The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical correlation which is coded in the mixed state of the physical system and a new correlation, to be called probabilistic entanglement, which may occur also at pure states. We examine to what extent this characterization of correlations can be applied to quantum mechanics. Explicit calculations on simple examples outline that a same quantum state can show only classical correlations or only entanglement depending on its statistical content; situations may also arise in which the two kinds of correlations compensate each other.
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.
We consider composability of quantum channels from a limited amount of entanglement via local operations and classical communication (LOCC). We show that any $k$-partially entanglement breaking channel can be composed from an entangled state with Schmidt number of $k$ via one-way LOCC. From the entanglement assisted construction we can reach an alternative definition of partially entanglement breaking channels.
We investigate the entanglement dynamics of a quantum system consisting of two-level atoms interacting with vacuum or thermal fields with classical driving fields. We find that the entanglement of the system can be improved by adjusting the classical driving field. The influence of the classical field and the purity of the initial state on the entanglement sudden death is also studied. It is shown that the time of entanglement sudden death can be controlled by the classical driving fields. Particularly, the entanglement sudden death phenomenon will disappear if the classical driving fields are…
Bipartite operations underpin both classical communication and entanglement generation. Using a superposition of classical messages, we show that the capacity of a two-qubit operation for error-free entanglement-assisted bidirectional classical communication can not exceed twice the entanglement capability. In addition we show that any bipartite two-qubit operation can increase the communication that may be performed using an ensemble by twice the entanglement capability.
We show that quantum entanglement has a very close classical analogue, namely secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogies follow. In particular teleportation is analogous to the one-time-pad, the concept of ``pure state'' exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single copy entangleme…
Phenomena induced by the existence of entanglement, such as nonlocal correlations, exhibit characteristic properties of quantum mechanics distinguishing from classical theories. When entanglement is accompanied by classical communication, it enhances the power of quantum operations jointly performed by two spatially separated parties. Such a power has been analyzed by the gap between the performances of joint quantum operations implementable by local operations at each party connected by classical communication with and without the assistance of entanglement. In this work, we present a new for…
We analyze the connections between entanglement dynamics and classical trajectories in a semiclassi-cal regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on classical invariant tori and such phenomenon is closely related to the power spectra of classical trajectories. Classical power spectrum with a larger number of frequency com-ponents corresponds to larger entanglement. We introduce a frequency entropy to describe the classical frequency distribution, and find that there is good correspondence between the classi…
It is well known that entanglement is the resource of quantum teleportation. Teleportation can be accomplished using classical correlation (CC) with a teleportation fidelity (TF) upto $2/3$. In the present work we have studied TF, entanglement and CC in the presence of decoherence. We have found that significant increment of CC with respect to the strength of decoherence can lead TF in the non-classical region while entanglement is decreasing. We have also studied the protection of TF and entanglement using the technique of weak measurement and reverse weak measurement (WMRWM). Here we found t…
Entanglement bits or ``ebits'' have been proposed as a quantitative measure of a fundamental resource in quantum information processing. For such an interpretation to be valid, it is important to show that the same number of ebits in different forms or concentrations are inter-convertible in the asymptotic limit. Here we draw attention to a very important but hitherto unnoticed aspect of entanglement manipulation --- the classical communication cost. We construct an explicit procedure which demonstrates that for bi-partite pure states, in the asymptotic limit, entanglement can be concentrated …
We present an improved protocol for entanglement purification of bipartite mixed states. The protocol requires two-way classical communication and hence implies an improved lower bound on the quantum capacity with two-way classical communication of the quantum depolarizing channel.
We investigate entanglement for a composite closed system endowed with a scaling property allowing to keep the dynamics invariant while the effective Planck constant hbar_eff of the system is varied. Entanglement increases as hbar_eff goes to 0. Moreover for sufficiently low hbar_eff the evolution of the quantum correlations, encapsulated for example in the quantum discord, can be obtained from the mutual information of the corresponding \emph{classical} system. We show this behavior is due to the local suppression of path interferences in the interaction that generates the entanglement. This …
The property of the optimal signal ensembles of entanglement assisted channel capacity is studied. A relationship between entanglement assisted channel capacity and one-shot capacity of unassisted channel is obtained. The data processing inequalities, convexity and additivity of the entanglement assisted channel capacity are reformulated by simple methods.
Non-classical states that are characterized by their non-positive quasi-probabilities in phase space are known to be the basis for various quantum effects. In this work, we investigate the interrelation between the non-classicality and entanglement, and then characterize the non-classicality that precisely corresponds to entanglement. The results naturally follow from two findings: one is the general structure among non-classical, entangled, separable, and classical states over Hermitian operators, and the other a general scheme to detect non-classical states.
