Science Bulletin 64 (2019) 580–585 Contents lists available at ScienceDirect Science Bulletin journal homepage: www.elsevier.com/locate/scib Article Emergence of classical objectivity of quantum Darwinism in a photonic quantum simulator Ming-Cheng Chen a,b, Han-Sen Zhong a,b, Yuan Li a,b, Dian Wu a,b, Xi-Lin Wang a,b,LiLia,b, Nai-Le Liu a,b, ⇑ Chao-Yang Lu a,b, , Jian-Wei Pan a,b a Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China b CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China article info abstract Article history: Quantum-to-classical transition is a fundamental open question in physics frontier. Quantum decoher- Received 4 September 2018 ence theory points out that the inevitable interaction with environment is a sink carrying away quantum Received in revised form 12 March 2019 coherence, which is responsible for the suppression of quantum superposition in open quantum system. Accepted 26 March 2019 Recently, quantum Darwinism theory further extends the role of environment, serving as communication Available online 29 March 2019 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 quan- Keywords: tum Darwinism process. In the simulation, many environmental photons are scattered from an observed Quantum measurement quantum system and they are collected and used to infer the system’s state. We observed redundancy of Quantum Darwinism Hovelo bound system’s classical information and suppression of quantum correlation in the fragments of environmental Quantum discord photons. Our results experimentally show that the classical objectivity of quantum system can be estab- Single photons lished through quantum Darwinism mechanism. Ó 2019 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved. 1. Introduction with the quantum system. They perceive the system by collecting information from its surrounding environment. Quantum mechanics is a spectacularly successful predictive Recently, quantum Darwinism explains the emergence of classi- theory, but there is still an unresolved problem about its interpre- cal objectivity of a single quantum system through classical infor- tation in quantum measurement problem [1]. The orthodox mation broadcasting and proliferating in its environment [5,6]. The Copenhagen interpretation separates the world into quantum key idea is that the environment acts as communication channel domain and classical domain, which is bridged by observation- and only classical information about the system can reach obser- induced collapse [2]. How the wave function collapses and classical vers. The environment selects system’s classical information to objectivity emerges from a quantum substrate? A detailed mecha- broadcast and proliferate, and observers use the redundant classi- nism of this quantum-to-classical transition is of fundamentally cal information in local environment fragments to perceive the importance for developing a unified view of our physical world. state of system. In this process, many observers can independently Quantum decoherence theory identifies that the uncontrolled and simultaneously query separate fragments of the environment interactions with the environment can destroy the coherence of a and reach a consensus about the system’s classical state. Specifi- quantum system into a mixed state. In the theory, the environment cally, the quantum Darwinism theory singles out a branch struc- is traced out and thus the system’s classical behavior is explained ture of system-environment (observers) composite quantum in the level of ensemble average [3,4]. How the quantum system’s states [7–9] from measurement-like interaction to explain the classical objectivity arises in a single measurement event is still appearance of classical pointer states. The classical pointer states unresolved. Classical objectivity is a property that many observers are the eigenstates of the measurement observable. can independently observe and establish a consensus view of the In this work, we report a test of quantum Darwinism principle state of a quantum system without perturbing it [5]. In a general on a photonic quantum simulator [10,11] in view of information observation process, observers do not directly touch and interact theory. We measured the information correlations between system and environment, where the system is a single photon and the environment is another five photons. Quantum mutual informa- ⇑ Corresponding author. tion, Holevo bound, and quantum discord [12–15] are used to E-mail address: [email protected] (C.-Y. Lu). https://doi.org/10.1016/j.scib.2019.03.032 2095-9273/Ó 2019 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved. M.