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Quantum Entanglement of Local Operators in Conformal Field Theories  [PDF]
Masahiro Nozaki,Tokiro Numasawa,Tadashi Takayanagi
Physics , 2014, DOI: 10.1103/PhysRevLett.112.111602
Abstract: We introduce a series of quantities which characterizes a given local operator in conformal field theories from the viewpoint of quantum entanglement. It is defined by the increased amount of (Renyi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in 2, 4 and 6 dimensions. We find that these results are interpreted in terms of quantum entanglement of finite number states, including EPR states. They agree with a heuristic picture of propagations of entangled particles.
Non-local scaling operators with entanglement renormalization  [PDF]
G. Evenbly,P. Corboz,G. Vidal
Physics , 2009, DOI: 10.1103/PhysRevB.82.132411
Abstract: The multi-scale entanglement renormalization ansatz (MERA) can be used, in its scale invariant version, to describe the ground state of a lattice system at a quantum critical point. From the scale invariant MERA one can determine the local scaling operators of the model. Here we show that, in the presence of a global symmetry $\mathcal{G}$, it is also possible to determine a class of non-local scaling operators. Each operator consist, for a given group element $g\in\mathcal{G}$, of a semi-infinite string $\tGamma_g$ with a local operator $\phi$ attached to its open end. In the case of the quantum Ising model, $\mathcal{G}= \mathbb{Z}_2$, they correspond to the disorder operator $\mu$, the fermionic operators $\psi$ and $\bar{\psi}$, and all their descendants. Together with the local scaling operators identity $\mathbb{I}$, spin $\sigma$ and energy $\epsilon$, the fermionic and disorder scaling operators $\psi$, $\bar{\psi}$ and $\mu$ are the complete list of primary fields of the Ising CFT. Thefore the scale invariant MERA allows us to characterize all the conformal towers of this CFT.
Properties of Local Quantum Operations with Shared Entanglement  [PDF]
Gus Gutoski
Physics , 2008,
Abstract: Multi-party local quantum operations with shared quantum entanglement or shared classical randomness are studied. The following facts are established: (i) There is a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. (ii) The existence of the ball of local operations with shared randomness is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. (iii) Local operations with shared entanglement are characterized in terms of linear functionals that are ``completely'' positive on a certain cone K of separable Hermitian operators, under a natural notion of complete positivity appropriate to that cone. Local operations with shared randomness (but not entanglement) are also characterized in terms of linear functionals that are merely positive on that same cone K. (iv) Existing characterizations of no-signaling operations are generalized to the multi-party setting and recast in terms of the Choi-Jamiolkowski representation for quantum super-operators. It is noted that the standard nonlocal box is an example of a no-signaling operation that is separable, yet cannot be implemented by local operations with shared entanglement.
Charged Entanglement Entropy of Local Operators  [PDF]
Pawel Caputa,Masahiro Nozaki,Tokiro Numasawa
Physics , 2015,
Abstract: In this work we consider the time evolution of charged Renyi entanglement entropies after exciting the vacuum with local fermionic operators. In order to explore the infor- mation contained in charged Renyi entropies, we perform computations of their excess due to the operator excitation in 2d CFT, free fermionic field theories in various di- mensions as well as holographically. In the analysis we focus on the dependence on the entanglement charge, the chemical potential and the spacetime dimension. We find that excesses of charged (Renyi) entanglement entropy can be interpreted in terms of charged quasiparticles. Moreover, we show that by appropriately tuning the chemical potential charged Renyi entropies can be used to extract entanglement in a certain charge sector of the excited state.
Entanglement of Local Operators in large N CFTs  [PDF]
Pawel Caputa,Masahiro Nozaki,Tadashi Takayanagi
Physics , 2014, DOI: 10.1093/ptep/ptu122
Abstract: We study Renyi and von-Neumann entanglement entropy of excited states created by local operators in large N (or large central charge) CFTs. First we point that a naive large N expansion can break down for the von-Neumann entanglement entropy, while it does not for the Renyi entanglement entropy. This happens even for the excited states in free Yang-Mills theories. Next, we analyze strongly coupled large N CFTs from both field theoretic and holographic viewpoints. We find that the Renyi entanglement entropy of the excited state produced by a local operator, grows logarithmically under its time evolution and its coefficient is proportional to the conformal dimension of the local operator.
Local distinguishability of quantum states and the distillation of entanglement  [PDF]
Ping-Xing Chen,Cheng-Zu Li
Physics , 2002,
Abstract: This paper tries to probe the relation between the local distinguishability of orthogonal quantum states and the distillation of entanglement. An new interpretation for the distillation of entanglement and the distinguishability of orthogonal quantum states in terms of information is given, respectively. By constraining our discussion on a special protocol we give a necessary and sufficient condition for the local distinguishability of the orthogonal pure states, and gain the maximal yield of the distillable entanglement. It is shown that the information entropy, the locally distinguishability of quantum states and the distillation of entanglement are closely related.
Quantum entanglement of unitary operators on bi-partite systems  [PDF]
X. Wang,P. Zanardi
Physics , 2002, DOI: 10.1103/PhysRevA.66.044303
Abstract: We study the entanglement of unitary operators on $d_1\times d_2$ quantum systems. This quantity is closely related to the entangling power of the associated quantum evolutions. The entanglement of a class of unitary operators is quantified by the concept of concurrence.
Experimental detection of entanglement via witness operators and local measurements  [PDF]
O. Guehne,P. Hyllus,D. Bruss,A. Ekert,M. Lewenstein,C. Macchiavello,A. Sanpera
Physics , 2002, DOI: 10.1080/09500340308234554
Abstract: In this paper we address the problem of detection of entanglement using only few local measurements when some knowledge about the state is given. The idea is based on an optimized decomposition of witness operators into local operators. We discuss two possible ways of optimizing this local decomposition. We present several analytical results and estimates for optimized detection strategies for NPT states of 2x2 and NxM systems, entangled states in 3 qubit systems, and bound entangled states in 3x3 and 2x4 systems.
Local Operators in Massive Quantum Field Theories  [PDF]
Anni Koubek
Physics , 1995, DOI: 10.1007/BFb0102567
Abstract: Contribution to the proceedings of Schladming 1995. A review of the form factor approach and its utilisation to determine the space of local operators of integrable massive quantum theories is given. A few applications are discussed.
Local Entanglement and quantum phase transition in spin models  [PDF]
Shi-Jian Gu,Guang-Shan Tian,Hai-Qing Lin
Physics , 2005, DOI: 10.1088/1367-2630/8/4/061
Abstract: Due to the phase interference of electromagnetic wave, one can recover the total image of one object from a small piece of holograph, which records the interference pattern of two laser light reflected from it. Similarly, the quantum superposition principle allows us to derive the global phase diagram of quantum spin models by investigating a proper local measurement. In the present paper, we study the two-site entanglement in the antifferomagnetic spin models with both spin-1/2 and 1. We show that its behaviors reveal some important information on the global properties and the quantum phase transition of these systems.
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