2D quantum gravity from quantum entanglement

In quantum systems with many degrees of freedom the replica method is a useful tool to study the entanglement of arbitrary spatial regions. We apply it in a way that allows them to backreact. As a consequence, they become dynamical subsystems whose position, form, and extension are determined by their interaction with the whole system. We analyze, in particular, quantum spin chains described at criticality by a conformal field theory. Its coupling to the Gibbs' ensemble of all possible subsystems is relevant and drives the system into a new fixed point which is argued to be that of the 2D quantum gravity coupled to this system. Numerical experiments on the critical Ising model show that the new critical exponents agree with those predicted by the formula of Knizhnik, Polyakov, and Zamolodchikov.     

Extended entanglement to quantum networks

Connecting individual quantum systems through quantum channels leads to develop quantum networks crucial to perform multipartite communication or quantum cryptography. We present two techniques to generate entanglement among different parties at larger scale. In the first approach cavity QED technique is used to produce extended entanglement in atomic internal and external degrees of freedom. In this scheme we entangle two tagged atoms in their momentum state with cavity fields. Later, interaction of two auxiliary atoms with the two cavity fields in non-dispersive and dispersive fashion transforms the atoms–fields entanglement to atoms–atoms entanglement. Quantum measurement on auxiliary atoms generates extended entangled state in atomic degrees of freedom. In the second approach we take three cavities in which the two cavities have separate entangled state with third cavity in two modes which are distinguishable. Applying quantum measurement process on third cavity, we develop extended entangled state among the three cavities. We provide experimental parameters to realize the work in laboratory experiment.     

Quantum entanglement and quantum operation

It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction. Supported by the National Fundamental Research Program of China (Grant No. 2001CB309306), the National Natural Science Foundation of China (Grant Nos. 60621064 and 10674127) and the Innovation Funds from Chinese Academy of Sciences     

Complete quantum measurements break entanglement

A complete measurement of a quantum observable (POVM) is a measurement of the maximally refined version of the POVM. Complete measurements give information on multiplicities of measurement outcomes and can be used as state preparation procedures. Moreover, any observable can be measured completely. In this Letter, we show that a complete measurement breaks entanglement completely between the system, ancilla and their environment. Finally, consequences for the quantum Zeno effect and complete position measurements are discussed.     

Sophisticated quantum search without entanglement

The basic principle of entanglement processing says that entanglement cannot increase under local operations and classical communication. Based on this principle, we show that any entanglement measure E suitable for the regime of a high number of identically prepared entangled pairs satisfies ED < or = E < or = EF, where ED and EF are the entanglement of distillation and formation, respectively. Moreover, we exhibit a theorem establishing a very general form of bounds for distillable entanglement.     

General approach to quantum entanglement

We examine quantum entanglement as a physical phenomenon independent of specific problems of quantum information technologies. Within the dynamic symmetry approach, we briefly discuss the role of quantum fluctuations in formation of entangled states, including single-particle entanglement, relativity of entanglement with respect to the choice of basic observables, and stabilization of robust entanglement.     

Measuring entanglement using quantum quenches

We show that block entanglement entropies in one-dimensional systems close to a quantum critical point can, in principle, be measured in terms of the population of low-lying energy levels following a certain type of local quantum quench.     

Remote entanglement for quantum networks

Quantum networks are distributed many-body quantum systems with tailored topology and controlled information exchange. We present two schemes to generate remote entanglement, in atomic external degrees of freedom and between cavities. In the first scheme, we entangle two atoms with their cavities in momentum space through Bragg diffraction. Thereafter, in order to trace out the cavities, we let resonantly interact an auxiliary atom with each cavity. In the last, we perform quantum measurement on two auxiliary atoms and get remote entangled state in atomic external degrees of freedom. In the second scheme, we have a three cavities system. The other two cavities, A and B, are entangled with indistinguishable modes of cavity, C. Performing quantum measurement on third cavity, C, we disentangle it from the system and the cavities, A and B, become entangled.     