-C. Chen et al. / Science Bulletin 64 (2019) 580–585 581 account for the total correlation, classical correlation, and pure a Hamiltonian form of Hi ¼ giA Bi, the eigenstates of monitored quantum correlation, respectively. We used these correlations to observable A are the pointer states, where A and Bi are two observ- investigate information broadcasting and proliferating. ables on system and environment particle i, respectively [5]. In our r r = ; r D h = simulator setting, A ¼ð I À Z Þ 2 Bi ¼ X and gi t ¼ i 2, there- D fore, the pointer states from interaction U h eÀiHi t are 0 and 2. Theory ð iÞ¼ ji ji1 , respectively. The pointer states can be quantified by the disappearance of The basic process of quantum Darwinism is shown in Fig. 1a. A quantum coherence central quantum system (single photon) is monitored by particles (photons) in the environment [16,17]. The particles are scattered CðÞ¼q HclðÞÀq HðÞq ; ð2Þ from the system and caught by observers. These environment par- S S S ticles serve as individual memory cells which are imprinted of sys- q where S is the reduced density matrix of system, tem’s pointer-state information. When there are random q q q HðÞ¼ÀS trðÞSlog2 S is quantum von-Neumann entropy and interactions among the environment’s particles, the stored infor- q HclðÞ¼ÀS trðÞpSlog2pS is classical Shannon entropy, pS is the diag- mation will be inevitably scrambled out. Hence, only non- q onal elements of density matrix S in pointer-state bases [18,19]. interaction environment is good memory for redundant records The reality of pointer states will emerge when the quantum system of system’s state. is completely decohered by the environment. In this case, the clas- We design a quantum Darwinism simulator shown in Fig. 1bto sical entropy will equal to the quantum entropy. The efficiency of simulate non-interaction environment, such as daily photonic decoherence depends on the initial states of environment [17,20]. environment. In the simulator, a central qubit interacts with the Impure or misaligned (close to the eigenstate of observable Bi) envi- environment qubits through two-qubit controlled-rotation gates ronment will reduce the decoherence efficiency. In our simulation, h h Uð Þ¼ji0 hj0 I þ ji1 hj1 Ryð Þ with random angles to mimic the ji0 states are used as initial environment states with optimal h h random scattering process, where Ryð Þ rotates a qubit by angle efficiency. along the y axis of Bloch sphere. When the system qubit is initial- In quantum Darwinism process, the information about the a b ized in superposition state ji0 S þ ji1 S, the simulator will produce quantum system is broadcast to the environment. Local observers Darwinist states with branch structure can only access small fragments of the whole environment. The h h quantum mutual information aji0 N ji0 þ bji1 N cos i ji0 þ sin i ji1 ; ð1Þ S i¼1 i S i¼1 2 i 2 i ISðÞ¼: E HðÞþq H q À H q ; ð3Þ i S Ei SEi where jja 2 þ jjb 2 ¼ 1 and N is the number of environment qubits. The interaction with environment selects preferred pointer can be used to quantify how much information an observer Ei states of the observed system, which are the states left unchanged (accessing the environment fragment Ei) knows about the quantum : q under the interactions and thus multiple records of the state can be system [5]. When ISðÞEi HðÞS for all observers fEig, the system’s faithfully copied into environment. For interactions generated from state can be determined by all the observers and thus the quantum system becomes objective. 3. Experiment We use a photonic simulator [10,11] (shown in Fig. 2)to produce quantum Darwinism states consisted of a central system qubit (photon 1) and five environment qubits (photons 2–6). The quantum state of system is observed at the pffiffiffi superposition state ðji0 þ jiÞ1 = 2. Two sets of rotation- ~ angle parameter, hA ¼ð180 ; 180 ; 180 ; 180 ; 180 Þ and ~ hB ¼ð180 ; 180 ; 180 ; 72 ; 100 Þ, are used in the experiments from ~ the following considerations. Note that here the phases in hB are chosen merely to represent nonorthogonal case to simulate the small environment fragment without specific optimization. A real environment fragment can contain many elementary subsystems. If the fragment is large, its quantum states can be sim- n plified and expressed as orthogonal logical statesji 0L ¼i¼1ji0 i h h Q h n i i n i andji 1L ¼i¼1ðcos 2 ji0 i þ sin 2 ji1 iÞ, due tohi 0Lj1L ¼ i¼1 cos 2 ! 0 for sufficiently large number n of subsystems in a fragment. Furthermore, if the fragment is small, its quantum states can be expressed as nonorthogonal logical statesji 0L and h h Fig. 1. (Color online) Quantum Darwinism process. (a) Multiple observers use cos 2 ji0L þ sin 2 ji1L .