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Density matrix exponentiation (DME) is a quantum algorithm that processes multiple copies of a program state $\sigma$ to realize the Hamiltonian evolution $e^{-i \sigma t}$. While serving as a prototypical sample-based quantum algorithm, DME is a powerful tool for various quantum information processing tasks, such as quantum principal component analysis and Hamiltonian simulation. In this work, we present a detailed sample complexity analysis of DME and sample-based Hamiltonian simulation. In particular, we prove that the sample complexity of DME is no larger than $4t^2/\varepsilon$, where $t$ is the desired evolution time and $\varepsilon$ is the desired imprecision level, as quantified by the normalized diamond distance. We also establish a fundamental lower bound on the sample complexity of sample-based Hamiltonian simulation, which matches our DME sample complexity bound up to a constant multiplicative factor, thereby proving that DME is optimal for sample-based Hamiltonian simulation. Finally, we point out that the DME sample complexity analysis in Appendix A of [Kimmel et al., npj Quantum Information 3, 13 (2017)] appears to be incomplete, highlighting the need for the results presented here, given the extensive use of DME over the past decade since its original proposal., Comment: 20 pages

Quantum resources like entanglement and magic are essential for characterizing the complexity of quantum states. However, when the number of copies of quantum states and the computational time are limited by numbers polynomial in the system size $n$, accurate estimation of the amount of these resources becomes difficult. This makes it impossible to distinguish between ensembles of states with relatively small resources and one that has nearly maximal resources. Such ensembles with small resources are referred to as "pseudo-quantum" ensembles. Recent studies have introduced an ensemble known as the random subset phase state ensemble, which is pseudo-entangled, pseudo-magical, and pseudorandom. While the current state-of-the-art implementation of this ensemble is conjectured to be realized by a circuit with $O(nt)$ depth, it is still too deep for near-term quantum devices to execute for small $t$. In addition, the strict linear dependence on $t$ has only been established as a lower bound on the circuit depth. In this work, we present significantly improved implementations that only require $\omega(\log n)\cdot O(t[\log t]^2)$ depth circuits, which almost saturates the theoretical lower bound. This is also the fastest known for generating pseudorandom states to the best of our knowledge. We believe that our findings will facilitate the implementation of pseudo-ensembles on near-term devices, allowing executions of tasks that would otherwise require ensembles with maximal quantum resources, by generating pseudo-ensembles at a super-polynomially fewer number of entangling and non-Clifford gates., Comment: 8 pages, 1 figure

We introduce a new class of quantum many-body dynamics in quantum simulations, namely 'pseudochaotic dynamics,' which generates computationally indistinguishable states from Haar-random states within the limited access to the measurement outcomes and runtime of quantum computations. While it is not chaotic, a defining characteristics of many-body quantum chaos, namely out-of-time-ordered correlators, fail to differentiate the pseudochaotic dynamics from chaotic one. We systematically construct such pseudochaotic unitary evolution and investigate their nature through extensive numerical and analytic calculations. Remarkably, we show that the pseudochaotic dynamics can generate a representative pseudo-quantum state, specifically a random subset-phase state, from initial computational states with a depth tightly bound by polylog(n) with the system size n, which opens up a practical route to realize pseudorandom states in near term quantum devices., Comment: 7 pages, 3 figures

Quantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its performance often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We explicitly design two coherent state discrimination protocols based on non-Gaussian unitary operations combined with homodyne detection and orthogonal polynomials, which surpass the Gaussian limit. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes., Comment: 14 pages, 6 figures

Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid algorithm proposed with the goal of approximately solving combinatorial optimization problems such as the MAX-CUT problem. It has been considered a potential candidate for achieving quantum advantage in the Noisy Intermediate-Scale Quantum era and has been extensively studied. However, the performance limitations of low-level QAOA have also been demonstrated across various instances. In this work, we first analytically prove the performance limitations of level-1 QAOA in solving the MAX-CUT problem on bipartite graphs. To this end, we derive an upper bound for the approximation ratio based on the average degree of bipartite graphs. Second, we demonstrate that Recursive QAOA (RQAOA), which recursively reduces graph size using QAOA as a subroutine, outperforms the level-1 QAOA. However, the performance of RQAOA exhibits limitations as the graph size increases. Finally, we show that RQAOA with a restricted parameter regime can fully address these limitations. Surprisingly, this modified RQAOA always finds the exact maximum cut for any bipartite graphs and even for a more general graph with parity-signed weights., Comment: 16 pages, 3 figures

