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Homodyne measurement is a crucial tool widely used to address continuous variables for bosonic quantum systems. While an ideal homodyne detection provides a powerful analysis, e.g. to effectively measure quadrature amplitudes of light in quantum optics, it relies on the use of a strong reference field, the so-called local oscillator typically in a coherent state. Such a strong coherent local oscillator may not be readily available particularly for a massive quantum system like Bose-Einstein condensate (BEC), posing a substantial challenge in dealing with continuous variables appropriately. It is necessary to establish a practical framework that includes the effects of non-ideal local oscillators for a rigorous assessment of various quantum tests and applications. We here develop entanglement criteria beyond Gaussian regime applicable for this realistic homodyne measurement that do not require assumptions on the state of local oscillators. We discuss the working conditions of homodyne detection to effectively detect non-Gaussian quantum entanglement under various states of local oscillators., Comment: 9 pages, 5 figures

Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state has been largely unexplored so far; the quantum state of data was simply assumed to be prepared and accessed by a black-box operation -- so-called oracle, even though this process, if not appropriately designed, may adversely diminish the quantum query advantage. Here, we introduce an efficient quantum data-access process, dubbed as quantum data-access machine (QDAM), and present a general architecture for quantum search algorithm. We analyze the runtime of our algorithm in view of the fault-tolerant quantum computation (FTQC) consisting of logical qubits within an effective quantum error correction code. Specifically, we introduce a measure involving two computational complexities, i.e. quantum query and $T$-depth complexities, which can be critical to assess performance since the logical non-Clifford gates, such as the $T$ (i.e., $\pi/8$ rotation) gate, are known to be costliest to implement in FTQC. Our analysis shows that for $N$ searching data, a QDAM model exhibiting a logarithmic, i.e., $O(\log{N})$, growth of the $T$-depth complexity can be constructed. Further analysis reveals that our QDAM-embedded quantum search requires $O(\sqrt{N} \times \log{N})$ runtime cost. Our study thus demonstrates that the quantum data search algorithm can truly speed up over classical approaches with the logarithmic $T$-depth QDAM as a key component., Comment: 16 pages, 8 figures / Published version

The minimum time required for a quantum system to evolve to a distinguishable state is set by the quantum speed limit, and consequently influences the change of quantum correlations and other physical properties. Here we study the time required to maximally entangle two principal systems interacting either directly or via a mediating ancillary system, under the same energy constraints. The direct interactions are proved to provide the fastest way to entangle the principal systems, but it turns out that there exist mediated dynamics that are just as fast. We show that this can only happen if the mediator is initially correlated with the principal systems. These correlations can be fully classical and can remain classical during the entangling process. The final message is that correlations save energy: one has to supply extra energy if maximal entanglement across the principal systems is to be obtained as fast as with an initially correlated mediator., Comment: 8 pages, 3 figures

State disturbance by a quantum measurement is at the core of foundational quantum physics and constitutes a fundamental basis of secure quantum information processing. While quantifying an information-disturbance relation has been a long-standing problem, recently verified reversibility of a quantum measurement requires to refine such a conventional information trade-off toward a complete picture of information conservation in quantum measurement. Here we experimentally demonstrate complete trade-off relations among all information contents, i.e., information gain, disturbance and reversibility in quantum measurement. By exploring various quantum measurements applied on a photonic qutrit, we observe that the information of a quantum state is split into three distinct parts accounting for the extracted, disturbed, and reversible information. We verify that such different parts of information are in trade-off relations not only pairwise but also globally all-at-once, and find that the global trade-off relation is tighter than any of the pairwise relations. Finally, we realize optimal quantum measurements that inherently preserve quantum information without loss of information, which offer wider applications in measurement-based quantum information processing., Comment: 8 pages, 4 figures, Supplementary Note

Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation., Comment: 12 pages, 3 figures

