The coherence resource theory needs to study the operational value and efficiency which can be broadly formulated as the question: when can one coherent state be converted into another under incoherent operations. We answer this question completely for one-mode continuous-variable systems by characterizing conversion of coherent Gaussian states under incoherent Gaussian operations in terms of their first and second moments. The no-go theorem of purification of coherent Gaussian states is also built. The structure of incoherent Gaussian operations of two-mode continuous-variable systems is discussed further and is applied to coherent conversion for pure Gaussian states with standard second moments. The standard second moments are images of all second moments under local linear unitary Bogoliubov operations. As concrete applications, we obtain some peculiarities of a Gaussian system: (1) There does not exist a maximally coherent Gaussian state which can generate all coherent Gaussian states; (2) The conversion between pure Gaussian states is reversible; (3) The coherence of input pure state and the coherence of output pure state are equal.
We show that the dynamical Casimir effect in an optomechanical system can be achieved under incoherent mechanical pumping. We adopt a fully quantum-mechanical approach for both the cavity field and the oscillating mirror. The dynamics is then evaluated using a recently-developed master equation approach in the dressed picture, including both zero and finite temperature photonic reservoirs. This analysis shows that the dynamical Casimir effect can be observed even when the mean value of the mechanical displacement is zero. This opens up new possibilities for the experimental observation of this…
Quantum states transformation under free operations plays a central role in the resource theory of coherence. In this paper, we investigate the transformation from a mixed coherent state into a pure one by using both incoherent operations and stochastic incoherent operations. We show that contrary to the strictly incoherent operations and the stochastic strictly incoherent operations, both the incoherent operations and the stochastic incoherent operations can increase the dimension of the maximal pure coherent subspace of a state. This means that the incoherent operations are generally stronge…
Mechanisms controlling excitation energy transport (EET) in light-harvesting complexes remain controversial. Following the observation of long-lived beats in two-dimensional electronic spectroscopy of PC645, vibronic coherence, the delocalization of excited states between pigments supported by a resonant vibration, has been proposed to enable direct down-conversion from the highest-energy states to the lowest-energy pigments. Here, we instead show that for phycobiliprotein PC645 an incoherent vibronic transport mechanism is at play. We quantify the solvation dynamics of individual pigments usi…
Considerable work has recently been directed toward developing resource theories of quantum coherence. In most approaches, a state is said to possess quantum coherence if it is not diagonal in some specified basis. In this letter we establish a criterion of physical consistency for any resource theory in terms of physical implementation of the free operations, and we show that all currently proposed basis-dependent theories of coherence fail to satisfy this criterion. We further characterize the physically consistent resource theory of coherence and find its operational power to be quite limit…
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…
In this paper, we address the issue of enhancing coherence of a state under stochastic strictly incoherent operations. Based on the $l_1$ norm of coherence, we obtain the maximal value of coherence that can be achieved for a state undergoing a stochastic strictly incoherent operation and the maximal probability of obtaining the maximal coherence. Our findings indicate that a pure state can be transformed into a maximally coherent state under a stochastic strictly incoherent operation if and only if all the components of the pure state are nonzero while a mixed state can never be transformed in…
It has been asked by different authors whether the two classes of Schatten-$p$-norm-based functionals $C_p(ρ)=\min_{σ\in\mathcal{I}}||ρ-σ||_p$ and $ \tilde{C}_p(ρ)= \|ρ-Δρ\|_{p}$ with $p\geq 1$ are valid coherence measures under incoherent operations, strictly incoherent operations, and genuinely incoherent operations, respectively, where $\mathcal{I}$ is the set of incoherent states and $Δρ$ is the diagonal part of density operator $ρ$. Of these questions, all we know is that $C_p(ρ)$ is not a valid coherence measure under incoherent operations and strictly incoherent operations, but all othe…
We found that the Wigner-Yanase skew information, which has been recently proposed as a measure of coherence in [Phys. Rev. Lett. \textbf{113}, 170401(2014)], can increase under a class of operations which may be interpreted as incoherent following the framework of Baumgratz et al., while being phase sensitive.
