We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed to another one if and only if a majorization relationship holds between their partial coherence vectors. As a consequence, we introduce the concept of maximal partial coherent states in the sense that they can be used to construct any bipartite state of the same system via partial incoherent operations. Second, we provide a strategy to construct measures of partial coherence by the use of symmetric concave functions. Third, we establish some relationships between partial coherence and entanglement. We show that the minimal partial coherence under local unitary operations is a measure of entanglement for bipartite pure states, which can be extended to all mixed states by convex-roof. We also show that partial coherence measures are induced through maximal entanglement under partial incoherent operations for bipartite pure states. There is a one-to-one correspondence between entanglement and partial coherence measures.
We study entanglement properties of all eigenstates of the Heisenberg XXX model, and find that the entanglement and mixedness for a pair of nearest-neighbor qubits are completely determined by the corresponding eigenenergies. Specifically, the negativity of the eigenenergy implies pairwise entanglement. From the relation between entanglement and eigenenergy, we obtain finite-size behaviors of the entanglement. We also study entanglement and mixedness versus energy in the quantum Heisenberg XY model.
In this paper, the theory of coherence frame is developed. Two kinds of coherence frame are classified. Under coherence frame, the entanglement is conserved in the entanglement swapping process, without entanglement sudden death and birth. The einselection method for the preferred basis problem in the entangle process is shown as incomplete.
In this work we derive analytical relations between Entanglement and Coherence as well as between Discord and Coherence, for Bell-diagonal states and for X states, evolving under the action of several noise channels: Bit Flip, Phase Damping and Depolarizing. We demonstrate that for these families, Coherence is the fundamental correlation, that is: Coherence is necessary for the presence of Entanglement and Discord.
We consider the quantum discord in a two-particle spin-1/2 system (dimer) governed by the standard multiple quantum (MQ) Hamiltonian and reveal the relation between the discord and the intensity of the second-order MQ coherence. Since the coherence intensities may be measured in experiment, we obtain a method of detecting the quantum discord in experiment. Comparison of discord and concurrence is represented.
A general scheme to seek for the relations between entanglement and bservables is proposed in principle. In two-qubit systems with enough general Hamiltonian, we find the entanglement to be the functions of observables for six kinds of chosen state sets and verify how these functions be invariant with time evolution. Moreover, we demonstrate and illustrate the cases with entanglement versus a set of commutable observables under eight kinds of given initial states. Our conclusions show how entanglement become observable even measurable by experiment, and they are helpful for understanding of th…
With atomic spontaneously generated coherence (SGC), we propose a novel scheme to coherently control the atom--photon momentum entanglement through atomic internal coherence. A novel phenomena of ``phase entanglement in momentum'' is proposed, and we found, under certain conditions, that super--high degree of momentum entanglement can be produced with this scheme.
In this short note we discuss the relation between the so-called Off-Diagonal-Long-Range-Order in many-body interacting quantum systems introduced by C. N. Yang in Rev. Mod. Phys. {\bf 34}, 694 (1962) and entanglement. We argue that there is a direct relation between these two concepts.
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
We review the problem of discriminating entangled states from separable states for bipartite systems. We formally define what entangled states are, present some important criteria to detect entanglement, and show how they can be classified according to their capability to perform some precisely defined tasks.
We show, by explicit examples, that the Jaynes inference scheme based on maximization of entropy can produce inseparable states even if there exists a separable state compatible with the measured data. It can lead to problems with processing of entanglement. The difficulty vanishes when one uses inference scheme based on minimization of entanglement.
We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence measure of pure states, with extension to mixed states by convex roof, is the maximum entanglement generated by incoherent operations acting on the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is the universal optimal incoherent operation. In this way, all convex-roof coherence measures, including the coherence of formation, are end…
Quantification of entanglement against mixing is given for a system of coupled qubits under a phase damping channel. A family of pure initial joint states is defined, ranging from pure separable states to maximally entangled state. An ordering of entanglement measures is given for well defined initial state amount of entanglement.
Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted…
We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, we observe that, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find that when the cavity entanglement suddenly disappear, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this {\it entanglement sudden birth} can manifest before, simultaneously, or even after {\it entanglement sudden death}. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems.
