Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement, quantum discord, and Bell correlations. It can be distributed in a multipartite system in various ways -- for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence) and exhibits a trade-off relation. In quantum systems with more than two subsystems, there are more trade-off relations, due to the various decomposition ways of the coherence. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved quantum systems using a spin system by changing the state from a product state to a tripartite entangled state. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous except for the initial product state. We find that despite the different types of states involved, the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states.
We construct the tripartite Bell-type inequalities of product states for l1-norm of coherence, relative entropy of coherence and skew information. Some three-qubit entangled states violate these inequalities. Particulary, the tripartite Bell-type inequality for relative entropy of coherence is always violated by the W class pure or mixed states as well as the GHZ class pure or mixed states, being used as entanglement witness.
Quantum coherence and quantum entanglement are two strong pillars in quantum information theory. We study here for the possibility of any connection between these two important aspects of quantum mechanics while studying the entanglement detection problem for the detection of bipartite higher dimensional entangled states and multipartite entangled states. To achieve our goal, we derive the lower bound $L$ of $l_{1}$ norm of coherence of bipartite qubit-qudit system using the criterion that detect entanglement. Furthermore, we deduce the upper bound $U$ of $l_{1}$ norm of coherence of separable…
In quantum resource theories (QRTs), there exists evidences of intrinsic connections among different measures of quantum resources, including entanglement, coherence, quantum steering, and so on. However, building the relations among different quantum resources is a vital yet challenging task in multipartite quantum systems. Here, we focus on a unified framework of interpreting the interconversions among different quantum resources in tripartite systems. In particular, an exact relation between the generalized geometric measure and the genuinely multipartite concurrence are derived for tripart…
Quantum information processing exploits non-local functionality that has led to significant breakthroughs in the successful deployment of quantum mechanical protocols. In this regard, we address the dynamics of entanglement and coherence for three non-interacting qubits initially prepared as maximally entangled GHZ-like state coupled with independent classical environments. Two different Gaussian noises in pure and mixed noisy situations, namely, pure power-law noise, pure fractional Gaussian noise, power-law noise maximized and fractional Gaussian noise maximized cases are assumed to characte…
The time evolution of the distribution and shareability of quantum coherence of a tripartite system in a non-Markovian environment is examined. The total coherence can be decomposed into various contributions, ranging from local, global bipartite and global tripartite, which characterize the type of state. We identify coherence revivals for non-Markovian systems for all the contributions of coherence. The local coherence is found to be much more robust under the environmental coupling due to an effective smaller coupling to the reservoir. This allows us to devise a characterization of a quantu…
Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, we investigate the correlations of the tripartite W-type states based on bipartite quantum resources. The interrelations among the degree of coherence, concurrence, Bell nonlocality and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser-Horne-Shimony-Holt inequality) states for the two-qubit subsystems derived from the…
We propose to quantify three qubit entanglement using global negativity along with K-way negativities, where K=2 and 3. K-way partial transpose with respect to a subsystem is defined so as to shift the focus to K-way coherences of the composite system instead of K subsystems of the composite system. While genuine tripartite entanglement of three qubit composite system is generated by 3-way coherences, tripartite entanglement can be present due to 2-way coherences as well.
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…
We address measurement-based generation of quantum coherence in continuous variable systems. We consider Gaussian measurements performed on Gaussian states and focus on two scenarios. In the first one, we assume an initially correlated bipartite state shared by two parties and study how correlations may be exploited to remotely create quantum coherence via measurement back-action. In particular, we focus on conditional states with zero first moments, so as to address coherence due to properties of the covariance matrix. We consider different classes of bipartite states with incoherent marginal…
We study the properties of bi-squeezed tripartite Gaussian states created by two spontaneous parametric down-conversion processes that share a common idler. We give a complete description of the quantum correlations across of all partitions, as well as of the genuine multipartite entanglement, obtaining analytical expressions for most of the quantities of interest. We find that the state contains genuine tripartite entanglement, in addition to the bipartite entanglement among the modes that are directly squeezed. We also investigate the effect of homodyne detection of the photons in the common…
We study a quantum absorption refrigerator, in which a target qubit is cooled by two machine qubits in a nonequilibrium steady state. It is realized by a strong internal coupling in the two-qubit fridge and a vanishing tripartite interaction among the whole system. The coherence of a \emph{machine virtual qubit} is investigated as quantumness of the fridge. A necessary condition for cooling shows that the quantum coherence is beneficial to the nonequilibrium fridge, while it is detrimental as far as the maximum coefficient of performance (COP) and the COP at maximum power are concerned. Here, …
Molecular Nanomagnet $\text{Cu}^\text{II}\text{Ni}^\text{II}\text{Cu}^\text{II}$ as Resource for Bipartite and Tripartite Quantum Entanglement and Coherence