Entangled photons produced by spontaneous parametric down-conversion have been of paramount importance for our current understanding of quantum mechanics and advances in quantum information. In this process, the quantum correlations of the down-converted photons are governed by the optical properties of the pump beam illuminating the non-linear crystal. Extensively, the pump beam has been modeled by either coherent beams or by the well-know Gaussian-Schell model, which leads to the natural conclusion that a high degree of optical coherence is required for the generation of highly entangled sta…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and inter-conversion of the resource. Here we solve this question completely for qubit states by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. Extending the discussion to distributed scenarios, we introduce and address the task of assisted incoherent state conversion where the process is enhanced by making use of correlations with a second party. Building on these…
We build the counterpart of the celebrated Nielsen's theorem for coherence manipulation in this paper. This offers an affirmative answer to the open question: whether, given two states $ρ$ and $σ$, either $ρ$ can be transformed into $σ$ or vice versa under incoherent operations [Phys. Rev. Lett. \textbf{113}, 140401(2014)]. As a consequence, we find that there exist essentially different types of coherence. Moreover, incoherent operations can be enhanced in the presence of certain coherent states. These extra states are coherent catalysts: they allow uncertain incoherent operations to be reali…
Quantum coherence is a fundamental property that can emerge within any quantum system. Incoherent operations, defined in terms of the Kraus decomposition, take an important role in state transformation. The maximum number of incoherent Kraus operators has been presented in [A. Streltsov, S. Rana, P. Boes, J. Eisert, Phys. Rev. Lett. 119. 140402 (2017)]. In this work, we show that the number of incoherent Kraus operators for a single qubit can be reduced from 5 to 4 by constructing a proper unitary matrix. For qutrit systems we further obtain 32 incoherent Kraus operators, while the upper bound…
Resource theory of quantum coherence originated like entanglement in quantum information theory. However, still now proper classification of quantum states is missing under coherence. In this work, we have provided a classification of states under local incoherent operations. We have succeeded in deriving the necessary and sufficient condition for which two pure multipartite states are equivalent under stochastic local incoherent operations and classical communications (SLICC) and local incoherent operations and classical communications (LICC). In particular, we have succeeded in characterizin…
Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this paper, we present the necessary and sufficient conditions under which a mixed state can be distilled into a pure coherent state via stochastic incoherent operations (sIOs). With the help of this result, we further show the following: (i) Any $2$-dimensional coherent state is distillable via sIOs if and only if it is a pure coherent state; (ii) a state $ρ$ is n-distillable via sIOs if and only if it is 1-distillable; and (iii) the set of distillable states via stochastic maximally incoheren…
Manipulation and quantification of quantum resources are fundamental problems in quantum physics. In the asymptotic limit, coherence distillation and dilution have been proposed by manipulating infinite identical copies of states. In the non-asymptotic setting, finite data-size effects emerge, and the practically relevant problem of coherence manipulation using finite resources has been left open. This letter establishes the one-shot theory of coherence dilution, which involves converting maximally coherent states into an arbitrary quantum state using maximally incoherent operations, dephasing…
We experimentally investigate problems of one-shot coherence distillation [Regula, Fang, Wang, and Adesso, Phys. Rev. Lett. 121, 010401 (2018)]. Based on a set of optical devices, we design a type of strictly incoherent operation (SIO), which is applicable in high-dimensional cases and can be applied to accomplish the transformations from higher-dimensional states to lower-dimensional states. Furthermore, a relatively complete process of the one-shot coherence distillation is experimentally demonstrated for three- and four-dimensional input states. Experimental data reveal an interesting resul…
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…
Experimental challenges and prospects for quantum-enhanced energy conversion: Stationary Fano coherence in V-type qutrits interacting with polarized incoherent radiation
Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家光学研究所）；European Laboratory for Non-linear Spectroscopy (LENS), Università degli Studi di Firenze（佛罗伦萨大学非线性光谱学欧洲实验室）；Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze（佛罗伦萨大学物理与天文学系）；Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (CNR-ISC)（意大利复杂系统研究所）
We characterize the distillation of quantum coherence in the one-shot setting, that is, the conversion of general quantum states into maximally coherent states under different classes of quantum operations. We show that the maximally incoherent operations (MIO) and the dephasing-covariant incoherent operations (DIO) have the same power in the task of one-shot coherence distillation. We establish that the one-shot distillable coherence under MIO and DIO is efficiently computable with a semidefinite program, which we show to correspond to a quantum hypothesis testing problem. Further, we introdu…
We investigate the coherence of quantum channels using the Choi-Jamiołkowski isomorphism. The relation between the coherence and the purity of the channel respects a duality relation. It characterizes the allowed values of coherence when the channel has certain purity. This duality has been depicted via the Coherence-Purity (Co-Pu) diagrams. In particular, we study the quantum coherence of the unital and non-unital qubit channels and find out the allowed region of coherence for a fixed purity. We also study coherence of different incoherent channels, namely, incoherent operation (IO), strictly…
In the task of assisted coherence distillation via the set of operations X, where X is either local incoherent operations and classical communication (LICC), local quantum-incoherent operations and classical communication (LQICC), separable incoherent operations (SI), or separable quantum incoherent operations (SQI), two parties, namely Alice and Bob, share many copies of a bipartite joint state. The aim of the process is to generate the maximal possible coherence on the subsystem of Bob. In this paper, we investigate the assisted coherence distillation of some special mixed states, the states…
The correlation properties of the pump field in spontaneous parametric down-conversion are crucial in determining the degree of entanglement of generated signal and idler photons. We find theoretically that continuous-variable entanglement of the transverse positions and momenta of these photons can be achieved only if the coherence of the pump beam is sufficiently high. The positions of signal and idler photons are found to be correlated, even for an incoherent pump. However, the momenta of the signal and idler photons are not anti-correlated, even though transverse momentum is conserved.