In this work we review and further develop the controversial concept of "classical entanglement" in optical beams. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results shed new light upon the physics at the debated border between the classical and the quantum representations of the world.
In this paper, we calculate the entanglement-assisted classical information capacity of amplitude damping channel and compare it with the particular mutual information which is considered as the entanglement-assisted classical information capacity of this channel in Ref. 6. It is shown that the difference between them is very small. In addition, we point out that using partial symmetry and concavity of mutual information derived from dense coding scheme one can simplify the calculation of entanglement-assisted classical information capacities for non-unitary-covariant quantum noisy channels.
Electronic devices all around us contain classical control circuits. Such circuits consist of a network of controllers which can read and write signals to wires of the circuit with the goal to minimize the cost function of the circuit's output signal. Here, we propose the use of shared entanglement between controllers as a resource to improve the performance of otherwise purely classical control circuits. We study a well-known example from the classical control literature and demonstrate that allowing two controllers to share entanglement improves their ability to control. More precisely, we e…
We investigate the entanglement dynamics and purity of a two-level atom, which is additionally driven by a classical field, interacting with a coherent field in a dissipative environment. It is shown that the amount of entanglement and the purity of the system can be improved by controlling the classical field.
The stabilization of steady state entanglement caused by action of a classical driving field in the system of two-level atoms with the dipole interaction accompanied by spontaneous emission is discussed. An exact solution shows that the maximum amount of concurrence that can be achieved in Lamb-Dicke limit is 0.43, which corresponds to the entanglement $\mathcal{E}_{max}=0.285$ ebit. Dependence of entanglement on interatomic distance and classical driving field is examined numerically.
We use the noisy entanglement-assisted classical capacity formula [arXiv:1609.08592] to create a coherent-attack security framework for Gaussian two-way quantum key distribution protocols in the asymptotic region.
This paper is essentially a lecture from the author's course on quantum information theory, which is devoted to the result of C. H. Bennett, P. W. Shor, J. A. Smolin and A. V. Thapliyal (quant-ph/0106052) concerning entanglement-assisted classical capacity of a quantum channel. A modified proof of this result is given and relation between entanglement-assisted and unassisted classical capacities is discussed.
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 numerically analyze the dynamical generation of quantum entanglement in a system of 2 interacting particles, started in a coherent separable state, for decreasing values of $\hbar$. As $\hbar\to 0$ the entanglement entropy, computed at any finite time, converges to a finite nonzero value. The limit law that rules the time dependence of entropy is well reproduced by purely classical computations. Its general features may then be explained by simple classical arguments, which expose the different ways entanglement is generated in systems which are classically chaotic or regular.
The generation of entanglement produced by a local potential interaction in a bipartite system is investigated. The degree of entanglement is contrasted with the underlying classical dynamics for a Rydberg molecule (a charged particle colliding on a kicked top). Entanglement is seen to depend on the structure of classical phase-space rather than on the global dynamical regime. As a consequence regular classical dynamics can in certain circumstances be associated with higher entanglement generation than chaotic dynamics. In addition quantum effects also come into play: for example partial reviv…
We analyze interrelation of quantum and classical entanglement. The latter notion is widely used in classical optic simulation of some quantum-like features of light. We criticize the common interpretation that "quantum nonlocality" is the basic factor differing quantum and classical realizations of entanglement. Instead, we point to the breakthrough Grangier et al. experiment on coincidence detection which was done in 1986 and played the crucial role in rejection of (semi-)classical field models in favor of quantum mechanics. Classical entanglement sources produce light beams with the coeffic…
Prior entanglement between sender and receiver, which exactly doubles the classical capacity of a noiseless quantum channel, can increase the classical capacity of some noisy quantum channels by an arbitrarily large constant factor depending on the channel, relative to the best known classical capacity achievable without entanglement. The enhancement factor is greatest for very noisy channels, with positive classical capacity but zero quantum capacity. Although such quantum channels can be simulated classically, no violation of causality is implied, because the simulation requires at least as …
In this work, the entanglement dynamics of a moving-biparticle system driven by an external classical field are investigated, where the moving-biparticle system is coupled with a zero temperature common environment. The analytical expressions of the density operator and the entanglement can be obtained by using the dressed-state basis when the total excitation number is one. We also discuss in detail the effects of different parameters on the entanglement dynamics. The results show that the classical driving can not only protect the entanglement, but also effectively eliminate the influence of…
Entanglement has been shown to be necessary for pure state quantum computation to have an advantage over classical computation. However, it remains open whether entanglement is necessary for quantum computers that use mixed states to also have an advantage. The one clean qubit model is a form of quantum computer in which the input is the maximally mixed state plus one pure qubit. Previous work has shown that there is a limited amount of entanglement present in these computations, despite the fact that they can efficiently solve some problems that are seemingly hard to solve classically. This c…
Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that are interacting solely via a mediator implies non-classicality of the mediator. Indeed, under certain assumptions regarding the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactio…
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedankenexperiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that …
It is known that if the quantum gates in a proposed quantum computer are so noisy that they are incapable of generating entanglement, then the device can be efficiently simulated classically. If the measurements and single particle operations are restricted, then the same statement can be true for generalised non-quantum notions of entanglement. Here we show that this can improve the applicability of limited-entanglement simulation algorithms. In particular, we show that by using a non-quantum notion of separability a classical simulation algorithm of Harrow & Nielsen can efficiently simulate …
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the case where the mapping is of order k, we prove a theorem that gives us the function of the entangled state. A useful generalization beyond this research will be the implementation of quantum states with arbitrary probability amplitude functions.