Detection of entanglement in quantum states is one of the most important problems in quantum information processing. However, it is one of the most challenging tasks to find a universal scheme which is also desired to be optimal to detect entanglement for all states of a specific class--as always preferred by experimentalists. Although, the topic is well studied at least in case of lower dimensional compound systems, e.g., two-qubit systems, but in the case of continuous variable systems, this remains as an open problem. Even in the case of two-mode Gaussian states, the problem is not fully solved. In our work, we have tried to address this issue. At first, a limited number of Hermitian operators is given to test the necessary and sufficient criterion on the covariance matrix of separable two-mode Gaussian states. Thereafter, we present an interferometric scheme to test the same separability criterion in which the measurements are being done via Stokes-like operators. In such case, we consider only single-copy measurements on a two-mode Gaussian state at a time and the scheme amounts to the full state tomography. Although this latter approach is a linear optics based one, nevertheless it is not an economic scheme. Resource-wise a more economical scheme than the full state tomography is obtained if we consider measurements on two copies of the state at a time. However, optimality of the scheme is not yet known., Comment: 15 pages, 2 figures

This work analyzes correlations arising from quantum systems subject to sequential projective measurements to certify that the system in question has a quantum dimension greater than some $d$. We refine previous known methods and show that dimension greater than two can be certified in scenarios which are considerably simpler than the ones presented before and, for the first time in this sequential projective scenario, we certify quantum systems with dimension strictly greater than three. We also perform a systematic numerical analysis in terms of robustness and conclude that performing random projective measurements on random pure qutrit states allows a robust certification of quantum dimensions with very high probability.

We introduce two types of statistical quasi-separation between local observables to construct two-party Bell-type inequalities for an arbitrary dimensional systems and arbitrary number of measurement settings per site. Note that, the main difference between statistical quasi-separations and the usual statistical separations is that the former are not symmetric under exchange of the two local observables, whereas latter preserve the symmetry. We show that a variety of Bell inequalities can be derived by sequentially applying triangle inequalities which statistical quasi-separations satisfy. A sufficient condition is presented to show quantum violations of the Bell-type inequalities with infinitesimal values of critical visibility $v_c$., Comment: 12 pages, 2 figures

Rydberg-atom quantum simulators are of keen interest because of their possibilities towards high-dimensional qubit architectures. Here we report three-dimensional conformation spectra of quantum-Ising Hamiltonian systems with programmed qubit connections. With a Rydberg-atom quantum simulator, various connected graphs, in which vertices and edges represent atoms and blockaded couplings, respectively, are constructed in two or three-dimensional space and their eigenenergies are probed during their topological transformations. Star, complete, cyclic, and diamond graphs, and their geometric intermediates, are tested for four atoms and antiprism structures for six atoms. Spectroscopic resolution (dE/E) less than 10% is achieved and the observed energy level shifts and merges through structural transformations are in good agreement with the model few-body quantum-Ising Hamiltonian., Comment: 8 pages, 4 figures

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.

We experimentally implement a machine-learning method for accurately identifying unknown pure quantum states. The method, called single-shot measurement learning, achieves the theoretical optimal accuracy for $\epsilon = O(N^{-1})$ in state learning and reproduction, where $\epsilon$ and $N$ denote the infidelity and number of state copies, without employing computationally demanding tomographic methods. This merit results from the inclusion of weighted randomness in the learning rule governing the exploration of diverse learning routes. We experimentally verify the advantages of our scheme by using a linear-optics setup to prepare and measure single-photon polarization qubits. The experimental results show highly accurate state learning and reproduction exhibiting infidelity of $O(N^{-0.983})$ down to $10^{-5}$, without estimation of the experimental parameters., Comment: 5 pages, 3 figures

We employ the relative entropy as a measure to quantify the difference of eigenmodes between Hermitian and non-Hermitian systems in elliptic optical microcavities. We have found that the average value of the relative entropy in the range of the collective Lamb shift is large, while that in the range of self-energy is small. Furthermore, the weak and strong interactions in the non-Hermitian system exhibit rather different behaviors in term of the relative entropy, and thus it displays an obvious exchange of eigenmodes in the elliptic microcavity., Comment: 9 pages, 5 figures; Close to published version

