We experimentally show how classical correlations can be turned into quantum entanglement, via the presence of non-unital local noise and the action of a CNOT gate. We first implement a simple two-qubit protocol in which entanglement production is not possible in the absence of local non-unital noise, while entanglement arises with the introduction of noise, and is proportional to the degree of noisiness. We then perform a more elaborate four-qubit experiment, by employing two hyperentangled photons initially carrying only classical correlations. We demonstrate a scheme where the entanglement is generated via local non-unital noise, with the advantage to be robust against local unitaries performed by an adversary.
Quantum entanglement is notorious for being a very fragile resource. Significant efforts have been put into the study of entanglement degradation in the presence of a realistic noisy environment. Here, we present a theoretical and an experimental study of the decoherence properties of entangled pairs of qubits. The entanglement dynamics of maximally entangled qubit pairs is shown to be related in a simple way to the noise representation in the Bloch sphere picture. We derive the entanglement level in the case when both qubits are transmitted through any arbitrary unital Pauli channel, and comp…
We define an entanglement witness in a composite quantum system as an observable having nonnegative expectation value in every separable state. Then a state is entangled if and only if it has a negative expectation value of some entanglement witness. Equivalent representations of entanglement witnesses are as nonnegative biquadratic forms or as positive linear maps of Hermitian matrices. As reported elsewhere, we have studied extremal entanglement witnesses in dimension $3\times 3$ by constructing numerical examples of generic extremal nonnegative forms. These are so complicated that we do not…
Negative quantum conditional entropy states are key ingredients for information theoretic tasks such as superdense coding, state merging and one-way entanglement distillation. In this work, we ask: how does one detect if a channel is useful in preparing negative conditional entropy states? We answer this question by introducing the class of A-unital channels, which we show are the largest class of conditional entropy non-decreasing channels. We also prove that A-unital channels are precisely the completely free operations for the class of states with non-negative conditional entropy. Furthermo…
We study the problem of optimal preparation of a bipartite entangled state, which remains entangled the longest time under action of local qubit noises. We show that for unital noises such a state is always maximally entangled, whereas for nonunital noises, it is not. We develop a decomposition technique relating nonunital and unital qubit channels, based on which we find the explicit form of the ultimately robust state for general local noises. We illustrate our findings by amplitude damping processes at finite temperature, for which the ultimately robust state remains entangled up to two tim…
We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor product space. If a linear map is entanglement breaking after finite iterations, we say the map has a finite index of separability. In particular we show that every unital PPT-channel becomes entanglement breaking after a finite number of iterations. It turns out that the class of unital channels that have finite index of separability is a dens…
We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channel this is indeed the case: the amount of quantum correlations can only decrease under the action of unital channels. However, non-unital channels (e.g. such as dissipation) can create quantum correlations for some initially classical state. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintu…
In this paper we study the $C^*$-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of $C^*$-extreme points are discussed. By establishing a Radon-Nikodym type theorem for a class of EB-maps we give a complete description of the $C^*$-extreme points. It is shown that a unital EB-map $Φ:M_{d_1}\to M_{d_2}$ is $C^*$-extreme if and only if it has Choi-rank equal to $d_2$. Finally, as a direct consequence of the Holevo form of EB-maps, we derive a noncommutative analogue of the Krein-Milman theorem for $C^*$-convexity of the…
We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a theorem to reduce LOCC via a local unital qubit channel to local filtering. We also present an optimal protocol based on beam splitters and a quantum nondemolition (QND) measurement on photons. Even if we replace the QND measurement with photon detectors, the protocol outperforms known entanglement generation schemes.