The Schrödinger dynamics of photon excitation numbers together with entanglement in two non-resonant time-dependent coupled oscillators is investigated. By considering $ π-$periodically pumped parameters and using suitable transformations, we obtain the coupled Meissner oscillators. Consequently, our analytical study shows two interesting results, which can be summarized as follows. (i): Classical instability of classical analog of quantum oscillators and photon excitation {averages $\left\langle N_{j}\right\rangle $} are strongly correlated. (ii): Photon excitation's and entanglement are conn…
We study entanglement dynamics in dispersive optomechanical systems consisting of two optical modes and a mechanical oscillator inside an optical cavity. The two optical modes interact with the mechanical oscillator, but not directly with each other. The appearance of optical entanglement witnesses non-classicality of the oscillator. We study the dependence of the entanglement dynamics with the optomechanical coupling, the mean photon number in the cavity and the oscillator temperature. An experimental realization with ultracold atomic ensembles is proposed.
In this paper, we study the effect of classical driving field on the spontaneous emission spectrum of a qubit embedded in a dissipative cavity. Furthermore, we monitor the entanglement dynamics of the driven qubit with its radiative decay under the action of the classical field. Afterwards, we carry out an investigation on the possibility of entanglement swapping between two such distinct driven qubits. The swapping will be feasible with the aid of a Bell state measurement performing on the photons leaving the cavities. It is demonstrated that the classical driving field has a beneficial effec…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical entanglement. This paper presents a simple example, including a way in which the system can be measured to violate Bell's inequalities. This classical simulation of a quantum system allows us to visualize entanglement and also helps us to see what aspects of quantum mechanical systems are truly nonclassical.
We consider a Fabry-Perot cavity made by two moving mirrors and driven by an intense classical laser field. We show that stationary entanglement between two vibrational modes of the mirrors, with effective mass of the order of micrograms, can be generated by means of radiation pressure. The resulting entanglement is however quite fragile with respect to temperature.
L. Lamata et al. have presented an entanglement classification of four qubits under stochastic local operation and classical communication (SLOCC) based on inductive approach [Phys. Rev. A \textbf{75}, 022318 (2007)]. While it works well for three qubits, we show that some of the families for four qubits have overlaps and hence this approach is not valid for entanglement classification of four or more qubits under SLOCC.
In a recent paper [Phys. Rev. A 76, 032304(2007)], Li et al. proposed the definition of the residual entanglement for n qubits by means of the Stochastic local operations and classical communication. Here we argue that their definition is not suitable for the case of odd-n qubits.
We analyse the role of entanglement for transmission of classical information through a memoryless depolarising channel. Using the isotropic character of this channel we prove analytically that the mutual information cannot be increased by encoding classical bits into entangled states of two qubits.
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.
Entanglement monotone is defined as a convex measure of entanglement that does not increase on average under local operations and classical communication (LOCC). Here we call an entanglement monotone a strict entanglement monotone (SEM) if it decreases strictly on average under LOCC. We show that, for any convex roof extended entanglement monotone that on pure states is given by a function of the reduced states, if the function is strictly concave, then it is a SEM. Moreover, we prove that the negativity and the relative entropy of entanglement, which are not defined by the convex roof structu…
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 …
In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible.
We investigate new features, especially of entanglement dynamics, which arise in a quantum-classical hybrid. As a model, we study the coupling between two quantum mechanical two-level systems, i.e. two q-bits, and a classical harmonic oscillator. Their interaction is described by a hybrid coupling, in accordance with a recently developed quantum-classical hybrid theory. We discuss various situations in which entanglement of the q-bits does (not) evolve. Furthermore, we point out an experimental application in a hybrid cooling scheme and indicate topics for future study.