In this paper, we are interested in detecting the presence of a nearby phase-sensitive object, where traveling light works out under a low-photon loss rate. Here we investigate the optimal quantum phase estimation with generalized multi-component Schrodinger cat states. In addition, we show the optimal conditions of the generalized multi-component cat states for the phase estimation in a lossless scenario. We then demonstrate that the generalized multi-component cat states can beat the performances of the NOON and two-mode squeezed vacuum states in the presence of small loss, while maintaining the quantum advantage over the standard quantum limit, attainable by coherent states. Finally, we propose a generation scheme of the entangled multi-component cat states with current or near-term optical technologies., Comment: 8 pages, 5 figures

As a variant of the original quantum teleportation, the port-based teleportation has been proposed, and its various kinds of useful applications in quantum information processing have been explored. Two users in the port-based teleportation initially share an arbitrary pure state, which can be represented by applying one user's local operation to a bipartite maximally entangled state. If the maximally entangled state is a $2M$-qudit state, then it can be expressed as $M$ copies of a two-qudit maximally entangled state, where $M$ is the number of the ports. We here consider a generalization of the original port-based teleportation obtained from employing copies of an arbitrary bipartite (mixed) resource instead of copies of a pure maximally entangled one. By means of the generalization, we construct a concept of the controlled port-based teleportation by combining the controlled teleportation with the port-based teleportation, and analyze its performance in terms of several meaningful quantities such as the teleportation fidelity, the entanglement fidelity, and the fully entangled fraction. In addition, we present new quantities called the control power and the minimal control power for the new controlled version on a given tripartite quantum state., Comment: 6 pages, 1 figure; Close to published version

We introduce a method for testing quantum correlations in terms of quasiprobability functions in the presence of noise. We analyze the effects of measurement imperfection and thermal environment on quantum correlations and show that their noise effects can be well encapsulated into the change of the order parameter of the generalized quasiprobability function. We then formulate a noise-adaptive entanglement witness in the form of a Bell-type inequality by using the generalized quasiprobability function. Remarkably, it allows us to observe quantum correlations under severe noise. Our method provides a useful tool to test quantum correlations in near-term noisy quantum processors with continuous-variable systems., Comment: 9 pages, 3 figures, published version

Studies addressing the question "Can a learner complete the learning securely?" have recently been spurred from the standpoints of fundamental theory and potential applications. In the relevant context of this question, we present a classical-quantum hybrid sampling protocol and define a security condition that allows only legitimate learners to prepare a finite set of samples that guarantees the success of the learning; the security condition excludes intruders. We do this by combining our security concept with the bound of the so-called probably approximately correct (PAC) learning. We show that while the lower bound on the learning samples guarantees PAC learning, an upper bound can be derived to rule out adversarial learners. Such a secure learning condition is appealing, because it is defined only by the size of samples required for the successful learning and is independent of the algorithm employed. Notably, the security stems from the fundamental quantum no-broadcasting principle. No such condition can thus occur in any classical regime, where learning samples can be copied. Owing to the hybrid architecture, our scheme also offers a practical advantage for implementation in noisy intermediate-scale quantum devices., Comment: 8 pages, 5 figures

Quantum measurement is a basic tool to manifest intrinsic quantum effects from fundamental tests to quantum information applications. While a measurement is typically performed to gain information on a quantum state, its role in quantum technology is indeed manifold. For instance, quantum measurement is a crucial process element in measurement-based quantum computation. It is also used to detect and correct errors thereby protecting quantum information in error-correcting frameworks. It is therefore important to fully characterize the roles of quantum measurement encompassing information gain, state disturbance and reversibility, together with their fundamental relations. Numerous efforts have been made to obtain the trade-off between information gain and state disturbance, which becomes a practical basis for secure information processing. However, a complete information balance is necessary to include the reversibility of quantum measurement, which constitutes an integral part of practical quantum information processing. We here establish all pairs of trade-off relations involving information gain, disturbance, and reversibility, and crucially the one among all of them together. By doing so, we show that the reversibility plays a vital role in completing the information balance. Remarkably, our result can be interpreted as an information-conservation law of quantum measurement in a nontrivial form. We completely identify the conditions for optimal measurements that satisfy the conservation for each tradeoff relation with their potential applications. Our work can provide a useful guideline for designing a quantum measurement in accordance with the aims of quantum information processors., Comment: 15 pages, 5 figures, final version

Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set of samples, a hidden vector or structure involved in $\mathbf{b}$ is obtained by solving a noise-corrupted linear equation $\hat{A}\mathbf{x} \approx \mathbf{b} + \boldsymbol\eta$, where $\boldsymbol\eta$ is a noise vector that cannot be identified. For solving such a noisy linear problem, we consider a quantum algorithm based on a divide-and-conquer strategy, wherein a large core process is divided into smaller subprocesses. The algorithm appropriately reduces both the computational complexities and size of a quantum sample. More specifically, if a quantum computer can access a particular reduced form of the quantum samples, polynomial quantum-sample and time complexities are achieved in the main computation. The size of a quantum sample and its executing system can be reduced, e.g., from exponential to sub-exponential with respect to the problem length, which is better than other results we are aware. We analyse the noise model conditions for such a quantum advantage, and show when the divide-and-conquer strategy can be beneficial for quantum noisy linear problems., Comment: published version

Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources. It would therefore be desirable to avoid it, if possible, for noisy intermediate-scale quantum (NISQ) implementation. Accordingly, we consider a classical-quantum hybrid architecture, which allows large classical input data, with a relatively small-scale quantum system. This hybrid architecture is used to implement an oracle. It is shown that in the presence of noise in the hybrid oracle, the effects of internal noise can cancel each other out and thereby improve the query success rate. It is also shown that such an immunity of the hybrid oracle to noise directly and tangibly reduces the sample complexity in the probably-approximately-correct learning framework. This NISQ-compatible learning advantage is attributed to the oracle's ability to handle large input features., Comment: 10 pages, 5 figures (including Appendix)

We present a logical type of proof of contextuality for a two-qubit state. We formulate a paradox that cannot be verified by a two-qubit system with local measurements while it is possible by using entanglement measurements. With our scheme we achieve $p_{\rm Hardy} \approx 0.167$, which is the highest probability obtained for a system of similar dimension. Our approach uses graph theory and the global exclusivity principle to give an interpretation of logical type of proofs of quantum correlations. We review the Hardy paradox and find connection to the KCBS inequality. We apply the same method to build a paradox based the CHSH inequality.

There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian one. We derive new upper bounds on the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low., Comment: 6 pages, 5 figures; 1 figure added and references are updated

By considering an unreliable oracle in a query-based model of quantum learning, we present a tradeoff relation between the oracle's reliability and the reusability of quantum state of the input data. The tradeoff relation manifests as the fundamental upper bound on the reusability. This limitation on the reusability would increase the quantum access to the input data, i.e., the usage of quantum random access memory (qRAM), repeating the preparation of a superposition of `big' input data on the query failure. However, it is found that, a learner can obtain a correct answer even from an unreliable oracle without any additional usage of qRAM---i.e., the complexity of qRAM query does not increase even with an unreliable oracle. This is enabled by repeatedly cycling the quantum state of the input data to the upper bound on the reusability., Comment: 5 pages, 1 figures

We propose a new scheme of measurement-based quantum computation (MBQC) using an error-correcting code against photon-loss in circuit quantum electrodynamics. We describe a specific protocol of logical single-qubit gates given by sequential cavity measurements for logical MBQC and a generalised Schr\"odinger cat state is used for a continuous-variable (CV) logical qubit captured in a microwave cavity. It is assumed that a three CV-qudit entangled state is initially prepared in three jointed cavities and the microwave qudit states are individually controlled, operated, and measured through a readout resonator coupled with an ancillary superconducting qubit. We then examine a practical approach of how to create the CV-qudit cluster state via a cross-Kerr interaction induced by intermediary superconducting qubits between neighbouring cavities under the Jaynes-Cummings Hamiltonian. This approach could be scalable for building 2D logical cluster states and therefore will pave a new pathway of logical MBQC in superconducting circuits toward fault-tolerant quantum computing., Comment: 2 figures, 18 pages

