Emergence of Classical Objectivity of Quantum Darwinism in a Photonic Quantum Simulator Ming-Cheng Chen1;2, Han-Sen Zhong1;2, Yuan Li1;2, Dian Wu1;2, Xi-Lin Wang1;2, Li Li1;2, Nai-Le Liu1;2, Chao-Yang Lu1;2,∗ and Jian-Wei Pan1;2 1 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China and 2 CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China. (Dated: August 6, 2019) Quantum-to-classical transition is a fundamental open question in physics frontier. Quantum decoherence theory points out that the inevitable interaction with environment is a sink carrying away quantum coherence, which is responsible for the suppression of quantum superposition in open quantum system. Recently, quantum Darwinism theory further extends the role of environment, serving as communication channel, to explain the classical objectivity emerging in quantum measurement process. Here, we used a six-photon quantum simulator to investigate classical and quantum information proliferation in quantum Darwinism process. In the simulation, many environmental photons are scattered from an observed quantum system and they are collected and used to infer the system’s state. We observed redundancy of system’s classical information and suppression of quan- tum correlation in the fragments of environmental photons. Our results experimentally show that the classical objectivity of quantum system can be established through quantum Darwinism mechanism. Key Words: Quantum Measurement, Quantum Darwin- (a) ism, Hovelo Bound, Quantum Discord Single Photons. Photons Observers INTRODUCTION Quantum system Quantum mechanics is a spectacularly successful predic- (b) tive theory, but there is still an unresolved problem about its 0 R rS interpretation in quantum measurement problem [1]. The or- 0 q thodox Copenhagen interpretation separates the world into 1 0 q quantum domain and classical domain, which is bridged by 2 0 rE observation-induced collapse [2]. How the wave function col- q3 0 lapses and classical objectivity emerges from a quantum sub- q4 strate? A detailed mechanism of this quantum-to-classical 0 q5 transition is of fundamentally importance for developing a unified view of our physical world. Figure 1: Quantum Darwinism process. (a) Multiple observers use Quantum decoherence theory identifies that the uncon- independent fragments of the scattered environment photons to re- trolled interactions with the environment can destroy the co- veal the state of observed quantum system. They can determine the herence of a quantum system into a mixed state. In the theory, pointer states of the observed quantum system without perturbing it the environment is traced out and thus the system’s classical and thus agree on the observed outcome. As a result, the quantum behavior is explained in the level of ensemble average [3,4]. system becomes classical and objective in this process. (b) A quan- arXiv:1808.07388v2 [quant-ph] 5 Aug 2019 tum simulator to simulate the system-environment interaction and How the quantum system’s classical objectivity arises in a sin- produce quantum Darwinism states. In the simulator, the fist qubit is gle measurement event is still unresolved. Classical objectiv- quantum system and the environment particles (other qubits) inter- ity is a property that many observers can independently ob- act with the system of arbitrary interaction strengths fθig in parallel serve and establish a consensus view of the state of a quan- and have no interaction between themselves. Measurements are per- tum system without perturbing it [5]. In a general observation formed on these particles to infer the information of quantum system. process, observers don’t directly touch and interact with the quantum system. They perceive the system by collecting in- formation from its surrounding environment. the system can reach observers. The environment selects sys- Recently, quantum Darwinism explains the emergence of tem’s classical information to broadcast and proliferate, and classical objectivity of a single quantum system through clas- observers use the redundant classical information in local en- sical information broadcasting and proliferating in its envi- vironment fragments to perceive the state of system. In this ronment [5,6]. The key idea is that the environment acts as process, many observers can independently and simultane- communication channel and only classical information about ously query separate fragments of the environment and reach a 2 2 3 THEORY 1 The basic process of quantum Darwinism is shown in Fig. 1(a). A central quantum system (single photon) is monitored EPR EPR EPR by particles (photons) in the environment [16, 17]. The par- ticles are scattered from the system and caught by observers. 