Experimentally obtaining maximal coherence via assisted distillation process

Abstract

Quantum coherence, which quantifies the superposition properties of a quantum state, plays an indispensable role in quantum resource theory. A recent theoretical work [Phys. Rev. Lett. 116, 070402 (2016)] studied the manipulation of quantum coherence in bipartite or multipartite systems under the protocol Local Incoherent Operation and Classical Communication (LQICC). Here we present the first experimental realization of obtaining maximal coherence in assisted distillation protocol based on linear optical system. The results of our work show that the optimal distillable coherence rate can be reached even in one-copy scenario when the overall bipartite qubit state is pure. Moreover, the experiments for mixed states showed that distillable coherence can be increased with less demand than entanglement distillation. Our work might be helpful in the remote quantum information processing and quantum control.Quantum coherence, which exhibits the fundamental signature of superposition in quantum mechanics, has been exploited in many fields of quantum physics, such as biological systems [1][2][3], transport theory [4,5], thermodynamics [6][7][8][9][10][11][12], nanoscale physics [13] and other scientific work associated with quantum theory [14][15][16][17][18][19][20][21]. Recently, rigorous and unambiguous framework for quantifying quantum coherence has also been put forward, which has enhanced the exploitation of its operational significance in the context of quantum resource theory [22][23][24].Quantifying quantum coherence starts from the definition of incoherent states (free states) and incoherent operations (free operations) [22,23,25]. A quantum state ρ is incoherent if it is diagonal in a given reference basis {|i }, i.e., ρ = i p i |i i|, with some probability {p i } [23,26]. Incoherent operators are required to fullfillK n IK † n ⊂ I for all n represented by the set of Kraus operators {K n }, where I is the set of incoherent states. Moreover, in a d-dimensional Hilbert space H, the maximally coherent state is |Φ d = 1/d i |i , and |Φ := |Φ 2 denotes the unit coherence resource state [22].As a quantification and measure of quantum superposition in a fixed basis {|i }, various coherence measures have been proposed [22,24,26,27]. In this paper, we choose relative entropy of coherence [22] as the measure of this property. Relative entropy of coherence of a quantum state ρ is given by C r (ρ) = S(∆(ρ))− S(ρ), where ∆(ρ) = Σ i |i i| ρ |i i| is the dephasing in the reference basis. In many recent works, this kind of measure has been endowed with special significance as well as operational meaning [22][23][24]. Winter and Yang [23] showed that asymptotically the standard distillable coherence of a general quantum state is given by the * These authors contributed equally to this work.† gyxiang@ustc.edu.cn relative entropy of quantum coherence. Likewise, Ma's group [24] has shown that the intrinsic randomness as a measure of coherence is just equal to the relative entropy of quantum coherence. Recently, the manipulation...

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

“…Experimental assisted coherence distillation in the single‐copy regime has been performed in ref. [146], based on a linear optical system. If Alice and Bob share a pure two‐photon state, then Alice can help Bob to increase his local coherence in the single‐copy setup, and the maximal relative entropy of coherence Bob can get is given by , as has also been shown experimentally in ref.…”

Coherence of assistance and assisted maximally coherent states

“…In this sense, the AMC states are potentially perfect quantum resources. In fact, the experimental realization in linear optical systems for obtaining the coherence of assistance with respect to the relative entropy coherence in two dimensional systems has already been presented 34 .…”

Hierarchy of quantum operations in manipulating coherence and entanglement

“…These resource theories for the distributed manipulation of coherence provide a framework for investigating an interplay between coherence and entanglement in various information processing tasks such as distillation and dilution of these resources [16], assisted distillation of coherence [10,52,59], quantum state merging [55], quantum state redistribution [2], and multipartite state transformation [9,39]. From a practical perspective, the distributed manipulation of coherence naturally arises in photonic systems as demonstrated in recent experiments [68][69][70].…”