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…
Strictly incoherent operations (SIO) proposed in [Phys. Rev. Lett. 116, 120404 (2016)] are promising to be a good candidate of free operations in the resource theory of quantum coherence, setting against the central role of local operations and classical communication in the resource theory of quantum entanglement. An important open problem is an efficient description for strictly incoherent operations in physical region. Such a description plays key role for axiomatic study of resource theory of quantum coherence. We are aimed to give a structural characterization of bistochastic SIOs in term…
We investigate the single qubit transformations under several typical coherence-free operations, such as, incoherent operation (IO), strictly incoherent operation (SIO), physically incoherent operation (PIO), and coherence preserving operation (CPO). Quantitative connection has been built between IO and SIO in single qubit systems. Moreover, these coherence-free operations have a clear hierarchical relationship in single qubit systems: CPO $\subset$ PIO $\subset$ SIO=IO. A new and explicit proof for the necessary and sufficient condition of single qubit transformation via IO or SIO has been pr…
We mainly study the block-coherence measures based on resource theory of block-coherence and the coherence measures based on positive-operator-valued measures (POVM). Several block-coherence measures including a block-coherence measure based on maximum relative entropy, the one-shot block coherence cost under the maximally block-incoherent operations, and a coherence measure based on coherent rank have been introduced and the relationships between these block-coherence measures have been obtained. We also give the definition of the maximally block-coherent state and describe the deterministic …
A major signature of quantum mechanics beyond classical physics is coherence, the existence of superposition states. The recently developed resource theory of quantum coherence allows the formalisation of incoherent operations -- those operations which cannot create coherence. We identify the set of operations which additionally do not use coherence. These are such that coherence cannot be exploited by a classical observer, who measures incoherent properties of the system, to go beyond classical dynamics. We give a physical interpretation in terms of interferometry and prove a dilation theorem…
The coherence-breaking channels play a significant role in quantum information theory. We study the coherence-breaking channels and give a method to amend the coherence-breaking channels by applying unitary operations. For given incoherent channel $Φ$, we give necessary and sufficient conditions for the channel to be a coherence-breaking channel and amend it via unitary operations. For qubit incoherent channels $Φ$ that are not coherence-breaking ones, we consider the mapping $Φ\circΦ$ and present the conditions for coherence-breaking and channel amendment as well.
Quantum coherence is an essential feature of quantum mechanics which is responsible for the departure between classical and quantum world. The recently established resource theory of quantum coherence studies possible quantum technological applications of quantum coherence, and limitations which arise if one is lacking the ability to establish superpositions. An important open problem in this context is a simple characterization for incoherent operations, constituted by all possible transformations allowed within the resource theory of coherence. In this work, we contribute to such a character…
To guarantee the security of uniform random numbers generated by a quantum random number generator, we study secure extraction of uniform random numbers when the environment of a given quantum state is controlled by the third party, the eavesdropper. Here we restrict our operations to incoherent strategies that are composed of the measurement on the computational basis and incoherent operations (or incoherence-preserving operations). We show that the maximum secure extraction rate is equal to the relative entropy of coherence. By contrast, the coherence of formation gives the extraction rate w…
Cohering power and de-cohering power have recently been proposed to quantify the ability of a quantum operation to produce and erase coherence respectively. In this paper, we investigate the properties of cohering power and de-cohering power. First, we prove the equivalence between two different kinds of cohering power for any quantum operation on single qubit systems, which implies that l1 norm of coherence is monotone under Maximally incoherent operation (MIO) and Dephasing-covariant operation (DIO) in 2-dimensional space. In higher dimensions, however, we show that the monotonicity under MI…
We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying Clifford gates. The Clifford gates are chosen from the comparisons between both codes. The fault tolerance of the conversion is guaranteed by quantum error correction in every step during the entire conversion process. As examples, we show three conversions: the $[[5,1,3]]$ stabilizer code and Steane code, Steane code and $[[15,1,3]]$ Reed-Muller code, and Stea…
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…
One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum coherence resource theory by introducing the generalized coherence vector of an arbitrary quantum state. The generalized coherence vector is a probability vector that can be interpreted as a concave roof extension of the pure states coherence vector. We show that it completely characterizes the notions of being incoherent, as well as being maximally coherent. Moreo…