We study a superposed weak coherent state that can fundamentally mimic an ideal single photon not only with respect to the number of photons but also in terms of an indeterminate phase. It is close to the single-photon state with high fidelity and exhibits fundamental features of single photons such as antibunching and Hong-Ou-Mandel interference. The emergence and vanishing of single-photon characteristics can be directly observed by changing two parameters, i.e., the mean photon number and number of phases. Our result shows that the uncertainty between the photon number and phase indeed constitutes the characteristics of single photons. Finally, we apply the superposed weak coherent state to quantum key distribution and demonstrate that it outperforms the typical approach using phase-randomized weak coherent states., Comment: 8 pages, 5 figures, title and abstract changed, published version

The central issue in quantum parameter estimation is to find out the optimal measurement setup that leads to the ultimate lower bound of an estimation error. We address here a question of whether a Gaussian measurement scheme can achieve the ultimate bound for phase estimation in single-mode Gaussian metrology that exploits single-mode Gaussian probe states in a Gaussian environment. We identify three types of optimal Gaussian measurement setups yielding the maximal Fisher information depending on displacement, squeezing, and thermalization of the probe state. We show that the homodyne measurement attains the ultimate bound for both displaced thermal probe states and squeezed vacuum probe states, whereas for the other single-mode Gaussian probe states, the optimized Gaussian measurement cannot be the optimal setup, although they are sometimes nearly optimal. We then demonstrate that the measurement on the basis of the product quadrature operators XP+PX, i.e., a non-Gaussian measurement, is required to be fully optimal., Comment: 13 pages, 6 figures

Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object., Comment: 7 pages, 2 figures

We present a study on two-particle indistinguishability and particle-species identification by introducing a Fisher-information (FI) approach---in which two particles pass through a two-wave mixing operation and the number of particles is counted in one of the output modes. In our study, we first show that FI can reproduce the Hong-Ou-Mandel (HOM) effect with two bosons or two fermions. In particular, it is found that even though bosons and fermions exhibit different physical behavior (i.e., "bunching" or "anti-bunching") due to their indistinguishability, the aspects of HOM-like dip are quantitatively same. We then provide a simple method for estimating the degree of two-particle indistinguishability in a Mach-Zehnder interferometer-type setup. The presented method also enables us to identify whether the particles are bosons or fermions. Our study will provide useful primitives for various study of boson and fermion characteristics., Comment: 11+1 pages, 6 figures. Corrected typos in page 6

Non-Hermitian properties of open quantum systems and their applications have attracted much attention in recent years. While most of the studies focus on the characteristic nature of non-Hermitian systems, here we focus on the following issue: A non-Hermitian system can be a subsystem of a Hermitian system as one can clearly see in Feshbach projective operator (FPO) formalism. In this case, the orthogonality of the eigenvectors of the total (Hermitian) system must be sustained, despite the eigenvectors of the subsystem (non-Hermitian) satisfy the bi-orthogonal condition. Therefore, one can predict that there must exist some remarkable processes that relate the non-Hermitian subsystem and the rest part, and ultimately preserve the Hermiticity of the total system. In this paper, we study such processes in open elliptical microcavities. The inner part of the cavity is a non-Hermitian system, and the outer part is the coupled bath in FPO formalism. We investigate the correlation between the inner- and the outer-part behaviors associated with the avoided resonance crossings (ARCs), and analyze the results in terms of a trade-off between the relative difference of self-energies and collective Lamb shifts. These results come from the conservation of the orthogonality in the total Hermitian quantum system., Comment: 11 pages, 5 figures