The standard quantum state discrimination problem can be understood as a communication scenario involving a sender and a receiver following these three steps: (i) the sender encodes information in pre-agreed quantum states, (ii) sends them over a noiseless channel, and (iii) the receiver decodes the information by performing appropriate measurements on the received states. In a practical setting, however, the channel is not only noisy but often also unknown, thus altering the states and making optimal decoding generally not possible. In this work, we study this noisy discrimination scenario using a protocol based on indefinite causal order. To this end, we consider the quantum switch and define its higher-order generalisations, which we call superswitches. We find that, for certain channels and ensembles, the guessing probability can be significantly improved compared to both single- and multi-copy state discrimination., Comment: 31 pages, 16 figures

Real photonic devices are subject to photon losses that can decohere quantum information encoded in the system. In the absence of full fault tolerance, quantum error mitigation techniques have been introduced to help manage errors in noisy quantum devices. In this work, we introduce an error mitigation protocol inspired by probabilistic error cancellation (a popular error mitigation technique in discrete variable systems) for continuous variable systems. We show that our quantum error cancellation protocol can undo photon losses in expectation value estimation tasks. To do this, we analytically derive the (non-physical) inverse photon loss channel and decompose it into a sum over physically realisable channels with potentially negative coefficients. The bias of our ideal expectation value estimator can be made arbitrarily small at the cost of increasing the sampling overhead. The protocol requires a noiseless amplification followed by a series of photon-subtractions. While these operations can be implemented probabilistically, for certain classes of initial state one can avoid the burden of carrying out the amplification and photon-subtractions by leveraging Monte-Carlo methods to give an unbiased estimate of the ideal expectation value. We validate our proposed mitigation protocol by simulating the scheme on squeezed vacuum states, cat states and entangled coherent states., Comment: Comments welcome. 22 pages, 10 figures

Why is it that a ticking clock typically becomes less accurate when subject to outside noise but rarely the reverse? Here, we formalize this phenomenon by introducing process causal asymmetry - a fundamental difference in the amount of past information an autonomous agent must track to transform one stochastic process to another over an agent that transforms in the opposite direction. We then illustrate that this asymmetry can paradoxically be reversed when agents possess a quantum memory. Thus, the spontaneous direction in which processes get 'simpler' may be different, depending on whether quantum information processing is allowed or not., Comment: 12 pages, 4 figures

Identifying Bell states without destroying it is frequently dealt with in nowadays quantum technologies such as quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties, and it might be required to determine them separately at each location, without inline communication between parties. We present a scheme for discriminating an arbitrary Bell state distributed to two distant parties without destroying it. The scheme requires two entangled states that are pre-shared between the parties, and we show that without these ancillary resources, the probability of non-destructively discriminating the Bell state is bounded by 1/4, which is the same as random guessing. Furthermore, we demonstrate a proof-of-principle experiment through an IonQ quantum computer that our scheme can surpass classical bounds when applied to practical quantum processor., Comment: 9 pages including Appendix, 7 figures and 2 tables

We establish an information gain-disturbance trade-off relation in local state discrimination. Our result demonstrates a fundamental limitation of local strategy to discriminate entangled quantum states without disturbance, which becomes more difficult as the entanglement of the states to be discriminated increases. For a set of maximally entangled states, the capability of local strategy is tightly suppressed, as random guessing without measurements saturates the bound provided by the trade-off relation. We also show that the trade-off can be circumvented when local operations are aided by pre-shared entanglement. To simultaneously achieve correct guessing of state and non-disturbance, an entirely different strategy from conventional state discrimination should be adopted to lower the cost of pre-shared entanglement. We explicitly propose an adaptive and non-destructive strategy based on the stabilizer formalism, which shows a strict advantage over conventional teleportation-based approaches in pre-shared entanglement cost for discriminating a set of maximally entangled states. As an application of the trade-off relation, we propose an entanglement certification protocol that is robust against depolarizing noise and generalize it to multipartite scenarios in a quantum network., Comment: 5+14 pages, 3 figures