4 LO 5 LO 6 These environment particles serve as individual memory cells which are imprinted of system’s pointer-state information. QWP When there are random interactions among the environment’s HWP Filter particles, the stored information will be inevitably scrambled PBS (q) out. Hence, only non-interaction environment is good mem- BD ory for redundant records of system’s state. BBO Coupler EPR LO BS PA We design a quantum Darwinism simulator shown in Fig.1(b) to simulate non-interaction environment, such as Figure 2: Experimental setup. A six-photon interferometer is used daily photonic environment. In the simulator, a central to produce the system-environment composite quantum Darwinism qubit interacts with the environment qubits through two-qubit states. Photon 1 is the central quantum system and photons 2 ∼ 6 controlled-rotation gates U(θ) = j0i h0j ⊗ I + j1i h1j ⊗ Ry(θ) are the environment. Infrared laser pulses (775 nm wavelength, 120 with random angles to mimic the random scattering process, fs pulse duration, 80 MHz repetition rate) pass through three beta- barium borate (BBO) nonlinear crystals sequentially to produce three where Ry(θ) rotates a qubit by angle θ along the y axis of pairs of Einstein-Podolsky-Rosen(EPR) polarization-entangled pho- Bloch sphere. When the system qubit is initialized in super- tons. The two components of EPR state are independently produced position state αj0iS + βj1iS, the simulator will produce Dar- and coherently combined by beam displacers (BDs). Three single winist states with branch structure photons, one from each pair (photons 1, 2 and 3), interfere on two po- θ θ larization beam splitters (PBSs) to generate an entangled six photons αj0i ⊗N j0i + βj1i ⊗N (cos i j0i + sin i j1i ); in Greenberger-Horne-Zeilinger (GHZ) state. Two single photons (5 S i=1 i S i=1 2 i 2 i and 6) pass through polarization-dependent Mach-Zehnder (MZ) in- (1) terferometers to realize local non-unitary operations (LOs). In the MZ interferometers, two polarization components of input photons where jαj2 + jβj2 = 1 and N is the number of environment are separated by polarization beam splitters and recombined on bal- qubits. anced beam splitters (BSs). The internal half-wave plates (HWP) are The interaction with environment selects preferred pointer set at angle θ5=4 and θ6=4, respectively. All the photons are sent to polarization analysis (PA) setups, each consisting of a quarter- states of the observed system, which are the states left un- wave plate (QWP), a HWP, a spectrum filter, and a PBS. The photons changed under the interactions and thus multiple records of are finally detected by fiber-coupled single-photon detectors and six- the state can be faithfully copied into environment. For inter- fold coincidence counting are registered. Note that our experimental actions generated from a Hamiltonian form of Hi = giA⊗Bi, setup is not a faithful simulator of the scattering process. Instead, the eigenstates of monitored observable A are the pointer we mainly want to simulate the process where scattered photons are states, where A and Bi are two observables on system and en- used to infer the state of quantum system. vironment particle i, respectively [5]. In our simulator setting, A = (σI − σZ )=2, Bi = σX and gi∆t = θi=2, therefore, the −iHi∆t pointer states from interaction U(θi) = e are j0i and j1i, respectively. consensus about the system’s classical state. Specifically, the The pointer states can be quantified by the disappearance of quantum Darwinism theory singles out a branch structure of quantum coherence system-environment(observers) composite quantum states [7– 9] from measurement-like interaction to explain the appear- C(ρS) = Hcl(ρS) − H(ρS) (2) ance of classical pointer states. The classical pointer states are the eigenstates of the measurement observable. where ρS is the reduced density matrix of system, H(ρS) = −tr(ρSlog2ρS) is quantum von-Neumann entropy and In this work, we report a test of quantum Darwinism princi- Hcl(ρS) = −tr(pslog2ps) is classical Shannon entropy, ps ple on a photonic quantum simulator [10, 11] in view of infor- is the diagonal elements of density matrix ρS in pointer-state mation theory. We measured the information correlations be- bases [18, 19]. The reality of pointer states will emerge when tween system and environment , where the system is a single the quantum system is completely decohered by the environ- photon and the environment is another five photons. Quan- ment. In this case, the classical entropy will equal to the quan- tum mutual information, Holevo bound, and quantum discord tum entropy. The efficiency of decoherence depends on the [12–15] are used to account for the total correlation, classical initial states of environment [17, 20]. Impure or misaligned correlation, and pure quantum correlation, respectively. We (close to the eigenstate of observable Bi) environment will re- used these correlations to investigate information broadcast- duce the decoherence efficiency. In our simulation, j0i states ing and proliferating. are used as initial environment states with optimal efficiency.