Linking quantum discord to entanglement in a measurement

We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one-way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system.     

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.     

Classical information and distillable entanglement

We establish a quantitative connection between the amount of lost classical information about a quantum state and the concomitant loss of entanglement. Using methods that have been developed for the optimal purification of mixed states, we find a class of mixed states with known distillable entanglement. These results can be used to determine the quantum capacity of a quantum channel which randomizes the order of transmitted signals.     

Secure key from bound entanglement

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.     

Quantum communication through an unmodulated spin chain

We propose a scheme for using an unmodulated and unmeasured spin chain as a channel for short distance quantum communications. The state to be transmitted is placed on one spin of the chain and received later on a distant spin with some fidelity. We first obtain simple expressions for the fidelity of quantum state transfer and the amount of entanglement sharable between any two sites of an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the realizable case of an open ended chain with nearest neighbor interactions. The fidelity of quantum state transfer is obtained as an inverse discrete cosine transform and as a Bessel function series. We find that in a reasonable time, a qubit can be directly transmitted with better than classical fidelity across the full length of chains of up to 80 spins. Moreover, our channel allows distillable entanglement to be shared over arbitrary distances.     

All nonclassical correlations can be activated into distillable entanglement

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.     

The Local Orthogonality Between Quantum States and Entanglement Decomposition

In the paper, we show that when a quantum state can be decomposed as a convex combination of locally orthogonal mixed states, its entanglement can be decomposed into the entanglement of these mixed states without losing them. The obtained result generalizes a corresponding one proved by Horodecki (Acta Phys. Slov. 48, 141 1998). But, for the entanglement cost it requires certain conditions for holding the decomposition, and the distillable entanglement only has a week result as inequality. Finally, we presented an example to show that the conditions of our conclusions are existence.     

Nonadditivity of bipartite distillable entanglement follows from a conjecture on bound entangled Werner states

Assuming the validity of a conjecture given by DiVincenzo et al. [Phys. Rev. A 61, 062312 (2000)] and by Dür et al. [Phys. Rev. A 61, 062313 (2000)], we show that the distillable entanglement for two bipartite states, each of which individually has zero distillable entanglement, can be nonzero. We show that this also implies that the distillable entanglement is not a convex function. Our example consists of the tensor product of a bound entangled state based on an unextendible product basis with an entangled Werner state which lies in the class of conjectured undistillable states.     

On entanglement distillation and quantum error correction for unknown states and channels

We consider the problem of invariance of distillable entanglement D and quantum capacities Q under erasure of information about single copy of quantum state or channel respectively. We argue that any 2 ⊗N two-way distillable state is still two-way distillable after erasure of single copy information. For some known distillation protocols the obtained two-way distillation rate is the same as if Alice and Bob knew the state from the very beginning. The isomorphism between quantum states and quantum channels is also investigated. In particular it is pointed out that any transmission rate down the channel is equal to distillation rate with formal LOCC-like superoperator that uses in general nonphysical Alice actions. This allows to we prove that if given channel Λ has nonzero capacity (Q _→ or Q _⟺) then the corresponding quantum state ϱ(Λ) has nonzero distillable entanglement (D _→ or D _⟺). Follwoing the latter arguments are provided that any channel mapping single qubit into N level system allows for reliable two-way transmission after erasure of information about single copy. Some open problems are discussed.     

Unified approach to quantum capacities: towards quantum noisy coding theorem

Based on a unified approach to all kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information. Moreover, we show that if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities. The inequality also implies that the decrease of distillable entanglement due to the mixing process does not exceed that of the corresponding loss of information about a system.     

Entanglement of the Antisymmetric State

We analyse the entanglement of the antisymmetric state in dimension d × d and present two main results. First, we show that the amount of secrecy that can be extracted from the state is low, more precisely, the distillable key is bounded by O(\frac1d){O(\frac{1}{d})}. Second, we show that the state is highly entangled in the sense that a large number of ebits are needed in order to create the state: entanglement cost is larger than a constant, independent of d. The second result is shown to imply that the regularised relative entropy with respect to separable states is also lower bounded by a constant. Finally, we note that the regularised relative entropy of entanglement is asymptotically continuous in the state.     

Information Theories with Adversaries,Intrinsic Information,and Entanglement

There are aspects of privacy theory that are analogous to quantum theory. In particular one can define distillable key and key cost in parallel to distillable entanglement and entanglement cost. We present here classical privacy theory as a particular case of information theory with adversaries, where similar general laws hold as in entanglement theory. We place the result of Renner and Wolf—that intrinsic information is lower bound for key cost—into this general formalism. Then we show that the question of whether intrinsic information is equal to key cost is equivalent to the question of whether Alice and Bob can create a distribution product with Eve using I_M bits of secret key. We also propose a natural analogue of relative entropy of entanglement in privacy theory and show that it is equal to the intrinsic information. We also provide a formula analogous to the entanglement of formation for classical distributions. It is our pleasure to dedicate this paper to Asher Peres on the occasion of his seventieth birthday.     