The paper titled "Tripartite entanglement versus tripartite nonlocality in 3-qubit GHZ-class states", (Physical Review Letters 102, 250404 (2009)), does very important work on studying the nature of Svetlichny Inequalities (which are Bell-type inequalities) and sheds light on some important properties and relationship between Svetlichny inequality and tripartite entanglement. It derives a result for the maximum expectation value of Svetlichny operator for GGHZ and MS states. In this comment, it is put forth that there is probably a mistake in the central result derived in the paper.
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while cannot enhanced for some other cases. For coherence-breaking channels with different types, the chann…
We give a simple example of the tight connection between entanglement and coherence for pure bipartite systems showing the double role played by entanglement; it allows for the creation of superpositions of macroscopic objects but at the same time makes subsystems lose their quantum mechanical coherence. For this we study the time evolution of the spin coherence in the Stern-Gerlach (SG) experiment. We also show that, contrary to the naive intuition, the spin coherence is lost before the two beams become separated in the spatial coordinates.
We study evolution of entanglement of two two-level atoms in the presence of dissipation caused by spontaneous emission. We find explicit fromulas for the amount of entanglement as a function of time, in the case of destruction of the initial entanglement and possible creation of a transient entanglement between atoms. We also discuss how spontaneous emission influences nonlocality of states expressed by violation of Bell - CHSH inequality. It is shown that evolving system very quickly becomes local, even if entanglement is still present or produced.
Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is essentially the normalized coherence of the entangled state in its Schmidt basis. Its value is 1 for maximally entangled states, and 0 for separable states, irrespective of the dimensionality of the Hilbert space. So a maximally entangled state is also the one which is maximally coherent in its Schmidt basis. Quantum entanglement and quantum coherence are thus intima…
Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements and find relations between them. For this, we conceive a relative entropy type quantity to account for the quantum resources of quantum measurements. The quantum coherence of a quantum measurement can be converted into the entanglement in a bipartite quantum measurement through coherence-non generating transformations. Conversely, a quantum entanglement monotone of quantum measurements induces a quan…
We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of coherence based entanglement monotones, which is always computable for pure states if the coherence measure is also computable. It is already known that every entanglement measure can be constructed as a coherence measure. The results presented here show that the converse is also true. The constructions that are presented can also be extended to also include more g…
In this article we make a comparison between the behavior of entanglement and quantum degree of polarization for a special class of states of the radiation field, namely the Bell-type diagonal mixed states. For the three-photon mixed states we have plotted the concurrence and the Chernoff quantum degree of polarization in terms of the parameter, which defines the state. We find the the entanglement and the quantum degree of polarization are incomparable measures.
Quantum coherence is a fundamental manifestation of the quantum superposition principle. Recently, Baumgratz \emph{et al}. [Phys. Rev. Lett. \textbf{113}, 140401 (2014)] presented a rigorous framework to quantify coherence from the view of theory of physical resource. Here we propose a new valid quantum coherence measure which is a convex roof measure, for a quantum system of arbitrary dimension, essentially using the generalized Gell-Mann matrices. Rigorous proof shows that the proposed coherence measure fulfills all the requirements dictated by the resource theory of quantum coherence measur…
For a class of mixed two -qubit states we show that it is not possible to discriminate between states violating or non - violating Bell - CHSH inequalities, knowing only their entanglement and mixedness. For a large set of possible values of these quantities, we construct pairs of states with the same entanglement and mixedness such that one state is violating but the other is non - violating Bell - CHSH inequality.
In this study, we model a harmonic oscillator that enters an interferometer partially coupled to a thermal bath of oscillatory fields by employing a Brownian-type Lindblad master equation. More specifically, we investigate the dynamics and the variations of the thermodynamic quantities of the system at different temperatures. We recognize that although the system can remain coherent during its interaction with the thermal bath in the low-temperature limit, the system's entropy production violates the Clausius inequality. Furthermore, we argue that the system's coherence is the source of this v…
We study the relations between quantum coherence and quantum nonlocality, genuine quantum entanglement and genuine quantum nonlocality. We show that the coherence of a qubit state can be converted to the nonlocality of two-qubit states via incoherent operations. The results are also generalized to qudit case. Furthermore, rigorous relations between the quantum coherence of a single-partite state and the genuine multipartite quantum entanglement, as well as the genuine three-qubit quantum nonlocality are established.