The measurement outcomes of two incompatible observables on a particle can be precisely predicted when it is maximally entangled with a quantum memory, as quantified recently [Nature Phys. 6, 659 (2010)]. We explore the behavior of the uncertainty relation under the influence of local unital and nonunital noisy channels. While the unital noises only increase the amount of uncertainty, the amplitude-damping nonunital noises may amazingly reduce the amount of uncertainty in the long-time limit. This counterintuitive phenomenon could be justified by different competitive mechanisms between quantu…
In quantum key distribution, one conservatively assumes that the eavesdropper Eve is restricted only by physical laws, whereas the legitimate parties, namely the sender Alice and receiver Bob, are subject to realistic constraints, such as noise due to environment-induced decoherence. In practice, Eve too may be bound by the limits imposed by noise, which can give rise to the possibility that decoherence works to the advantage of the legitimate parties. A particular scenario of this type is one where Eve can't replace the noisy communication channel with an ideal one, but her eavesdropping chan…
We study reachable sets of open n-qubit quantum systems, whose coherent parts are under full unitary control, by adding as a further degree of incoherent control switchable Markovian noise on a single qubit. In particular, adding bang-bang control of amplitude damping noise (non-unital) allows the dynamic system to act transitively on the entire set of density operators. Thus one can transform any initial quantum state into any desired target state. Adding switchable bit-flip noise (unital) instead suffices to get all states majorised by the initial state. Our open-loop optimal control package…
Gravity-mediated entanglement via infinite-dimensional systems
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院维也纳量子科学与技术中心）；Department of Science and Industry Systems, University of South-Eastern Norway（挪威东南大学科学与产业系统系）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
Fujian Key Laboratory of Quantum Information and Quantum Optics, Fuzhou University（福州大学量子信息与量子光学福建省重点实验室）；Department of Physics, Fuzhou University（福州大学物理系）
When a composite quantum state interacts with its surroundings, both quantum coherence of individual particles and quantum entanglement will decay. We have shown that under vacuum noise, i.e., during spontaneous emission, two-qubit entanglement may terminate abruptly in a finite time [T. Yu and J. H. Eberly, \prl {93}, 140404 (2004)], a phenomenon termed entanglement sudden death (ESD). An open issue is the behavior of mixed-state entanglement under the influence of classical noise. In this paper we investigate entanglement sudden death as it arises from the influence of classical phase noise …
We study entanglement dynamics in the presence of correlated environmental noises. Specifically, we investigate the quantum entanglement dynamics of two spins in the presence of correlated classical white noises, deriving Markov master equation and obtaining explicit solutions for several interesting classes of initial states including Bell states and X form density matrices. We show how entanglement can be enhanced or reduced by the correlation between the two participating noises.
We propose a method to improve the performance of two entanglement-based continuous-variable quantum key distribution protocols using noiseless linear amplifiers. The two entanglement-based schemes consist of an entanglement distribution protocol with an untrusted source and an entanglement swapping protocol with an untrusted relay. Simulation results show that the noiseless linear amplifiers can improve the performance of these two protocols, in terms of maximal transmission distances, when we consider small amounts of entanglement, as typical in realistic setups.
We address the problem of the robustness of entanglement of bipartite systems (qubits) interacting with dynamically independent environments. In particular, we focus on characterization of so-called local entanglement-annihilating two-qubit channels, which set the maximum permissible noise level allowing to perform entanglement-enabled experiments. The differences, but also subtle relations between entanglement-breaking and local entanglement-annihilating channels are emphasized. A detailed characterization of latter ones is provided for a variety of channels including depolarizing, unital, (g…
Entanglement and entanglement-assisted are useful resources to enhance the mutual information of the Pauli channels, when the noise on consecutive uses of the channel has some partial correlations. In this paper, We study quantum communication channels with correlated noise and derive a general expression for the mutual information of quantum channel, for the product, maximally entangled state coding and entanglement-assisted systems with correlated noise in the Pauli quantum channels. Hence, we suggest more efficient coding in the entanglement-assisted systems for the transmission of classica…
Two two-level atoms within a leaky optical cavity is driven by two independent external optical white noise fields. We investigate how entanglement between two atoms arises in such a situation. The steady state entanglement of two atoms is also investigated. A stochastic-resonance-like behavior of entanglement is revealed. Finally, the Bell violation between atoms is discussed.
The ping-pong protocol adapted for quantum key distribution is studied in the trusted quantum noise scenario, wherein the legitimate parties can add noise locally. For a well-studied attack model, we show how non-unital quantum non-Markovianity of the added noise can improve the key rate. We also point out that this noise-induced advantage cannot be obtained by Alice and Bob by adding local classical noise to their post-measurement data.
Correlated, non-Markovian noise is present in many solid-state systems employed as hosts for quantum information technologies, significantly complicating the realistic theoretical description of these systems. In this regime, the effects of noise on sequences of quantum gates cannot be described by concatenating isolated quantum operations if the environmental correlation times are on the scale of the typical gate durations. The filter function formalism has been successful in characterizing the decay of coherence under the influence of such classical, non-Markovian environments and here we sh…
The disentangling effect of repeated applications of the bit flip channel (I\otimesσ_x) on bipartite qubit systems is analyzed. It is found that the rate of loss of entanglement is not uniform over all states. The distillable entanglement of maximally entangled states decreases faster than that of less entangled states. The analysis is also generalized to noise channels of the form n.sigma.