Gaussian boson sampling (GBS) is a promising candidate for an experimental demonstration of quantum advantage using photons. However, sufficiently large noise might hinder a GBS implementation from entering the regime where quantum speedup is achievable. Here, we investigate how thermal noise affects the classical intractability of generic quantum optical sampling experiments, GBS being a particular instance of the latter. We do so by establishing sufficient conditions for an efficient simulation to be feasible, expressed in the form of inequalities between the relevant parameters that characterize the system and its imperfections. We demonstrate that the addition of thermal noise has the effect of tightening the constraints on the remaining noise parameters, required to show quantum advantage. Furthermore, we show that there exist a threshold temperature at which any quantum sampling experiment becomes classically simulable, and provide an intuitive physical interpretation by relating this occurrence with the disappearance of the quantum state's non-classical properties.

The Wigner function formalism has played a pivotal role in examining the non-classical aspects of quantum states and their classical simulatability. Nevertheless, its application in qubit systems faces limitations due to negativity induced by Clifford gates. In this work, we propose a novel classical simulation method for qubit Clifford circuits based on the framed Wigner function, an extended form of the Wigner function with an additional phase degree of freedom. In our framework, Clifford gates do not induce negativity by switching to a suitable frame; thereby, a wide class of nonstabilizer states can be represented positively. By leveraging this technique, we show that some marginal outcomes of Clifford circuits with nonstabilizer state inputs can be efficiently sampled at polynomial time and memory costs. We develop a graph-theoretical approach to identify classically simulatable marginal outcomes and apply it to log-depth random Clifford circuits. We also present the outcome probability estimation scheme using the framed Wigner function and discuss its precision. Our approach opens new avenues for utilizing quasi-probabilities to explore classically simulatable quantum circuits., Comment: 5+16 pages, 6 figures

Entropy plays a crucial role in both physics and information science, encompassing classical and quantum domains. In this work, we present the Quantum Neural Entropy Estimator (QNEE), a novel approach that combines classical neural network (NN) with variational quantum circuits to estimate the von Neumann and Renyi entropies of a quantum state. QNEE provides accurate estimates of entropy while also yielding the eigenvalues and eigenstates of the input density matrix. Leveraging the capabilities of classical NN, QNEE can classify different phases of quantum systems that accompany the changes of entanglement entropy. Our numerical simulation demonstrates the effectiveness of QNEE by applying it to the 1D XXZ Heisenberg model. In particular, QNEE exhibits high sensitivity in estimating entanglement entropy near the phase transition point. We expect that QNEE will serve as a valuable tool for quantum entropy estimation and phase classification., Comment: 14 pages, 5 figures; see also independent researches of Shin, Lee, and Jeong at arXiv:2306.14566v1 and Goldfeld, Patel, Sreekumar, Wilde at arXiv:2307.01171

Gaussian boson sampling constitutes a prime candidate for an experimental demonstration of quantum advantage within reach with current technological capabilities. The original proposal employs photon-number-resolving detectors, however the latter are not widely available. On the other hand, inexpensive threshold detectors can be combined into a single click-counting detector to achieve approximate photon number resolution. We investigate the problem of sampling from a general multi-mode Gaussian state using click-counting detectors and show that the probability of obtaining a given outcome is related to a new matrix function which is dubbed as the Kensingtonian. We show how the latter relates to the Torontonian and the Hafnian, thus bridging the gap between known Gaussian boson sampling variants. We then prove that, under standard complexity-theoretical conjectures, the model can not be simulated efficiently.