We suggest implementation of quantum teleportation protocol of unknown qubit beyond Bell states formalism. Hybrid entangled state composed of coherent components that belong to Alice and dual-rail single photon at Bob disposal is used. Nonlinear effect on the teleported state is realized due to peculiarity of interaction of coherent components with discrete variable state on a beam splitter. Bob performs unitary transformation after receiving the appropriate classical information. The protocol is nearly deterministic but the output state is subject to amplitude distortion which reduces the fidelity of the protocol. Final problem is reduced to finding a way to get rid of amplitude-distorting factor to restore the original qubit. Some strategies to increase the fidelity of the protocol are used. We show the teleportation can be implemented with arbitrary settings. Our approach is applicable to different basic number states of original unknown qubit. The scheme is realized by linear optics methods and requires an irreducible number of optical elements., Comment: 26 pages, 5 figures

We study a general corresponding principle between discrete-variable quantum states and continuous-variable (especially, restricted on Gaussian) states via quantum purification method. In the previous work, we have already investigated an information-theoretic correspondence between the Gaussian maximally mixed states (GMMSs) and their purifications known as Gaussian maximally entangled states (GMESs) in [Phys. Lett. A {\bf 380}, 3607 (2016)]. We here compare an $N\times N$-dimensional maximally entangled state to the GMES we proposed previously, through an explicit calculation of quantum fidelity between those entangled states. By exploiting the results, we naturally conclude that our GMES is more suitable to the concept of \emph{maximally entangled} state in Gaussian quantum information, and thus it might be useful or applicable for quantum information tasks than the two-mode squeezed vacuum (TMSV) state in the Gaussian regime., Comment: 5 pages, 2 figures; Minor changed and references updated

We formulate an effective-description framework for the dynamics of open quantum systems by extending the time-coarse-graining formalism to open systems. Our coarse-graining procedure efficiently removes high-frequency processes which are responsible for coherences between lower- and upper-manifold states and are irrelevant when considering only low-energy dynamics. We investigate the regime of validity of the resulting coarse-grained master equation by applying it to multi-level atoms driven by far-detuned lasers. Except for such high-frequency coherences, we find good agreement between the exact and coarse-grained dynamics unless the driving lasers are too strong or the initial high-frequency coherences are sizable.

We propose a model for a scalable quantum computing in the circuit-quantum electrodynamics(QED) architecture. In the Kagome lattice of qubits three qubits are connected to each other through a superconducting three-junction flux qubit at the vertices of the lattice. By controlling one of the three Josephson junction energies of the intervening flux qubit we can achieve the circulator function that couples arbitrary pair of two qubits among three. This selective coupling enables the interaction between two nearest neighbor qubits in the Kagome lattice, and further the two-qubit gate operation between any pair of qubits in the whole lattice by performing consecutive nearest neighbor two-qubit gates., Comment: 12 pages, 4 figures, to appear in Quantum Information Processing

We investigate quantum nonlocality of a single-photon entangled state under feasible measurement techniques consisting of on-off and homodyne detections along with unitary operations of displacement and squeezing. We test for a potential violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality, in which each of the bipartite party has a freedom to choose between 2 measurement settings, each measurement yielding a binary outcome. We find that single-photon quantum nonlocality can be detected when two or less of the 4 total measurements are carried out by homodyne detection. The largest violation of the CHSH inequality is obtained when all four measurements are squeezed-and-displaced on-off detections. We test robustness of violations against imperfections in on-off detectors and single-photon sources, finding that the squeezed-and-displaced measurement schemes perform better than the displacement-only measurement schemes., Comment: 7+ pages, 7 figures, 1 table, close to published version

