Quantum Communication Complexity

Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In some cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement.     

How much quantum noise of amplifiers is detrimental to entanglement

We analyze the effect of the quantum noise of an amplifier on the entanglement properties of an input state. We consider both phase insensitive and phase sensitive amplification and specialize to Gaussian states for which entanglement measures are well developed. In the case of phase insensitive amplification in which both the modes are symmetrically amplified, we find that the entanglement in the output state vanishes if the intensity gain exceeds a limiting value 2/(1+exp[-E_N]) where E_N is the logarithmic negativity of the input state which quantifies the initial entanglement between the two modes. The entanglement between the two modes at the output is found to be more robust if only one mode is amplified.     

Entanglement sudden death in qubit-qutrit systems

We demonstrate the existence of entanglement sudden death (ESD), the complete loss of entanglement in finite time, in qubit-qutrit systems. In particular, ESD is shown to occur in such systems initially prepared in a one-parameter class of entangled mixed states and then subjected to local dephasing noise. Together with previous results, this proves the existence of ESD for some states in all quantum systems for which rigorously defined mixed-state entanglement measures have been identified. We conjecture that ESD exists in all quantum systems prepared in appropriate bipartite states.     

Entanglement in the linear-chain Heisenberg antiferromagnet Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript>

Quantum correlations are generally impossible to address directly in bulk systems. Quantum measures extended only to a few number of parties can be discussed in practice. In the present work we study a cluster of spins belonging to a compound whose structure is that of a quantum magnet. We reproduce at a much smaller scale the experimental outcomes and then we study the role of quantum correlations there. A macroscopic entanglement witness has been introduced in order to reveal quantum correlations at nonzero temperatures. The critical point beyond which entanglement is zero is found at T _c = 15 K.     

Monogamy and entanglement in tripartite quantum states

We present an interesting monogamy equation for (2⊗2⊗n)-dimensional pure states, by which a quantity is found to characterize the tripartite entanglement with the GHZ type and W type entanglements as a whole. In particular, we, for the first time, reveals that for any quantum state of a pair of qubits, the difference between the two remarkable entanglement measures, concurrence and negativity, characterizes the W type entanglement of tripartite pure states with the two-qubit state as reduced density.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Multipartite non-locality and entanglement signatures of a field-induced quantum phase transition

Quantum correlation measures are limited in practice to a few number of parties, since no general theory is still capable of reaching the thermodynamic limit. In the present work we study entanglement and non-locality for a cluster of spins belonging to a compound that displays a magnetocaloric effect. A quantum phase transition (QPT) is induced by an external magnetic field B, in such a way that the corresponding quantum fluctuations are reproduced at a much smaller scale than the experimental outcomes, and then described by means of the aforementioned quantum measures.     

Correlation Dynamics of Three-Qubit System Under a Classical Dephasing Environment

By starting from the stochastic Hamiltonian of the three correlated spins and modeling their frequency fluctuations as caused by dephasing noisy environments described by Ornstein-Uhlenbeck (OU) processes, we study the dynamics of quantum correlations, including entanglement and quantum discord. Of course, in this article, we use two definitions for the quantum discord (global quantum discord and quantum dissension). We prepared initially our open system with the Greenberger-Horne-Zeilinger (GHZ) and W states and present the exact solutions for evolution dynamics of entanglement and quantum discord between three spins under both Markovian and non-Markovian regime of this classical noise. By comparison the dynamics of entanglement with that of quantum discord we find that entanglement can be more robust than quantum discord against this noise. It is shown that by considering non-Markovian extensions the survival time of correlations prolong. Also, we compare the results of two definitions of the quantum discord and show that the quantum dissension is equal to the global quantum discord for GHZ state, but they are unequal for the W state.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Quantum Correlation Properties Between Two Spatially Separated Atoms in Free Space Reinforced by Incoherent Pumping

Quantum correlation dynamics between two identical and spatially separated atoms in free space is investigated by the use of concurrence C and quantum discord (QD). The behaviors of QD differs in many unexpected ways from the entanglement in this system. Firstly, it shows the situations which the concurrence and QD can behave very differently with a “sudden birth” phenomenon of the former but not of the latter, and QD is only oscillating decays with time and the interqubit distance. We also verify the cases which QD is always greater than the concurrence and the region where the concurrence is vanished but with nonzero values for QD. Meanwhile an unexpected situation which the concurrence is greater than QD under the initial state |eg〉 is analyzed. It is revealed that the quantum correlation based only on QD is expected to be more robust than entanglement which is not suitable for all the initial states under the decoherence environment. Then, by introducing the incoherent pumping, we also study the different properties of the steady-state entanglement and QD about this atomic subsystem. It is shown that the incoherent pumping can overcome the decay of the atoms and the influences about the interqubit distance r ₁₂/λ on the steady-state correlation can make the decay of the concurrence obviously quicker than QD, the life of the steady-state QD is evidently larger than the steady-state entanglement.     