The question of whether quantum coherence is a resource beneficial or detrimental to the performance of quantum heat engines has been thoroughly studied but remains undecided. To isolate the contribution of coherence, we analyze the performance of a purely coherence-driven quantum heat engine, a device that does not include any heat flow during the thermodynamic cycle. The engine is powered by the coherence of a multiqubit system, where each qubit is charged via interaction with a coherence bath using the Jaynes-Cummings model. We demonstrate that optimal coherence charging and hence extractable work is achieved when the coherence bath has an intermediate degree of coherence. In our model, the extractable work is maximized when four copies of the charged qubits are used. Meanwhile, the efficiency of the engine, given by the extractable work per input coherence flow, is optimized by avoiding the coherence being stored in the system-bath correlations that is inaccessible to work. We numerically find that the highest efficiency is obtained for slightly lower temperatures and weaker system-bath coupling than those for optimal coherence charging., Comment: 11 pages, 7 figures

Measurement-induced state disturbance is a major challenge in obtaining quantum statistics at multiple time points. We propose a method to extract dynamic information from a quantum system at intermediate time points, namely snapshotting quantum dynamics. To this end, we apply classical post-processing after performing the ancilla-assisted measurements to cancel out the impact of the measurements at each time point. Based on this, we reconstruct a multi-time quasi-probability distribution (QPD) that correctly recovers the probability distributions at the respective time points. Our approach can also be applied to simultaneously extract exponentially many correlation functions with various time-orderings. We provide a proof-of-principle experimental demonstration of the proposed protocol using a dual-species trapped-ion system by employing $^{171}\rm{Yb}^+$ and $^{138}\rm{Ba}^+$ ions as the system and the ancilla, respectively. Multi-time measurements are performed by repeated initialization and detection of the ancilla state without directly measuring the system state. The two- and three-time QPDs and correlation functions are reconstructed reliably from the experiment, negativity and complex values in the QPDs clearly indicate a contribution of the quantum coherence throughout dynamics., Comment: 9 pages, 6 figures

The principle of microscopic reversibility lies at the core of fluctuation theorems, which have extended our understanding of the second law of thermodynamics to the statistical level. In the quantum regime, however, this elementary principle should be amended as the system energy cannot be sharply determined at a given quantum phase space point. In this Letter, we propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath through energy-preserving unitary dynamics. Quantum effects can be identified by noting that the backward process is less likely to happen in the existence of quantum coherence between the system's energy eigenstates. The experimental demonstration has been realized by mixing coherent and thermal states in a beam-splitter, followed by heterodyne detection in an optical setup. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit, while the quantum-to-classical transition is observed as the temperature of the thermal field gets higher., Comment: 6+3 pages

Outcome probability estimation via classical methods is an important task for validating quantum computing devices. Outcome probabilities of any quantum circuit can be estimated using Monte Carlo sampling, where the amount of negativity present in the circuit frame representation quantifies the overhead on the number of samples required to achieve a certain precision. In this paper, we propose two classical sub-routines: circuit gate merging and frame optimisation, which optimise the circuit representation to reduce the sampling overhead. We show that the runtimes of both sub-routines scale polynomially in circuit size and gate depth. Our methods are applicable to general circuits, regardless of generating gate sets, qudit dimensions and the chosen frame representations for the circuit components. We numerically demonstrate that our methods provide improved scaling in the negativity overhead for all tested cases of random circuits with Clifford+$T$ and Haar-random gates, and that the performance of our methods compares favourably with prior quasi-probability simulators as the number of non-Clifford gates increases., Comment: 15 pages, 5 figures. Comments welcome

Boson sampling, a computational problem conjectured to be hard to simulate on a classical machine, is a promising candidate for an experimental demonstration of quantum advantage using bosons. However, inevitable experimental noise and imperfections, such as loss in the interferometer and random counts at the detectors, could challenge the sampling task from entering the regime where quantum advantage is achievable. In this work we introduce higher order non-linearities as a mean to enhance the computational complexity of the problem and the protocol's robustness against noise, i.e. increase the noise threshold that allows to perform an efficient classical simulation of the problem. Using a phase-space method based on the negativity volume of the relevant quasi-probability distributions, we establish a necessary non-classicality condition that any experimental proof of quantum advantage must satisfy. Our results indicate that the addition of single-mode Kerr non-linearity at the input state preparation level, while retaining a linear-optical evolution, makes the Boson sampling protocol more robust against noise and consequently relaxes the constraints on noise parameters required to show quantum advantage.

Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a non-classical phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators., Comment: 12 pages, 3 figures

An important issue in developing quantum technology is that quantum states are so sensitive to noise. We propose a protocol that introduces reverse dynamics, in order to precisely control quantum systems against noise described by the Lindblad master equation. The reverse dynamics can be obtained by constructing the Petz recovery map in continuous time. By providing the exact form of the Hamiltonian and jump operators for the reverse dynamics, we explore the potential of utilizing the near-optimal recovery of the Petz map in controlling noisy quantum dynamics. While time-dependent dissipation engineering enables us to fully recover a single quantum trajectory, we also design a time-independent recovery protocol to protect encoded quantum information against decoherence. Our protocol can efficiently suppress only the noise part of dynamics thereby providing an effective unitary evolution of the quantum system., Comment: 6+16 pages

Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. We introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman transitions can be understood as a special case. We also show that the SG interferometer can keep high contrast against a misalignment in position and momentum caused by the field gradient., Comment: 9 pages, 4 figures, accepted for publication in Physical Review A

In an endeavour to better define the distinction between classical macroscopic and quantum microscopic regimes, the Leggett-Garg inequalities were established as a test of macroscopic-realistic theories, which are commonly thought to be a suitable class of descriptions for classical dynamics. The relationship between their violation and non-classicality is however not obvious. We show that classical states of light, which in the quantum optical sense are any convex sums of coherent states, may not satisfy the Leggett-Garg inequalities. After introducing a simple Mach-Zehnder setup and showing how to obtain a violation with a single photon using negative measurements, we focus on classical states of light, in particular those of low average photon number. We demonstrate how one can still perform negative measurements with an appropriate assignment of variables, and show that the inequalities are violable with coherent states. Finally, we abandon initial phase reference and demonstrate that the violation is still possible, in particular with thermal states of light, and we investigate the effect of intermediate dephasing., Comment: -Minor changes in abstract and introduction. -Added a comprehensive table with all possible cases for clarity. -Corrected result for thermal state. 10 pages, 5 figures

Classical mechanics obeys the intuitive logic that a physical event happens at a definite spatial point. Entanglement however, breaks this logic by enabling interactions without a specific location. In this work we study these delocalised-interactions. These are quantum interactions that create less locational information than would be possible classically, as captured by the disturbance induced on some spatial superposition state. We introduce quantum games to capture the effect and demonstrate a direct operational use for quantum concurrence in that it bounds the non-classical performance gain. We also find a connection with quantum teleportation, and demonstrate the games using an IBM quantum processor., Comment: 20 pages, 5 figures

The R\'enyi entanglement entropy (REE) is an entanglement quantifier considered as a natural generalisation of the entanglement entropy. When it comes to stochastic local operations and classical communication (SLOCC), however, only a limited class of the REEs satisfy the monotonicity condition, while their statistical properties beyond mean values have not been fully investigated. Here, we establish a general condition that the probability distribution of the REE of any order obeys under SLOCC. The condition is obtained by introducing a family of entanglement monotones that contain the higher-order moments of the REEs. The contribution from the higher-order moments imposes a strict limitation on entanglement distillation via SLOCC. We find that the upper bound on success probabilities for entanglement distillation exponentially decreases as the amount of raised entanglement increases, which cannot be captured from the monotonicity of the REE. Based on the strong restriction on entanglement transformation under SLOCC, we design a new method to estimate entanglement in quantum many-body systems from experimentally observable quantities., Comment: 6 + 13 pages

