Converting Nonclassicality into Entanglement

Abstract

Quantum mechanics exhibits a wide range of non-classical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well-known that nonclassicality (e.g., squeezing, spin-squeezing, coherence) can be converted into entanglement. In this work, we present a general framework, based on superposition, for structurally connecting and converting non-classicality to entanglement. In addition to capturing the previously known results, this framework also allows us to uncover new entanglement convertibility theorems in two broad scenarios, one which is discrete and one which is continuous. In the discrete setting, the classical states can be any finite linearly independent set. For the continuous setting, the pertinent classical states are 'symmetric coherent states,' connected with symmetric representations of the group SU (K). These results generalize and link convertibility properties from the resource theory of coherence, spin coherent states, and optical coherent states, while also revealing important connections between local and non-local pictures of non-classicality.Quantum mechanics currently provides our deepest description of nature. Despite this, much of our everyday experience can be accurately captured within a classical description. What is special about the nonclassical states of a physical system, and what distinguishes them from the more commonplace classical states? Certainly, one of the most important manifestations of non-classicality is entanglement of multipartite systems. Schrödinger even viewed entanglement as "the characteristic trait of quantum mechanics" [1]. Yet there are situations where entanglement has no natural role in describing non-classicality, such as Fock states in optics [2]. Particularly for non-composite systems, other notions of non-classicality appear better suited for characterizing quantum states.A key aspect where quantum mechanics departs from classical mechanics is the prominence of the superposition principle. This elementary tenet of quantum theory supplies a very general framework for categorizing classical and non-classical states. Depending on the particular setting, we may specify some important subset of pure states {|c } c∈I to be the 'classical' pure states of the system. We can then directly associate non-classicality with superposition: a state |ψ is non-classical if and only if it is a non-trivial superposition of classical states. In fact, entanglement fits naturally within this superposition framework, by specifying factorized states as the classical states.One famous example of classical states is that of optical coherent states, {|α } α∈C [2][3][4]. A completely different example is found in the resource theories of coherence [5] or reference frames [6], where the classical states are some fixed orthonormal basis {|k } M k=0 . In both examples, there is no distinction of subsystems, and entanglement is not obviously relevant. Nevertheless, there are fundamental connections between these single-system c...

Measures and applications of quantum correlations

“…[42,69,43,48,49,71,44,45,46,82,83,70,47] and the very recent review [84]. While several connections between coherence, entanglement, and QCs have been pointed out quite recently, including quantitative interconversion schemes [85,49,86,46,47] somehow analogous to the entanglement activation framework [36,35], a consistent definition of QCs quantifiers in terms of coherence has not been reported in full generality (to our knowledge), and will be introduced here.…”

Quantum Correlations in Nonlocal Boson Sampling

“…On the other hand, however, quantum correlations in quantum optics lack such a nonlocal operational justification, i.e., there is no particular quantum information protocol which exploits phase-space nonclassicality to outperform a classical counterpart protocol. Although, it has been recently shown that such nonclassicalities provide either necessary or sufficient resources for entanglement generation [11][12][13], which then can be used in various protocols.…”

Coherence number as a discrete quantum resource

“…It was shown that nonzero coherence is a necessary and sufficient condition for a state to be used to generate entanglement [8]. This result was generalized to a wider category in [24], which analyzed an extended form of nonclassicality. The authors presented a framework for the conversion of nonclassicality (including coherence) into entanglement.…”

“…So 1 ≤ r C ≤ d and all nonclassical pure states should have r C ≥ 2. It is proved that there exists a unitary incoherent operation Λ on a pure state |ψ such that the Schmidt rank of Λ|ψ is equal to the coherence rank of |ψ [24], and r C (|ψ ) is non-increasing under incoherent operations [3,36]. It is not hard to conceive generalized concepts of coherence rank to mixed states.…”

“…The conversion of coherence to entanglement is generalized to a wider category by [24], who analyzed the nonclassicality including coherence. During the discussion they introduced an analogous concept to the Schmidt rank in entanglement, the coherence rank of a pure state:…”