We propose a realistic scheme of generating a traveling odd Schr$\"o$dinger cat state and a generalized entangled coherent state in circuit quantum electrodynamics (circuit-QED). A squeezed vacuum state is used as initial resource of nonclassical states, which can be created through a Josephson traveling-wave parametric amplifier, and travels through a transmission line. Because a single-photon subtraction from the squeezed vacuum gives with very high fidelity an odd Schr$\"o$dinger cat state, we consider a specific circuit-QED setup consisting of the Josephson amplifier creating the traveling resource in a line, a beam-splitter coupling two transmission lines, and a single photon detector located at the end of the other line. When a single microwave photon is detected by measuring the excited state of a superconducting qubit in the detector, a heralded cat state is generated with high fidelity in the opposite line. For example, we show that the high fidelity of the outcome with the ideal cat state can be achieved with appropriate squeezing parameters theoretically. As its extended setup, we suggest that generalized entangled coherent states can be also built probabilistically and useful for microwave quantum information processing for error-correctable qudits in circuit-QED., Comment: 6 pages, 4 figures

The Lamb shift (self-energy) of an elliptic dielectric microcavity is studied. We show that the size of the Lamb shift, which is a small energy shift due to the system-environment coupling in the quantum regime, is dependent on the geometry of the boundary conditions. It shows a global transition depending on the eccentricity of the ellipsis. These transitions can be classified into three types of decay channels known as whispering-gallery modes, stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are manifested through the Poincar\'{e} surface of section with the Husimi distribution function in classical phase space. It is found that the similarity (measured in Bhattacharyya distance) between the Husimi distributions below critical lines of two different modes increases as the difference of their self-energies decreases when the quality factors of the modes are on the same order of magnitude., Comment: 8 pages, 9 figures

We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement if the parts are distinguished by polarization. It was shown in [PRL 110, 140404 (2013)] that this phenomenon can be exploited as a method to test indistinguishability of two particles and it was conjectured that one can also test indistinguishability of macroscopic systems. We propose a setup to test this conjecture. Contrary to the previous studies using two-particle interference effect as in Hong-Ou- Mandel setup, our setup neither assumes that the tested state is composed of single particles nor requires that the total number of particles be fixed. Consequently the notion of entanglement duality is shown to be compatible with a broader class of physical systems. Moreover, by observing duality in entanglement in the above system one can confirm that macroscopic systems exhibit quantum behaviour. As a practical side, entanglement duality is a useful concept that enables adaptive conversion of entanglement of one degree of freedom (DOF) to that of another DOF according to varying quantum protocols., Comment: 5+1 pages, 4 figures, Close to published version

We analyze a coupling scheme for qubits in different cavities of circuit-QED architecture. In contrast to the usual scheme where the cavities are coupled by an interface capacitance we employ a bridge qubit connecting cavities to mediate two-qubit coupling. This active coupling scheme makes it possible to switch on/off and adjust the strength of qubit-qubit coupling, which is essential for scalability of quantum circuit. By transforming the Hamiltonian we obtain an exact expression of two-qubit coupling in the rotating-wave approximation. For the general case of $n$ qubits the Hamiltonian can produce the W state as an eigenstate of the system. We calculate the decay rate of the coupled qubit-resonator system to find that it is viable in real experiments., Comment: 7 pages, 5 figures, some typos are corrected

We study the normal modes and quasi-normal modes (QNMs) in circular dielectric microcavities through non-Hermitian Hamiltonian, which come from the modifications due to system-environment coupling. Differences between the two types of modes are studied in detail, including the existence of resonances tails. Numerical calculations of the eigenvalues reveal the Lamb shift in the microcavity due to its interaction with the environment. We also investigate relations between the Lamb shift and quantized angular momentum of the whispering gallery mode as well as the refractive index of the microcavity. For the latter, we make use of the similarity between the Helmholtz equation and the Schr\"{o}dinger equation, in which the refractive index can be treated as a control parameter of effective potential. Our result can be generalized to other open quantum systems with a potential term., Comment: 8 pages, 8 figures

We generalize the control power of a perfect controlled teleportation of an entangled three-qubit pure state, suggested by Li and Ghose [Phys. Rev. A {\bf 90}, 052305 (2014)], to the control power of a general controlled teleportation of a multiqubit pure state. Thus, we define the minimal control power, and calculate the values of the minimal control power for a class of general three-qubit Greenberger-Horne-Zeilinger (GHZ) states and the three-qubit W class whose states have zero three-tangles. Moreover, we show that the standard three-qubit GHZ state and the standard three-qubit W state have the maximal values of the minimal control power for the two classes, respectively. This means that the minimal control power can be interpreted as not only an operational quantity of a three-qubit quantum communication but also a degree of three-qubit entanglement. In addition, we calculate the values of the minimal control power for general n-qubit GHZ states and the n-qubit W-type states., Comment: 5 pages, No figures; Close to published version