Double entanglement and quantum cryptography

We propose a quantum transmission based on bi-photons, which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when he steels the same information. Received 23 July 2001 / Received in final form 30 November 2001 Published online 24 September 2002     

Power of entanglement in quantum communication

A communication channel is a physical system that transfers information from one place to another. Examples of communication channels include wires, optical fibers, and chains of spins that propagate spin waves through a medium. This Letter shows that the power-limited communication capacity of a multimode optical fiber or a set of parallel spin chains can be enhanced by introducing nonlinear couplings between the modes or chains. In particular, M coupled, entangled modes can send M bits in the same time it takes a single mode to send a single bit, and in the same time it takes M uncoupled, unentangled modes to send sqrt[M] bits.     

Spin bath decoherence of quantum entanglement

We study an analytically solvable model for decoherence of a two spin system embedded in a large spin environment. As a measure of entanglement, we evaluate the concurrence for the Bell states (Einstein-Podolsky-Rosen pairs). We find that while for two separate spin baths all four Bell states lose their coherence with the same time dependence, for a common spin bath, two of the states decay faster than the others. We explain this difference by the relative orientation of the individual spins in the pair. We also examine how the Bell inequality is violated in the coherent regime. Both for one bath and two bath cases, we find that while two of the Bell states always obey the inequality, the other two violate the inequality at early times.     

Non-extensive statistical entropy,quantum groups and quantum entanglement

In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with S_Uq(2)$S{U}_q\left(2\right)$ symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with S_Uq(2)$S{U}_q\left(2\right)$ symmetry and conducted an investigation of quantum entanglement.     

Simulating maximal quantum entanglement without communication

It is known that all causal correlations between two parties which output each 1 bit, a and b, when receiving each 1 bit, x and y, can be expressed as convex combinations of local correlations (i.e., correlations that can be simulated with local random variables) and nonlocal correlations of the form a+b=xy mod 2. We show that a single instance of the latter elementary nonlocal correlation suffices to simulate exactly all possible projective measurements that can be performed on a maximally entangled state of two qubits, with no communication needed at all. This elementary nonlocal correlation thus defines some unit of nonlocality, which we call a nl bit.     

Generalized nonadditive entropies and quantum entanglement

We examine the inference of quantum density operators from incomplete information by means of the maximization of general nonadditive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1 / 2 system, the formalism allows one to avoid fake entanglement for data based on the Bell-Clauser-Horne-Shimony-Holt observable, and, in general, on any set of Bell constraints. Particular results obtained with the Tsallis entropy and with an introduced exponential entropic form are also discussed.     

Quantum entanglement in elliptical quantum corrals

Quantum corrals present interesting properties due to the combination of confinement and, in the case of elliptical corrals, to their focalizing properties. We study the case when two magnetic impurities are added to the non-interacting corral, where they interact via a superexchange AF interaction J with the surface electrons in the ellipse. Previous results showed that, when both impurities are located at the foci of the system, they experience an enhanced magnetic interaction, as compared to the one they would have in an open surface. For small J and even filling, they are locked in a singlet state, which weakens for larger values of this parameter. When J is much larger than the hopping parameter of the electrons in the ellipse, both spins decorrelate while forming a local singlet with the electrons of the ellipse, thus presenting a confined RKKY–Kondo transition.We interpret this behaviour by means of the von Neumann entropy between the localized impurities and the itinerant electrons of the ellipse: for small J the entropy is nearly zero while for large J it is maximum. In addition, the local density of states provides us with a concrete experimental tool for detecting the Kondo regime.     

Quantum entanglement and quantum computational algorithms

The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We demonstrate that the one- and the two-bit Deutsch-Jozsa algorithm does not require entanglement and can be mapped onto a classical optical scheme. It is only for three and more input bits that the DJ algorithm requires the implementation of entangling transformations and in these cases it is impossible to implement this algorithm classically.     

Efficient entanglement purification in quantum repeaters

We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F>1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.