Entanglement activation from quantum coherence and superposition

Abstract

Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics [1]. While considered as puzzling phenomena in the early days of quantum theory [2], it is only very recently that entanglement and coherence have been recognized as resources for the emerging quantum technologies, including quantum metrology, quantum communication, and quantum computing [3,4]. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of superposition does not allow for entanglement activation. By constructing a CNOT gate as a free operation, we experimentally show that such activation is possible within the more constrained framework of quantum coherence. Our results provide new insights into the interplay between coherence and entanglement, representing a substantial step forward for solving longstanding open questions in quantum information science.Quantum resource theories provide a fundamental framework for studying general notions of nonclassicality, including quantum entanglement [3,5] and coherence [4,6]. Any such resource theory is based on the notion of free states and free operations. Free operations are physical transformations which do not consume any resources. They strongly depend on the problem under study, and are usually motivated by physical or technological constraints. In entanglement theory, these constraints are naturally given by the distance lab paradigm: two spatially separated parties can perform quantum measurements in their local labs, but can only exchange classical information between each other.Free states of a resource theory are quantum states which can be produced without consuming any resources. In entanglement theory, these free states are called separable [7]. Various quantum protocols require the presence of entanglement. This includes quantum teleportation [8,9], quantum cryptography [10], and quantum state merging [11]. As has been demonstrated very recently, it is indeed possible to establish and maintain high degree of entanglement via large distances [12].The resource theory of quantum coherence studies technological limitations for establishing quantum superpositions [4,6]. This theory requires the existence of a distinguished basis, which can be interpreted as classical, and is usually present due to the unavoidable decoherence [13]. Quantum states belonging to this basis are then called incoherent, and considered as the free states of coherence theory. Superpositions of these free states are said to possess coherence. Incoherent operations are free operations of coherence theory: they correspond to quantum measurements which do not create coherence for individual measurement outcomes [6]. Recent results show that coherence plays a crucial role for quantum metrology [14,15], and that coherence might be more suitable than entanglement to capture the performance of quantum algorithms [16,17]. Recent inve...

Experimental Progress on Quantum Coherence: Detection, Quantification, and Manipulation

“…A theoretical investigation of this equivalence shows that coherence can be converted into entanglement via incoherent operations, leading also to a correspondence between coherence and entanglement quantifiers. [ 9,13 ] This equivalence has also been explored for the resource theories of entanglement and superposition, [ 38,152,153 ] and for coherence and general quantum correlations beyond entanglement. [ 37 ]…”

One-shot entanglement distillation beyond local operations and classical communication

“…This quantity, considered first in the resource theory of coherence as the modified trace distance [36], generalises the commonly employed trace distance measure  r s -sÎ   min 1 . The reason why  ( ) T 1 is a more suitable measure of entanglement than the trace distance itself is the fact that, contrary to  ( ) T 1 , the trace distance does not satisfy strong monotonicity under LOCC [36,37] (i.e. the requirement that a measure M obeys…”

Experimental progress on quantum coherence: detection, quantification, and manipulation

“…A theoretical investigation of this equivalence shows that coherence can be converted into entanglement via incoherent operations, leading also to a correspondence between coherence and entanglement quantifiers [9,13]. This equivalence has also been explored for the resource theories of entanglement and superposition [37,149,150], and for coherence and general quantum correlations beyond entanglement [36].…”