Motivated by the results of C. Macchiavello and G. M. Palma on entanglement-enhanced information transmission over a quantum channel with correlated noise, we demonstrate how the entanglement teleportation scheme of J. Lee and M. S. Kim gives rise to two uncorrelated generalized depolarizing channels. In an attempt to find a teleportation scheme which yields two correlated generalized depolarizing channels, we discover a novel teleportation scheme, which allows one to learn about the entanglement in an entangled pure input state, but without decreasing the amount of entanglement associated wit…
We discuss the generation of entangled states of two two-level atoms coupled simultaneously with a dissipated atom. The dissipation of the atom is supposed to come from its coupling to a noise with adjustable intensity. We describe how the entanglement between the atoms arise in such a situation, and wether a noise except the white one could help preparation of entanglement. Besides, we confirm that the entanglement is maximized for intermediate values of the noise intensity, while it is a monotonic function of the spontaneous rates. This resembles the phenomenon of stochastic resonance and sh…
This paper is to investigate the effects of quantum noises on entanglement localization by taking an example of reducing a three-qubit Greenberger-Horne-Zeilinger (GHZ) state to a two-qubit entangled state. We consider, respectively, two types of quantum decoherence, i.e., amplitude-damping and depolarizing decoherence, and explore the best von Neumann measurements on one of three qubits of the triple GHZ state for making the amount of entanglement of the collapsed bipartite state be as large as possible. The results indicate that different noises have different impacts on entanglement localiz…
We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two qubit/qudit and three qubit entangled states. In explicit examples of t…
We study the simplest optomechanical system in the presence of laser phase noise using the covariance matrix formalism. We show that the destructive effect of the phase noise is especially strong in the bistable regime. This explains why ground state cooling is still possible in the presence of phase noise, as it happens far away from the bistable regime. On the other hand, the optomechanical entanglement is strongly affected by phase noise.
The dynamical map of entanglement and mixedness in four-qubit maximally entangled GHZ state paired with classical channels driven by fractional Gaussian noise is investigated. The qubit-channel coupling is assumed in four distinct ways: common, bipartite, tripartite, and independent local channel-qubit configurations comprising single, double, triple, or independent noisy sources. Using entanglement witness, negativity, purity and von Neumann entropy, except for the independent configuration, we show that indefinite entanglement and purity preservation may be simulated in multipartite GHZ-like…
We show that entanglement is a useful resource to enhance the mutual information of the depolarizing channel when the noise on consecutive uses of the channel has some partial correlations. We obtain a threshold in the degree of memory, depending on the shrinking factor of the channel, above which a higher amount of classical information is transmitted with entangled signals.
Genuineness and distillability of entanglement play a key role in quantum information tasks, and they are easily disturbed by the noise. We construct a family of multipartite states without genuine entanglement and distillability sudden death across every bipartition, respectively. They are realized by establishing the noise as the multipartite high dimensional Pauli channels. Further, we construct a locally unitary channel as another noise such that the multipartite Greenberger-Horne-Zeilinger state becomes the D{ü}r's multipartite state. We also show that the quantum information masking stil…
Statistical Characterization of Entanglement Degradation Under Markovian Noise in Composite Quantum Systems
Scuola Normale Superiore（高等师范学院）；Center for Life Nano- & Neuro-Science, Italian Institute of Technology (IIT)（意大利理工学院生命纳米与神经科学中心）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Mathematics, University of Bologna（博洛尼亚大学数学系）；NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR（NEST，高等师范学院和CNR纳米科学研究所）
Recent experimental progress in prolonging the coherence time of a quantum system prompts us to explore the behavior of quantum entanglement at the beginning of the decoherence process. The response of the entanglement under an infinitesimal noise can serve as a signature of the robustness of entangled states. A crucial problem of this topic in multipartite systems is to compute the degree of entanglement in a mixed state. We find a family of global noise in three-qubit systems, which is composed of four W states. Under its influence, the linear response of the tripartite entanglement of a sym…
The finite time disentanglement or entanglement sudden death, when only one part of the composite system is subjected to a single noise, is examined. While it is shown that entanglement sudden death can occur when a part of the entangled mixed state is subjected to either amplitude noise or phase noise, local action of either of them does not cause entanglement sudden death in pure entangled states. In contrast, depolarizing noise is shown to have an abilitiy to cause sudden death of entanglement even in pure entangled states, when only one part of the state is exposed to it. The result is ill…
We experimentally demonstrate a general criterion to identify entangled states useful for the estimation of an unknown phase shift with a sensitivity higher than the shot-noise limit. We show how to exploit this entanglement on the examples of a maximum likelihood as well as of a Bayesian phase estimation protocol. Using an entangled four-photon state we achieve a phase sensitivity clearly beyond the shot-noise limit. Our detailed comparison of methods and quantum states for entanglement enhanced metrology reveals the connection between multiparticle entanglement and sub-shot-noise uncertainty…
We present an efficient quantum entanglement distribution over an arbitrary collective-noise channel. The basic idea in the present scheme is that two parties in quantum communication first transmit the entangled states in the frequency degree of freedom which suffers little from the noise in an optical fiber. After the two parties share the photon pairs, they add some operations and equipments to transfer the frequency entanglement of pairs into the polarization entanglement with the success probability of 100\%. Finally, they can get maximally entangled polarization states with polarization …
Entanglement recovery by reversing the effect of noise in quantum repeater
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Ewha Womans University（梨花女子大学）；Korea Institute for Advanced Study（韩国高等研究院）；Korea University of Science and Technology（韩国科学技术院）；Pohang University of Science and Technology (POSTECH)（浦项科技大学）