An effective simulation of quantum entanglement is presented using classical fields modulated with n pseudorandom phase sequences (PPSs) that constitute a n2^n-dimensional Hilbert space with a tensor product structure. Applications to classical fields are examplied by effective simulation of both Bell and GHZ states, and a correlation analysis was performed to characterize the simulation. Results that strictly comply with criteria of quantum entanglement were obtained and the approach was also shown to be applicable to a system consisting of n quantum particles.
We present an analysis of the entangling quantum kicked top focusing on the few qubit case and the initial condition dependence of the time-averaged entanglement $S_Q$ for spin-coherent states. We show a very strong connection between the classical phase space and the initial condition dependence of $S_Q$ even for the extreme case of two spin-$1/2$ qubits. This correlation is not related directly to chaos in the classical dynamics. We introduce a measure of the behavior of a classical trajectory which correlates far better with the entanglement and show that the maps of classical and quantum i…
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of the physical principles that give rise to entanglement. Why does nature have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? One important feature of quantum theory is that it has a classical limit, recovering classical theory through the process of decoheren…
Two-qubit operations may be characterized by their capacities for communication, both with and without free entanglement, and their capacity for creating entanglement. We establish a set of inequalities that give an ordering to the capacities of two-qubit unitary operations. Specifically, we show that the capacities for entanglement creation and bidirectional communication without entanglement assistance are at least as great as half the bidirectional communication capacity with entanglement assistance. In addition, we show that the bidirectional communication that can be performed using an en…
One of the most striking features of quantum theory is the existence of entangled states, responsible for Einstein's so called "spooky action at a distance". These states emerge from the mathematical formalism of quantum theory, but to date we do not have a clear idea of which physical principles give rise to entanglement. Why does quantum theory have entangled states? Would any theory superseding classical theory have entangled states, or is quantum theory special? We demonstrate that without entanglement, non-classical degrees of freedom cannot reversibly interact. We present two postulates,…
The entangled behavior of different dimensional systems driven by classical external random field is investigated. The amount of the survival entanglement between the components of each system is quantified. There are different behaviors of entanglement that come into view decay, sudden death, sudden birth and long-lived entanglement. The maximum entangled states which can be generated from any of theses suggested systems are much fragile than the partially entangled ones. The systems of larger dimensions are more robust than those of smaller dimensions systems, where the entanglement decay sm…
We present and experimentally demonstrate a communication protocol that employs shared entanglement to reduce errors when sending a bit over a particular noisy classical channel. Specifically, it is shown that, given a single use of this channel, one can transmit a bit with higher success probability when sender and receiver share entanglement compared to the best possible strategy when they do not. The experiment is realized using polarization-entangled photon pairs, whose quantum correlations play a critical role in both the encoding and decoding of the classical message. Experimentally, we …
Coherent states with large amplitudes are traditionally thought of as the best quantum mechanical approximation of classical behavior. Here we argue that, far from being classical, coherent state are in fact highly entangled. We demonstrate this by showing that a general system of indistinguishable bosons in a coherent state can be used to entangle, by local interactions, two spatially separated and distinguishable non-interacting quantum systems. Entanglement can also be extracted in the same way from number states or any other nontrivial superpositions of them.
In this paper, we present schemes for a type of one-parameter bipartite quantum states to probe the quantum entanglement, the quantum discord, the classical correlation and the quantum state based on the cavity QED. It is shown that our detection does not influence all these measured quantities. We also discuss how the spontaneous emission introduced by our probe atom influences our detection.
Recently, Vedral and one of us proposed an entanglement-based witness of non-classicality in systems that need not obey quantum theory, based on constructor-information-theoretic ideas, which offers a robust foundation for recently proposed table-top tests of non-classicality in gravity. The witness asserts that if a mediator can entangle locally two quantum systems, then it has to be non-classical. Hall and Reginatto claimed that there are classical systems that can entangle two quantum systems, thus violating our proposed witness. Here we refute that claim, explaining that the counterexample…
Entanglement appears under two different forms in quantum theory, namely as a property of states of joint systems and as a property of measurement eigenstates in joint measurements. By combining these two aspects of entanglement, it is possible to generate nonlocality between particles that never interacted, using the protocol of entanglement swapping. We show that even in the more constraining bilocal scenario where distant sources of particles are assumed to be independent, i.e. to share no prior randomness, this process can be simulated classically with bounded communication, using only 9 b…