Coherence and entanglement are the two most crucial resources for various quantum information processing tasks. Here, we study the interplay of coherence and entanglement under the action of different three qubit quantum cloning operations. Considering certain well-known quantum cloning machines (input state independent and dependent), we provide examples of coherent and incoherent operations performed by them. We show that both the output entanglement and coherence could vanish under incoherent cloning operations. Coherent cloning operations on the other hand, could be used to construct a uni…
We present a review of the problem of finding out whether a quantum state of two or more parties is entangled or separable. After a formal definition of entangled states, we present a few criteria for identifying entangled states and introduce some entanglement measures. We also provide a classification of entangled states with respect to their usefulness in quantum dense coding, and present some aspects of multipartite entanglement.
We establish a set of resource conversion relationships between quantum coherence and multipartite entanglement in many-body systems, where the operational measures of resource cost and distillation are focused. Under the multipartite incoherent operation, the initial coherence of single-party system bounds the maximal amounts of corresponding operational entanglement in an arbitrary bipartite partition as well as the genuine multipartite entanglement in many-body systems. Furthermore, the converted multipartite entanglement can be transferred to its subsystems and restored to coherence of a s…
The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. It shows that the entanglement is dependent on the initial atomic states. The possibility of considerable growth of atomic entanglement due atomic coherence and dipole-dipole interaction is shown in the case of great mean values of thermal photons.
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction of the system state. We show that one can extract quantitative bounds to the relative entropy of coherence and the coherent information, coherence and entanglement quantifiers respectively, by a limited number of purity measurements. The scheme is readily implementable with current technology to verify quantum computations in large scale registers, without c…
Quantum coherence and quantum entanglement represent two fundamental features of non-classical systems that can each be characterized within an operational resource theory. In this paper, we unify the resource theories of entanglement and coherence by studying their combined behavior in the operational setting of local incoherent operations and classical communication (LIOCC). Specifically we analyze the coherence and entanglement trade-offs in the tasks of state formation and resource distillation. For pure states we identify the minimum coherence-entanglement resources needed to generate a g…
We develop and exploit a source of two-photon four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a non-contextuality ssumption. Our experimental results are in well agreement with quantum mechanics while in extreme contradiction with local realism. Potential applications of our experiment are briefly discussed.
We use a Heisenberg spin-1/2 chain to investigate how chaos and localization may affect the entanglement of pairs of qubits. To measure how much entangled a pair is, we compute its concurrence, which is then analyzed in the delocalized/localized and in the chaotic/non-chaotic regimes. Our results indicate that chaos reduces entanglement and that entanglement decreases in the region of strong localization. In the transition region from a chaotic to a non-chaotic regime localization increases entanglement. We also show that entanglement is larger for strongly interacting qubits (nearest neighbor…
We consider quantum computing with pseudo-pure states. This framework arises in certain implementations of quantum computing using NMR. We analyze quantum computational protocols which aim to solve exponential classical problems with polynomial resources and ask whether or not entanglement of the pseudo-pure states is needed to achieve this aim. We show that for a large class of such protocols, including Shor's factorization, entanglement is necessary. We also show that achieving entanglement is not sufficient: if the noise in the state is sufficiently large, exponential resources are needed e…
We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining max…
Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. Quantum coherence, a quantum resource, is the basic ingredient in many quantum information tasks. It is a subject of broad and current interest in quantum information, and many new concepts have been introduced and generalized since its establishment. Here we show that the block coherence can be transformed into entanglement via a block incoherent operation. Moreover, we find that the POVM-based coherence associated with block coherence through the Naimark extension act…
Quantum correlations represent a fundamental tool for studies ranging from basic science to quantum technologies. Different non-classical correlations have been identified and studied, as entanglement and discord. In view of future applications in this letter we explore experimentally the rich geometry of Bell-diagonal states, measuring the values of entanglement and discord and highlighting the effect of decoherence in real experiments.
Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics. While considered as puzzling phenomena in the early days of quantum theory, it is only very recently that entanglement and coherence have been recognized as resources for the emerging quantum technologies, including quantum metrology, quantum communication, and quantum computing. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of sup…
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the sense that a pure bipartite quantum state, having nonvanishing entanglement, always violates a Bell inequality. We construct Bell-type inequalities for product states in quantum coherence theory for different measures of coherence, and find that the maximally entangled states violate these inequalities. We further show that Bell-type inequalities for relative …
Experimentally quantifying entanglement and coherence are extremely important for quantum resource theory. However, because the quantum state tomography requires exponentially growing measurements with the number of qubits, it is hard to quantify entanglement and coherence based on the full information of the experimentally realized multipartite states. Fortunately, other methods have been found to directly measure the fidelity of experimental states without quantum state tomography. Here we present a fidelity-based method to derive experimentally accessible lower bounds for measures of genuin…
With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the "differentiated" intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest nei…
The remote control of coherence is a crucial step for its application in quantum computation. We investigate the maximal steered coherence (MSC) and its conversion to entanglement in multiple bosonic reservoirs. It is shown that the MSC decays with time in the Markovian regime and behaves as damped oscillations in the non-Markovian regime. The MSC can also be connected directly to the strength of non-Markovianity, through which we show that it can be noticeably enhanced by taking full advantage of the non-Markovian effects. Besides, the MSC can be converted completely to entanglement via optim…
Quantum coherence as an important quantum resource plays a key role in quantum theory. In this paper, using entropy-based measures, we investigate the relations between quantum correlated coherence, which is the coherence between subsystems [K. C. Tan, H. Kwon, C. Y. Park, and H. Jeong, Phys. Rev. A 94, 022329 (2016)], and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement meas…
Quantum devices are systems that can explore quantum phenomena, like entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as main element in its high performance in the charging powerful. In this paper, we explore the quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two and three-cell battery, our results suggest that entanglement is not the main resource t…
We suggest a formalism to illustrate the entanglement of identical particles in the first quantization language (1QL). Our 1QL formalism enables one to exploit all the well-established quantum information tools to understand the indistinguishable ones, including the reduced density matrix and familiar entanglement measures. The rigorous quantitative relation between the amount of entanglement and the spatial coherence of particles is possible in this formalism. Our entanglement detection process is a generalization of the entanglement extraction protocol for identical particles with mode split…
Complete complementarity relations, as e.g. $P(ρ_{A})^{2} + C(ρ_{A})^{2} + E(|Ψ\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-ba…
Coherent superposition and entanglement are two fundamental aspects of non-classicality. Here we provide a quantitative connection between the two on the level of operations by showing that the dynamical coherence of an operation upper bounds the dynamical entanglement that can be generated from it with the help of additional incoherent operations. In case a particular choice of monotones based on the relative entropy is used for the quantification of these dynamical resources, this bound can be achieved. In addition, we show that an analog to the entanglement potential exists on the level of …
Strong correlations in two conjugate variables are the signature of quantum entanglement and have played a key role in the development of modern physics. Entangled photons have become a standard tool in quantum information and foundations. An impressive example is position-momentum entanglement of photon pairs, explained heuristically through the correlations implied by a common birth zone and momentum conservation. However, these arguments entirely neglect the importance of the `quantumness', i.e. coherence, of the driving force behind the generation mechanism. We study theoretically and expe…
In this paper, we investigate preservation of quantum coherence of a single-qubit interacting with a zero-temperature thermal reservoir through the addition of noninteracting qubits in the reservoir. Moreover, we extend this scheme to preserve quantum entanglement between two and three distant qubits, each of which interacts with a dissipative reservoir independently. At the long time limit, we obtained analytical expressions for the coherence measure and the concurrence of two and three qubits in terms of the number of additional qubits. It is observed that, by increasing the number of additi…
The concept of physical twin observables (PTO) for bipartite quantum states,introduced and proved relevant for quantum information theory in recent work, is substantially simplified. The relation of observable and state is studied in detail from the point of view of coherence entropy. Properties of this quantity are further explored. It is shown that, besides for pure states, quantum discord (measure of entanglement) can be expressed through the coherence entropy of a PTO complete in relation to the state.
For quantum states of two subsystems, entanglement measures are related to capacities of communication tasks -- highly entangled states give higher capacity of transmitting classical as well as quantum information. However, we show that this is no more the case in general: quantum capacities of multi-access channels, motivated by communication in quantum networks, do not have any relation with genuine multiparty entanglement measures. Along with revealing the structural richness of multi-access channel capacities, this gives us a tool to classify multiparty quantum states from the perspective …