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

The commodity-based cryptography is an alternative approach to realize conventionally impossible cryptographic primitives such as unconditionally secure bit-commitment by consuming pre-established correlation between distrustful participants. A unit of such classical correlation is known as the one-time table (OTT). In this paper, we introduce a new example besides quantum key distribution in which quantum correlation is useful for cryptography. We propose a scheme for unconditionally secure qubit-commitment, a quantum cryptographic primitive forbidden by the recently proven no-masking theorem in the standard model, based on the consumption of the quantum generalization of the OTT, the bipartite quantum state we named quantum one-time tables (QOTT). The construction of the QOTT is based on the newly analyzed internal structure of quantum masker and the quantum secret sharing schemes. Our qubit-commitment scheme is shown to be universally composable. We propose to measure the randomness cost of preparing a (Q)OTT in terms of its entropy, and show that the QOTT with superdense coding can increase the security level with half the cost of OTTs for unconditionally secure bit-commitment. The QOTT exemplifies an operational setting where neither maximally classically correlated state nor maximally entangled state, but rather a well-structured partially entangled mixed state is more valuable resource., Comment: 9+8 pages, to be published in Quantum: Creative Commons issue updated

We establish the general framework of quantum fluctuation theorems by finding the symmetry between the forward and backward transitions of any given quantum channel. The Petz recovery map is adopted as the reverse quantum channel, and the notion of entropy production in thermodynamics is extended to the quantum regime. Our result shows that the fluctuation theorems, which are normally considered for thermodynamic processes, can be a powerful tool to study the detailed statistics of quantum systems as well as the effect of coherence transfer in an arbitrary non-equilibrium quantum process. We introduce a complex-valued entropy production to fully understand the relation between the forward and backward processes through the quantum channel. We find the physical meaning of the imaginary part of entropy production to witness the broken symmetry of the quantum channel. We also show that the imaginary part plays a crucial role in deriving the second law from the quantum fluctuation theorem. The dissipation and fluctuation of various quantum resources including quantum free energy, asymmetry and entanglement can be coherently understood in our unified framework. Our fluctuation theorem can be applied to a wide range of physical systems and dynamics to query the reversibility of a quantum state for the given quantum processing channel involving coherence and entanglement., Comment: 24 pages, 8 figures

We establish the nonclassicality of continuous-variable states as a resource for quantum metrology. Based on the quantum Fisher information of multimode quadratures, we introduce the metrological power as a measure of nonclassicality with a concrete operational meaning of displacement sensitivity beyond the classical limit. This measure belongs to the resource theory of nonclassicality, which is nonincreasing under linear optical elements. Our Letter reveals that a single copy, highly nonclassical quantum state is intrinsically advantageous when compared to multiple copies of a quantum state with moderate nonclassicality. This suggests that metrological power is related to the degree of quantum macroscopicity. Finally, we demonstrate that metrological resources useful for nonclassical displacement sensing tasks can be always converted into a useful resource state for phase sensitivity beyond the classical limit., Comment: 6 + 10 pages, 3 figures, close to published version

We show that contrary to the claim in Sci. Rep. 7, 15492 (2017), the quantum Fisher information itself is not a valid coherence measure based on the resource theory of coherence because it can increase via an incoherent operation.

We demonstrate that quantum Fisher information and superradiance can be formulated as coherence measures in accordance with the resource theory of coherence, thus establishing a direct link between metrological information, superradiance and coherence. We also show that the trivial coherence measure has a metrological interpretation. The arguments are then generalized to show that coherence may be considered as the underlying fundamental resource for any functional of state that is first of all faithful, and second of all concave or linear. Arguments are then presented that show quantum Fisher information and the superradiant quantity are in fact antithetical resources in the sense that if coherence were directed to saturate one quantity, then it must come at the expense of the other. Finally, a key result of the paper is to demonstrate that coherence, quantum Fisher information, superradiant quantity, and entanglement are mutually interconvertible resources under incoherent operations., Comment: 11 pages, 3 figures

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 constraints that relate to quantum metrology and macroscopicity, while for the former, we show that quantum states exist that have finite internal coherence yet with zero deterministic work value. Finally, under minimal thermodynamic assumptions, we establish a clock/work tradeoff relation between these two types of coherences. This can be viewed as a form of time-energy conjugate relation within quantum thermodynamics that bounds the total maximum of clock and work resources for a given system., Comment: 6 + 10 pages

