiting indefinite causal structure as the sole resource, it is possible to perfectly teleport the state of one agent's subsystem to the other distant lab. We present a protocol for perfect local discrimination of the set of four Bell states that exploits indefinite causal structure as the sole resource.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spatial separation restricts the set of locally implementable quantum operations on distributed multipartite quantum systems. We propose that indefinite causal structure arising due to quantum superposition of different spacetime geometries can be used as an independent universal resource for local implementation of any quantum operation on spatially distributed quantum systems. Consequently, all such quantum tasks that are not accomplishable by LOCC only also become locally accomplishable. We show that exploiting indefinite causal structure as the sole resource, it is possible to perfectly teleport the state of one agent's subsystem to the other distant lab in such a way that the agent at the distant lab can have access to the whole initially shared state in his/her lab and can perform any global quantum operation on the joint state locally. We further find that after the teleportation process, the resource -- indefinite causal structure of the spacetime does not get destroyed. Hence, after implementing the desired quantum operation the state of the first agent's subsystem can be teleported back to its previous lab using the same resource. We show that this two-way teleportation is not always necessary for locally executing all nonlocal quantum tasks that are not realisable by LOCC only. Without invoking any kind of teleportation, we present a protocol for perfect local discrimination of the set of four Bell states that exploits indefinite causal structure as the sole resource. As immediate upshots, we present some more examples of such nonlocal tasks like local discrimination of the set of states exhibiting `quantum nonlocality without entanglement' and activation of bound entangled states that are also achievable by our proposed protocol incorporating indefinite causal structure as resource.

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