Given an orthonormal basis in a $d$-dimensional Hilbert space and a unital quantum operation $\cal E$ acting on it one can define a non-linear mapping that associates to $\cal E$ a $d\times d$ real-valued matrix that we call the Coherence Matrix of $\cal E$ with respect to $B$. We show that one can use this coherence matrix to define vast families of measures of the coherence generating power (CGP) of the operation. These measures have a natural geometrical interpretation as separation of $\cal E$ from the set of incoherent unital operations. The probabilistic approach to CGP discussed in P. Z…
We compute analytically the maximal rates of distillation of quantum coherence under strictly incoherent operations (SIO) and physically incoherent operations (PIO), showing that they coincide for all states, and providing a complete description of the phenomenon of bound coherence. In particular, we establish a simple, analytically computable necessary and sufficient criterion for the asymptotic distillability under SIO and PIO. We use this result to show that almost every quantum state is undistillable --- only pure states as well as states whose density matrix contains a rank-one submatrix …
The intensity transverse profile of the light produced in the process of stimulated down-conversion is derived. A quantum-mechanical treatment is used. We show that the angular spectrum of the pump laser can be transferred to the stimulated down-converted beam, so that images can also be transferred from the pump to the down-converted beam. We also show that the transfer can occur from the stimulating beam to the down-converted one. Finally, we study the process of diffraction through an arbitrarily shaped screen. For the special case of a double-slit, the interference pattern is explicitly ob…
It is well known that the majorization condition is the necessary and sufficient condition for the deterministic transformations of both pure bipartite entangled states by local operations and coherent states under incoherent operations. In this paper, we present two explicit protocols for these transformations. We first present a permutation-based protocol which provides a method for the single-step transformation of $d$-dimensional coherent states. We also obtain generalized solutions of this protocol for some special cases of $d$-level systems. Then, we present an alternative protocol where…
Conversions between the ground states in quantum critical systems via entanglement-assisted local operations and classical communications (eLOCC) are studied. We propose a new method to reveal the different convertibility by local operations when a quantum phase transition occurs. We have studied the ground state local convertibility in the one dimensional transverse field Ising model, XY model and XXZ model. It is found that the eLOCC convertibility sudden changes at the phase transition points. In transverse field Ising model the eLOCC convertibility between the first excited state and the g…
We develop the Keldysh formalism for the polarization dynamics of an open spin system. We apply it to the swapping between two qubit states in a model describing an NMR cross-polarization experiment. The environment is a set of interacting spins. For fast fluctuations in the environment, the analytical solution shows effects missed by the secular approximation of the Quantum Master Equation for the density matrix: a frequency decrease depending on the system-environment escape rate and the quantum quadratic short time behavior. Considering full memory of the bath correlations yields a progress…
We propose a simple setup for the conversion of multipartite entangled states in a quantum network with restricted access. The scheme uses nonlocal operations to enable the preparation of states that are inequivalent under local operations and classical communication, but most importantly does not require full access to the states. It is based on a flexible linear optical conversion gate that uses photons, which are ideally suited for distributed quantum computation and quantum communication in extended networks. In order to show the basic working principles of the gate, we focus on converting…
We study when a non--local unitary operation acting on two $d$--level systems can probabilistically simulate another one when arbitrary local operations and classical communication are allowed. We provide necessary and sufficient conditions for the simulation to be possible. Probabilistic interconvertability is used to define an equivalence relation between gates. We show that this relation induces a finite number of classes, that we identify. In the case of two qubits, two classes of non--local operations exist. We choose the CNOT and SWAP as representatives of these classes. We show how the …
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…
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…
Quantum coherence, like entanglement, is a fundamental resource in quantum information. In recent years, remarkable progress has been made in formulating resource theory of coherence from a broader perspective. The notions of block-coherence and POVM-based coherence have been established. Certain challenges, however, remain to be addressed. It is difficult to define incoherent operations directly, without requiring incoherent states, which proves a major obstacle in establishing the resource theory of dynamical coherence. In this paper, we overcome this limitation by introducing an alternate d…