We investigate a measure of quantum coherence and its extension to quantify quantum macroscopicity. The coherence measure can also quantify the asymmetry of a quantum state with respect to a given group transformation. We then show that a weighted sum of asymmetry in each mode can be applied as a measure of macroscopic coherence. To exclude the effects of microscopic superpositions, we suggest a method to introduce a cutoff to the weighted sum that will specify the macroscopic portion of the coherence. This cutoff may be interpreted as the fuzziness for a given measurement outcome. Based on the suggested measures, we investigate the quantum macroscopicity for particular concrete examples in N-partite spin systems., Comment: 12 pages, 3 figures

In this paper, we detail an orthogonalization procedure that allows for the quantification of the amount of coherence present an arbitrary superposition of coherent states. The present construction is based on the quantum coherence resource theory introduced by Baumgratz et al., and the coherence resource monotone that we identify is found to characterize the nonclassicality traditionally analyzed via the Glauber-Sudarshan $P$ distribution. This suggests that identical quantum resources underlie both quantum coherence in the discrete finite dimensional case and the nonclassicality of quantum light. We show that our construction belongs to a family of resource monotones within the framework of a resource theory of linear optics, thus establishing deeper connections between the class of incoherent operations in the finite dimensional regime and linear optical operations in the continuous variable regime., Comment: 8 pages, 2 figures

We propose a measure of macroscopic coherence based on the degree of disturbance caused by a coarse-grained measurement. Based on our measure, we point out that recently proposed criteria of macroscopic coherence may lead to inconsistent results when considering certain states such as a product of microscopic superpositions. An inequality relation is proved that relates the Wigner-Yanase-Dyson skew information and the measurement disturbance, providing arguments as to why our approach is able to rule out such inconsistencies. We show that our measure can also quantify the fragility of a quantum state to a certain type of decoherence. Our work provides a general framework of quantifying macroscopic coherence from an operational point of view, based on the relationship between the precision of the measurement and disturbance of the quantum state., Comment: 17 pages, 3 figures

In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind quantum correlation which we call correlated coherence. We demonstrate that the framework provided by correlated coherence allows us retrieve the same concepts of quantum correlations as defined by the asymmetric and symmetrized versions of quantum discord as well as quantum entanglement, thus providing a unified view of these correlations. We also prove that correlated coherence can be formulated as an entanglement monotone, thus demonstrating that entanglement may be viewed as a specialized form of coherence., Comment: 17 pages

We propose a scheme to generate entanglement between a single-photon qubit in the polarization basis and a coherent state of light. The required resources are a superposition of coherent states, a polarization entangled photon pair, beam splitters, the displacement operation, and four photodetectors. Even when realistic detectors with a limited efficiency are used, an arbitrarily high fidelity can be obtained by adjusting a beam-splitter ratio and the displacement amplitude at the price of reducing the success probability. Our analysis shows that high fidelities may be obtained using on-off detectors with low efficiencies and available resource states under current technology., Comment: 6 pages, 5 figures

We present a review and discussions on characterizations and quantifications of macroscopic quantum states as well as their implementations and applications in optical systems. We compare and criticize different measures proposed to define and quantify macroscopic quantum superpositions and extend such comparisons to several types of optical quantum states actively considered for experimental implementations within recent research topics., Comment: 13 pages, 2 figures, references added, review article to be published in the Special Issue of Optics Communications on Macroscopic Quantumness: Theory and Applications in Optical Sciences

We show that a Bell inequality test using an optical hybrid state between a polarized single photon and a coherent field can be highly robust against detection inefficiency. The Bell violation occurs until the efficiency becomes as low as 67% even though its degree becomes small as the detection efficiency degrades. We consider on/off and photon number parity measurements, respectively, for the Bell test and they result in the similar conditions. If the detection efficiency is higher than 98.68%, parity measurements give larger Bell violations close to Cirel'son's bound, while on/off measurements give larger but moderate violations for realistic values of detector efficiency. Experimental realization of our proposal seems feasible in the near future for the implementation of a loophole-free Bell inequality test., Comment: 8 pages, 9 figures, references added, to be published in Phys. Rev. A