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 entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice-versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement it allows one to identify those aspects of entanglement which are uniquely quantum mechanical.
The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to exploit this resource efficiently. We learn how to exploit entanglement efficiently by applying analogues of thermodynamical concepts. These concepts include reversibility, entropy, and the distinction between intensive and extensive quantities. We discuss some of these analogues and show how they lead to a measure of entanglement for pure states. We also ask whether these analogues are more than analogues, and note that, l o c a l l y, entropy of entangle…
Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied in great detail and it is known that entanglement between the qubits is necessary to gain a quadratic speedup, for pure state implementation of the Grover search algorithm. Here, we systematically investigate the behavior of quantum coherence and monogamy of entanglement in the discrete analogue of the $\textit{analog analogue of Grover search algorithm}$. …
We consider an analogue of entanglement-swapping for a set of black boxes with the most general non-local correlations consistent with relativity (including correlations which are stronger than any attainable in quantum theory). In an attempt to incorporate this phenomenon, we consider expanding the space of objects to include not only correlated boxes, but `couplers', which are an analogue for boxes of measurements with entangled eigenstates in quantum theory. Surprisingly, we find that no couplers exist for two binary-input/binary-output boxes, and hence that there is no analogue of entangle…
We study the quantum entanglement of the quasiparticle pairs emitted by analogue black holes. We use a phenomenological description of the spectra in dispersive media to study the domains in parameter space where the final state is non-separable. In stationary flows, three modes are involved in each sector of fixed frequency, and not two as in homogeneous situations. The third spectator mode acts as an environment for the pairs, and the strength of the coupling significantly reduces the quantum coherence. The non-separability of the pairs emitted by white holes are also considered, and compare…
We investigate the possibility to generate quantum-correlated quasi-particles utilizing analogue gravity systems. The quantumness of these correlations is a key aspect of analogue gravity effects and their presence allows for a clear separation between classical and quantum analogue gravity effects. However, experiments in analogue systems, such as Bose-Einstein condensates, and shallow water waves, are always conducted at non-ideal conditions, in particular, one is dealing with dispersive media at nonzero temperatures. We analyze the influence of the initial temperature on the entanglement ge…
A general geometrical structure of the entanglement entropy for spatial partition of a relativistic QFT system is established by using methods of the effective gravity action and the spectral geometry. A special attention is payed to the subleading terms in the entropy in different dimensions and to behaviour in different states. It is conjectured, on the base of relation between the entropy and the action, that in a fundamental theory the ground state entanglement entropy per unit area equals $1/(4G_N)$, where $G_N$ is the Newton constant in the low-energy gravity sector of the theory. The co…
The purpose of this short article is to build on the work of Ghirardi, Marinatto and Weber (Ghirardi, Marinatto & Weber 2002; Ghirardi & Marinatto 2003, 2004, 2005) and Ladyman, Linnebo and Bigaj (2013), in supporting a redefinition of entanglement for "indistinguishable" systems, particularly fermions. According to the proposal, non-separability of the joint state is insufficient for entanglement. The re-definition is justified by its physical significance, as enshrined in three biconditionals whose analogues hold of "distinguishable" systems.
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.
Chirped-pulse interferometry (CPI) captures the metrological advantages of quantum Hong-Ou-Mandel (HOM) interferometry in a completely classical system. Modified HOM interferometers are the basis for a number of seminal quantum-interference effects. Here, the corresponding modifications to CPI allow for the first observation of classical analogues to the HOM peak and quantum beating. They also allow a new classical technique for generating phase super-resolution exhibiting a coherence length dramatically longer than that of the laser light, analogous to increased two-photon coherence lengths i…
We investigate quantum entanglement in an analogue black hole realized in the flow of a Bose-Einstein condensate. The system is described by a three-mode Gaussian state and we construct the corresponding covariance matrix at zero and finite temperature. We study associated bipartite and tripartite entanglement measures and discuss their experimental observation. We identify a simple optical setup equivalent to the analogue Bose-Einstein black hole which suggests a new way of determining the Hawking temperature and grey-body factor of the system.
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.
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…
Recently, it was discovered that the `quantum partial information' needed to merge one party's state with another party's state is given by the conditional entropy, which can be negative [Horodecki, Oppenheim, and Winter, Nature 436, 673 (2005)]. Here we find a classical analogue of this, based on a long known relationship between entanglement and shared private correlations: namely, we consider a private distribution held between two parties, and correlated to a reference system, and ask how much secret communication is needed for one party to send her distribution to the other. We give optim…
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.
Quantum separable operations are defined as those that cannot produce entanglement from separable states, and it is known that they strictly surpass local operations and classical communication (LOCC) in a number of tasks, which is sometimes referred to as "quantum nonlocality without entanglement." Here we consider a task with such a gap regarding the trade-off between state discrimination and preservation of entanglement. We show that this task along with the gap has an analogue in a purely classical setup, indicating that the quantum properties are not essential in the existence of a nonzer…
A quantum theory of light propagation in two optical channel waveguides tunnelling-coupled to a common continuum of modes (such as those of a slab waveguide) is presented, and classical and quantum interference effects are investigated. For classical light, the photonic system realizes an optical analogue of coherent population trapping in the continuum encountered in atomic physics, where destructive interference between different light leakage channels leads to the appearance of a trapped state embedded in the continuum. For nonclassical light, two-photon interference effects are predicted, …
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…
We demonstrate the existence of a non-local geometric phase in the intensity-intensity correlations of classical incoherent light, that is not seen in the lower order correlations. This two-photon Pancharatnam phase was observed and modulated in a Mach-Zehnder interferometer. Using acousto-optic interaction, independent phase noise was introduced to light in the two arms of the interferometer to create two independent incoherent classical sources from laser light. The experiment is the classical optical analogue of the multi-particle Aharonov-Bohm effect. As the trajectory of light over the Po…
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…
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.
A necessary and sufficient condition for characterization and quantification of entanglement of any bipartite Gaussian state belonging to a special symmetry class is given in terms of classicality measures of one-party states. For Gaussian states whose local covariance matrices have equal determinants it is shown that separability of a two-party state and classicality of one party state are completely equivalent to each other under a nonlocal operation, allowing entanglement features to be understood in terms of any available classicality measure.
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.