A scheme of quantum repeaters with single atom and cavity-QED

To implement long-distance quantum communication, quantum repeaters have been proposed. The distribution and storage of quantum entanglement are essential to implement quantum repeaters. Here, we propose a new quantum repeaters protocol which is based on single atom-cavity QED. We use simple long-life two-level atoms to store quantum entanglement unlike three-level atoms which are commonly used in other quantum repeaters proposals. The property of long life-time (T₁) and transverse decay time (T₂) between excited level and ground level, such as rare-earth atoms, may store quantum entanglement as long as possible. Modulations of cavity mode and rate of coupling between cavity mode and output mode are also key steps to our scheme. And the efficiency of our protocol is analyzed by quantum trajectory theory.     

Entanglement irreversibility from quantum discord and quantum deficit

We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.     

量子纠缠与宇宙学弗里德曼方程

量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球（a geodesic ball）的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.     

Entanglement Dynamics of the Mixed Two-qubit System in Different Noisy Channels

We investigate the entanglement dynamics of the two-qubit entanglement quantum system when they transmitted through the Pauli channels and the depolarizing channel both independently or collectively. Making use of the concurrence we found that the entanglement of a kind of mixed two-qubit system defined in this paper can be preserved in the collective Pauli σ _y noise channel, but the entanglement of the other kind of mixed two-qubit system can be preserved in the collective Pauli σ _z noise channel. Meanwhile, our quantum systems will undergoing the entanglement sudden death (ESD) in collective depolarizing channel when they return to the maximally entangled Bell states. The reason is the Landblad operators in depolarizing channel are non-commuting operators and this finding is in accord with the previous study.     

The Dynamics of Quantum Correlations Between Two Atoms in Two Coupled Cavities

The dynamics of the quantum correlation between two atoms in two single-mode cavities is studied. For the initial Bell state |Ψ ⁺〉, the quantum consonance is equal to the entanglement, and larger than quantum discord. For the initial Bell state |Φ ⁺〉, the quantum consonance is larger than entanglement, but not larger than quantum discord all the time. As the increase of the cavity-cavity coupling strength, the evolution period of quantum correlation becomes smaller. Consonance is not smooth at some points while cavities are coupled with each other.     

The Dynamics of Quantum Discord and Entanglement of Three Atoms Coupled to Three Spatially Separate Cavities

In this paper, we study the dynamics of quantum discord and entanglement of three identical two-level atoms simultaneously resonantly interacting with three spatially separate single-mode of high-Q cavities respectively. Taking advantage of the depiction quantum discord and entanglement of formation (EoF), we conclude that the discord and entanglement of atoms and cavities can be mediated by changing some parameters and the maximum values of discord and entanglement are independent on the couplings of cavities and atoms. In particular, there also exists quantum discord sudden death as well as entanglement sudden death and the time interval of the former is shorter than that of the later in the proposed quantum system. It is shown that the discord and entanglement of any two atoms among three atoms can be transferred to the corresponding cavities, and there exists discord and entanglement exchanging between the atoms and the corresponding cavities.     

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源. 然而当量子系统与环境相互作用时, 会不可避免地产生消相干导致纠缠下降, 因此保护纠缠不受环境的影响具有重要意义. 振幅衰减是一种典型的衰减机制. 如果探测环境保证没有激发从系统中流出, 即视为对系统的一种弱测量. 本文基于局域脉冲序列和弱测量, 提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案, 保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和Maximal slice态.     

Entanglement distribution and entangling power of quantum gates

Quantum gates, which play a fundamental role in quantum computation and other quantum information processes, are unitary evolution operators Û that act on a composite system, changing its entanglement. In the present contribution, we study some aspects of these entanglement changes. By recourse to a Monte Carlo procedure, we compute the so-called “entangling power” for several paradigmatic quantum gates and discuss results concerning the action of the CNOT gate. We pay special attention to the distribution of entanglement among the several parties involved.     

Two-point versus multipartite entanglement in quantum phase transitions

We analyze correlations between subsystems for an extended Hubbard model exactly solvable in one dimension, which exhibits a rich structure of quantum phase transitions (QPTs). The T = 0 phase diagram is exactly reproduced by studying singularities of single-site entanglement. It is shown how comparison of the latter quantity and quantum mutual information allows one to recognize whether two-point or shared quantum correlations are responsible for each of the occurring QPTs. The method works in principle for any number D of degrees of freedom per site. As a by-product, we are providing a benchmark for direct measures of bipartite entanglement; in particular, here we discuss the role of negativity at the transition.     

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous‐variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous‐variable entanglement and show how to make it. The members of a family of multi‐mode states are found to be truly multi‐party entangled with respect to all their modes. These states also violate multi‐party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi‐party continuous‐variable entanglement. Various quantum communication protocols based on the continuous‐variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous‐variable entanglement swapping. We highlight the similarities and differences between continuous‐variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi‐party generalization of quantum teleportation. This so‐called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no‐cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase‐insensitive amplifier and beam splitters.