Experimental extraction of secure correlations from a noisy private state

We report experimental generation of a noisy entangled four-photon state that exhibits a separation between the secure key contents and distillable entanglement, a hallmark feature of the recently established quantum theory of private states. The privacy analysis, based on the full tomographic reconstruction of the prepared state, is utilized in a proof-of-principle key generation. The inferiority of distillation-based strategies to extract the key is exposed by an implementation of an entanglement distillation protocol for the produced state.     

Quantum one-time pad in the presence of an eavesdropper

A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.     

Quantum key distribution based on arbitrarily weak distillable entangled states

States with private correlations but little or no distillable entanglement were recently reported. Here, we consider the secure distribution of such states, i.e., the situation when an adversary gives two parties such states and they have to verify privacy. We present a protocol which enables the parties to extract from such untrusted states an arbitrarily long and secure key, even though the amount of distillable entanglement of the untrusted states can be arbitrarily small.     

光学体系宏观-微观纠缠及其在量子密钥分配中的应用

宏观-微观纠缠最早起源于“薛定谔的猫”思想实验, 是指在宏观体系与微观体系之间建立量子纠缠. 实现宏观-微观纠缠可以利用多种物理体系来完成, 本文重点介绍了在光学体系中制备和检验宏观-微观纠缠的发展过程. 从最初的受激辐射单光子量子克隆到光学参量放大, 再到相空间的位移操作, 实验上制备宏观-微观纠缠的方法取得了长足的进步. 利用非线性光学参量放大过程制备的宏观-微观纠缠的光子数可以达到10⁴量级, 人眼已经可以观察到, 因此使用人眼作为探测器来检验宏观-微观纠缠的实验开始出现. 但随后人们意识到, 粗精度的光子数探测器, 例如人眼, 无法严格判定宏观-微观纠缠的存在. 为了解决这个难题, 提出了一种巧妙的方法, 即在制备宏-微观纠缠后, 利用局域操作过程将宏观态再变为微观态, 通过判定微观纠缠存在的方法来判定宏微观纠缠的存在. 之后相空间的位移操作方法将宏观态的粒子数提高到10⁸, 并且实现了纠缠的严格检验. 利用光机械实现宏观-微观纠缠的方案也被提出. 由于量子密钥分配中纠缠是必要条件, 而宏观-微观纠缠态光子数较多这一优势可能会对量子密钥分配的传输距离有所提高. 本文介绍了利用相位纠缠的相干态来进行量子秘钥分配的方案, 探讨了利用宏观-微观纠缠实现量子密钥分配的可能性.     

纠缠的纯化和提取

纠缠的纯化和提取在量子信息的理论和实验上都是一个重要的方向，简单回顾了这个方向上的一些主要进展，并重点介绍了有限个拷贝情况下的纠缠提取。提出了准分离态和提取子空间的概念，得到了从一个混合态的有限个拷贝中提取纯纠缠态的必要条件及充要条件；并得到了有限个拷贝情况下的最有效的提取方案；考虑了这些结论在无限个拷贝的情况下的推广。     

Superactivation of bound entanglement

We show that, in a multiparty setting, two nondistillable (bound-entangled) states tensored together can make a distillable state. This is an example of true superadditivity of distillable entanglement. We also show that unlockable bound-entangled states cannot be asymptotically unentangled, providing the first proof that some states are truly bound-entangled in the sense of being both nondistillable and nonseparable asymptotically.     

Optimizing quantum correlation dynamics by weak measurement in dissipative environment

We investigate the protection of quantum correlations of two qubits in independent vacuum reservoirs by means of weak measurements. It is found that the weak measurement can reduce the amount of quantum correlation for one type of initial state at the beginning in a non-Markovian environment and meanwhile it can reduce the occurrence time of entanglement sudden death(ESD) in the process of time evolution. In a Markovian environment, the quantum entanglements of the two kinds of initial states decay rapidly and the weak measurement can further weaken the quantum entanglement,therefore in this case the entanglement cannot be optimized in the evolution process.     

Locking entanglement with a single qubit

We study the loss of entanglement of a bipartite state subjected to discarding or measurement of one qubit. Examining behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, logarithmic negativity, and one-way distillable entanglement are lockable measures in that they can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically noncontinuous measure is lockable. As a consequence, all the convex-roof measures can be locked. The relative entropy of entanglement is shown to be a nonlockable measure.