We propose a quantum communication protocol that can be used to transmit any quantum state, one party to another via several intermediate nodes, securely on quantum communication network. The scheme makes use of the sequentially chained and approximate version of private quantum channels satisfying certain commutation relation of $n$-qubit Pauli operations. In this paper, we study the sequential structure, security analysis, and efficiency of the quantum sequential transmission (QST) protocol in depth., Comment: 5 pages, 1 figure

While the objective of conventional quantum key distribution (QKD) is to secretly generate and share the classical bits concealed in the form of maximally mixed quantum states, that of private quantum channel (PQC) is to secretly transmit individual quantum states concealed in the form of maximally mixed states using shared one-time pad and it is called Gaussian private quantum channel (GPQC) when the scheme is in the regime of continuous variables. We propose a GPQC enhanced with squeezed coherent states (GPQCwSC), which is a generalization of GPQC with coherent states only (GPQCo) [Phys. Rev. A 72, 042313 (2005)]. We show that GPQCwSC beats the GPQCo for the upper bound on accessible information. As a subsidiary example, it is shown that the squeezed states take an advantage over the coherent states against a beam splitting attack in a continuous variable QKD. It is also shown that a squeezing operation can be approximated as a superposition of two different displacement operations in the small squeezing regime., Comment: 7 pages, 2 figures

In quantum information processing, one of the most useful interaction between qubits is the Ising type interaction. We propose a scheme to implement the exact Ising interaction through magnetic dipole-dipole interaction. Although magnetic dipolar interaction is Heisenberg type in general, this interaction can bring about the exact mathematical form of the Ising interaction if qubit levels are chosen among the highest magnetic quantum number states. Real physical systems to which our scheme can be applied include rotational states of molecules, hyperfine states of atoms, or electronic states of nitrogen-vacancy centers in diamond. We analyze the feasibility of our scheme for these systems. For example, when the hyperfine levels of rubidium 87 atoms are chosen as qubits and the distance of the two atoms is 0.1 micrometer, controlled-Z gate time will be 8.5 ms. We suggest diverse search and study to achieve optimal implementation of this scheme.

We study how conditional photon operations can affect multipartite quantum correlations, specifically nonlocality and entanglement, of the continuous variable GHZ states. We find that the violation of the Mermin-Klyshko inequality revealing the multipartite nonlocality can be made stronger with photon subtraction applied on each mode of the original GHZ states, particularly in a weak squeezing regime. Photon addition applied on local modes also turns out to enhance the degree of multipartite nonlocality in a broad range of parameters. We further investigate the effects of the photon operations on the degree of multipartite entanglement by looking into the Gaussian tangle, the fidelity of teleportation network, and the quadrature correlations. We find that photon subtraction applied on two modes enhances those entanglement characteristics in a practical squeezing regime while there is no improvement made by photon addition., Comment: 11 pages, 10 figures, to appear in Phys. Rev. A

Defining a computational basis of pseudo-number states, we interpret a coherent state of large amplitude, $|\alpha|\gg\frac{d}{2\pi}$, as a qudit --- a $d$-level quantum system --- in a state that is an even superposition of $d$ pseudo-number states. A pair of such coherent-state qudits can be prepared in maximally entangled state by generalized Controlled-$Z$ operation that is based on cross-Kerr nonlinearity, which can be weak for large $d$. Hence, a coherent-state optical qudit cluster state can be prepared by repetitive application of the generalized Controlled-$Z$ operation to a set of coherent states. We thus propose an optical qudit teleportation as a simple demonstration of cluster state quantum computation., Comment: 5 figures