We study intrinsic coherence in the tripartite process to unambiguously discriminate two nonorthogonal states of a qubit, entangled with another one, and assisted by an auxiliary system. The optimal success probability is found to be benefited by initial intrinsic coherence, but no extra one is required. The transformations among different contributions of intrinsic coherence are necessary in this procedure, which increase with the overlap between the states to recognize. Such state discrimination is a key step of the probabilistic teleportation protocol. Entanglement of the quantum channel de…
We address entanglement, coherence, and information protection in a system of four non-interacting qubits coupled with different classical environments, namely: common, bipartite, tripartite, and independent environments described by Ornstein-Uhlenbeck (ORU) noise. We show that quantum information preserved by the four qubit state is more dependent on the coherence than the entanglement using time-dependent entanglement witness, purity, and Shannon entropy. We find these two quantum phenomena directly interrelated and highly vulnerable in environments with ORU noise, resulting in the pure expo…
One of the fundamental differences between classical and quantum mechanics is in the ways correlations can be distributed among the many parties that compose a system. While classical correlations can be shared among many subsystems, in general quantum correlations cannot be freely shared. This unique property is known as monogamy of quantum correlations. In this work, we study the monogamy properties of the correlated coherence for the l 1 -norm and relative entropy measures of coherence. For the l 1 -norm the correlated coherence is monogamous for a particular class of quantum states. For th…
As the precious resource for quantum information processing, quantum coherence can be created remotely if the involved two sites are quantum correlated. It can be expected that the amount of coherence created should depend on the quantity of the shared quantum correlation, which is also a resource. Here, we establish an operational connection between coherence induced by steering and the quantum correlation. We find that the steering-induced coherence quantified by such as relative entropy of coherence and trace-norm of coherence is bounded from above by a known quantum correlation measure def…
We study the trade-off relations given by the l_1-norm coherence of general multipartite states. Explicit trade-off inequalities are derived with lower bounds given by the coherence of either bipartite or multipartite reduced density matrices. In particular, for pure three-qubit states, it is explicitly shown that the trade-off inequality is lower bounded by the three tangle of quantum entanglement.
Within the unified framework of exploiting the relative entropy as a distance measure of quantum correlations, we make explicit the hierarchical structure of quantum coherence, quantum discord and quantum entanglement in multipartite systems. On this basis, we introduce a new measure of quantum coherence, the basis-free quantum coherence and prove that this quantity is exactly equivalent to quantum discord. Furthermore, since the original relative entropy of coherence is a basis-dependent quantity, we investigate the local and nonlocal unitary creation of quantum coherence, focusing on the two…
Quantum mechanics ensures that the information stored in a quantum state is secure and the ability to send private information through a quantum channel is at least as great as the coherent information. We derive trade-off relations between quantum privacy, information gain by Eve and the disturbance caused by Eve to the quantum state that is being sent through a noisy channel. For tripartite quantum states, we show that monogamy of privacy exists in the case of a single sender and multiple receivers. When Alice prepares a tripartite entangled state and shares it with Bob and Charlie through t…
Hybrid systems that combine spin ensembles and superconducting circuits provide a promising platform for implementing quantum information processing. We propose a non-Hermitian magnoncircuit-QED hybrid model consisting of two cavities and an yttrium iron garnet (YIG) sphere placed in one of the cavities. Abundant exceptional points (EPs), parity-time (PT )-symmetry phases and PT -symmetry broken phases are investigated in the parameter space. Tripartite highdimensional entangled states can be generated steadily among modes of the magnon and photons in PT -symmetry broken phases, corresponding …
In thermodynamics, quantum coherences - superpositions between energy eigenstates - behave in distinctly nonclassical ways. Recently mathematical frameworks have emerged to account for these features and have provided a range of novel insights. Here we describe how thermodynamic coherence splits into two kinds - "internal" coherence that admits an energetic value in terms of thermodynamic work, and "external" coherence that does not have energetic value, but instead corresponds to the functioning of the system as a quantum clock. For the latter form of coherence we provide dynamical constraint…
Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composit…
We investigate the issue of assisted coherence distillation in the asymptotic limit (considering infinite copies of the resource states), by coordinately performing the identical local operations on the auxiliary systems of each copy. When we further restrict the coordinate operations to projective measurements, the distillation process is branched into many sub-processes. Finally, a simple formula is given that the assisted distillable coherence should be the maximal average coherence of the residual states. The formula makes the experimental research of assisted coherence distillation possib…
We study the trade-off relations satisfied by the genuine tripartite nonlocality in multipartite quantum systems. From the reduced three-qubit density matrices of the four-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states and W states (4-qubit entangled state), we find that there exists a trade-off relation among the mean values of the Svetlichny operators associated with these reduced states. Namely, the genuine three-qubit nonlocalities are not independent. For four-qubit generalized GHZ states and W states, the summation of all their three-qubit maximal (squared) mean values of the…
Certain quantum states are well-known to be particularly fragile in the presence of decoherence, as illustrated by Schrodinger's famous gedanken cat experiment. It has been better appreciated more recently that quantum states can be characterized in a hierarchy of quantum quantities such entanglement, quantum correlations, and quantum coherence. It has been conjectured that each of these quantities have various degrees of fragility in the presence of decoherence. Here we experimentally confirm this conjecture by preparing tripartite photonic states and subjecting them to controlled amounts of …
