ioing biparite classical distributions and quantum states Rahul Jain,Yaoyun Shi,Zhaohui Wei,Shengyu Zhang
Rahul Jain, Yaoyun Shi, Zhaohui Wei, Shengyu Zhang
randomness/entanglement Shared randomness/entanglement is an important resource in distributive settings. Question:How hard to generate a bipartite classical distribution or quantum state?
randomness/entanglement • Shared randomness/entanglement is an important resource in distributive settings. • Question: How hard to generate a bipartite classical distribution or quantum state?
3 scenarios Distribution generation Distribution approximation Quantum state approximation
3 scenarios • Distribution generation • Distribution approximation • Quantum state approximation
Target distribution:p(x,y)} TB (x,y）~p Available resource:seed correlation r. Correlation complexity:Corr(p)=min size(r) classical:r =(x',y')is classical correlation.-RCorr(p) 一 quantum:r =PAB is quantum state. QCorr(p)
Target distribution: {𝑝 𝑥, 𝑦 } • Available resource: seed correlation r. • Correlation complexity: Corr(p) = min size(r) – classical: 𝑟 = (𝑥’,𝑦’) is classical correlation. - RCorr(𝑝) – quantum: 𝑟 = 𝜌𝐴𝐵 is quantum state. - QCorr(𝑝) 𝑟𝐵 𝑥 𝑦 r ( , ) 𝑝 𝑟𝐴
Target distribution:{p(x,y)} TB (x,y）~卫 Alternative resource:communication Communication complexity: Comm(p)=min size(message) classical:number of bits. RComm(p) quantum:number of qubits. QComm(p) -
Target distribution: {𝑝 𝑥, 𝑦 } • Alternative resource: communication • Communication complexity: Comm(p) = min size(message) – classical: number of bits. - RComm(p) – quantum: number of qubits. - QComm(p) 𝑟𝐵 (𝑥 , 𝑦 ) 𝑝 𝑟𝐴