The violation of the classical bounds imposed by Leggett-Garg inequalities has tested the quantumness of neutrino oscillations (NOs) over a long distance during the propagation. The measure of quantumness in experimentally observed NOs is studied via quantum resource theory (QRT). Here, we focus on the trade-off relations of QRT in the three-flavor NOs, based on Bell-type violations, first-order coherence and intrinsic concurrence, and the relative entropy of coherence. For the electron and muon antineutrino oscillations, the analytical trade-off relations obeyed by the Bell-CHSH inequality of…
We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ($\mathcal{C}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure ($\mathcal{C}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the s…
Quantum measurements necessarily disturb the state of physical system. Once we perform a complete measurement, the system undergoes decoherence and loses its coherence. If there is no disturbance, the state retains all of its coherence. It is therefore natural to ask if there is trade-off between disturbance caused to a state and its coherence. We present a coherence disturbance complementarity relation using the relative entropy of coherence. For bipartite states we prove a complementarity relation between the quantum coherence, entanglement and disturbance. Similar relation also holds for qu…
The quantum coherence of a multipartite system is investigated when some of the parties are moving with uniform acceleration and the analysis is carried out using the single mode approximation. Due to acceleration the quantum coherence is divided into two parts as accessible and inaccessible coherence and the entire analysis has been carried out in the single-mode approximation. First we investigate tripartite systems, considering both GHZ and W-states. We find that the quantum coherence of these states does not vanish in the limit of infinite acceleration, rather asymptoting to a non-zero val…
In the present work, we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pairwise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among subsystems. For a three-qubit system, it is impossible that all pairs of qubits violate …
Quantum coherence plays an important role in quantum information protocols that provide an advantage over classical information processing. The amount of coherence that can exist between two orthogonal subspaces is limited by the positivity constraint on the density matrix. On the level of multipartite systems, this gives rise to what is known as monogamy of entanglement. On the level of single systems this leads to a bound, and hence, a trade-off in coherence that can exist between different orthogonal subspaces. In this work we derive trade-off relations for the amount of coherence that can …
An uncertainty relation for the Rényi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(α)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any estimate of a random optical phase shift in terms of average photon number, where $f(α)$ is maximised for non-Shannon entropies. Related simple yet strong uncertainty relations linking phase uncertainty to the photon number distribution, such as $ΔΦ\geq \max_n p_n$, are also obtained. These results are significantly strengthened via upper and lower bounds on the Rény…
Symmetries of both closed and open-system dynamics imply many significant constraints. These generally have instantiations in both classical and quantum dynamics (Noether's theorem, for instance, applies to both sorts of dynamics). We here provide an example of such a constraint which has no counterpart for a classical system, that is, a uniquely quantum consequence of symmetric dynamics. Specifically, we demonstrate the impossibility of broadcasting asymmetry (symmetry-breaking) relative to a continuous symmetry group, for bounded-size quantum systems. The no-go theorem states that if two ini…
Experimentally realized local-global tradeoff in quantum resources
Ningbo University（宁波大学）；Suzhou City University（苏州城市学院）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；The Chinese University of Hong Kong（香港中文大学）
Quantum coherence and quantum correlations are studied in the strongly interacting system composed of two qubits and an oscillator with the presence of a parametric medium. To analytically solve the system, we employ the adiabatic approximation approach. It assumes each qubit's characteristic frequency is substantially lower than the oscillator frequency. To validate our approximation, a good agreement between the calculated energy spectrum of the Hamiltonian with its numerical result is presented. The time evolution of the reduced density matrices of the two-qubit and the oscillator subsystem…
This paper examines the coherence in multipartite systems. We first discuss the distribution of total coherence in a given multipartite quantum state into discord between subsystems and coherent dissonance in each individual subsystem, using the relative entropy as a distance measure. Then we give some trade-off relations between various types of coherence and discord within a bipartite system,and extend these results to the multipartite setting. Finally, the change of coherence in entanglement distribution is studied.
Quantum coherence can be used to infer the presence of a detector without triggering it. Here we point out that, according to quantum mechanics, such interaction-free measurements cannot be perfect, i.e., in a single-shot experiment one has strictly positive probability to activate the detector. We formalize the extent to which such measurements are forbidden by deriving a trade-off relation between the probability of activation and the probability of an inconclusive interaction-free measurement. Our description of interaction-free measurements is theory independent and allows derivations of s…
Producing a large current typically requires large dissipation, as is the case in electric conduction, where Joule heating is proportional to the square of the current. Stochastic thermodynamics offers a framework to study nonequilibrium thermodynamics of small fluctuating systems, and quite recently, microscopic derivations and universal understanding of the trade-off relation between the current and dissipation have been put forward. Here we establish a universal framework clarifying how quantum coherence affects the trade-off between the current and dissipation: a proper use of coherence en…
In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum c…
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.
