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Abstract The ultimate precision in quantum sensing could be achieved using optimal quantum probe states. However, current quantum sensing protocols do not use probe states optimally. Indeed, the calculation of optimal probe states remains an outstanding challenge. Here, we present an algorithm that efficiently calculates a probe state for correlated and uncorrelated measurement strategies. The algorithm involves a conic program, which minimizes a linear objective function subject to conic constraints on a operator-valued variable. Our algorithm outputs a probe state that is a simple function of the optimal variable. We prove that our algorithm finds the optimal probe state for channel estimation problems, even in the multiparameter setting. For many noiseless quantum sensing problems, we prove the optimality of maximally entangled probe states. We also analyze the performance of 3D-field sensing using various probe states. Our work opens the door for a plethora of applications in quantum metrology.

A Dicke state and its decohered state are invariant for permutation. However, when another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation. The amount of asymmetry can be measured by the number of distinguishable states under the group action or the mutual information. Generally, the amount of asymmetry of the whole state is larger than the amount of asymmetry of the added state. That is, the asymmetry activation happens in this case. This paper investigates the amount of the asymmetry activation under Dicke states. To address the asymmetry activation asymptotically, we introduce a new type of central limit theorem by using several formulas on hypergeometric functions. We reveal that the amounts of the asymmetry and the asymmetry activation with a Dicke state have a strictly larger order than those with the decohered state in a specific type of the limit.

Abstract Blind quantum computation (BQC) is a secure quantum computation method that protects the privacy of clients. Measurement-based quantum computation (MBQC) is a promising approach for realizing BQC. To obtain reliable results in blind MBQC, it is crucial to verify whether the resource graph states are accurately prepared in the adversarial scenario. However, previous verification protocols for this task are too resource-consuming or noise-susceptible to be applied in practice. Here, we propose a robust and efficient protocol for verifying arbitrary graph states with any prime local dimension in the adversarial scenario, which leads to a robust and efficient protocol for verifying the resource state in blind MBQC. Our protocol requires only local Pauli measurements and is thus easy to realize with current technologies. Nevertheless, it can achieve optimal scaling behaviors with respect to the system size and the target precision as quantified by the infidelity and significance level, which has never been achieved before. Notably, our protocol can exponentially enhance the scaling behavior with the significance level.

In quantum theory, a quantum state on a composite system of two parties realizes a non-negative probability with any measurement element with a tensor product form. However, there also exist non-quantum states which satisfy the above condition. Such states are called beyond-quantum states, and cannot be detected by standard Bell tests. To distinguish a beyond-quantum state from quantum states, we propose a measurement-device-independent (MDI) test for beyond-quantum state detection, which is composed of quantum input states on respective parties and quantum measurements across the input system and the target system on respective parties. The performance of our protocol is independent of the forms of the tested states and the measurement operators, which provides an advantage in practical scenarios. We also discuss the importance of tomographic completeness of the input sets to the detection.

It is a key issue to characterize the model of standard quantum theory out of general models by an operational condition. The framework of general probabilistic theories (GPTs) is a new information theoretical approach to single out standard quantum theory. It is known that traditional properties, for example, Bell-CHSH inequality, are not sufficient to single out standard quantum theory among possible models in GPTs. As a more precise property, we focus on the bound of the performance for an information task called state discrimination in general models. We give an equivalent condition for outperforming the minimum discrimination error probability under the standard quantum theory given by the trace norm. Besides, by applying the equivalent condition, we characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.

Abstract Complex processes often arise from sequences of simpler interactions involving a few particles at a time. These interactions, however, may not be directly accessible to experiments. Here we develop the first efficient method for unravelling the causal structure of the interactions in a multipartite quantum process, under the assumption that the process has bounded information loss and induces causal dependencies whose strength is above a fixed (but otherwise arbitrary) threshold. Our method is based on a quantum algorithm whose complexity scales polynomially in the total number of input/output systems, in the dimension of the systems involved in each interaction, and in the inverse of the chosen threshold for the strength of the causal dependencies. Under additional assumptions, we also provide a second algorithm that has lower complexity and requires only local state preparation and local measurements. Our algorithms can be used to identify processes that can be characterized efficiently with the technique of quantum process tomography. Similarly, they can be used to identify useful communication channels in quantum networks, and to test the internal structure of uncharacterized quantum circuits.

Herein, we report the copper-catalyzed dehydrogenative C(sp2)–N bond formation of 4-pentenamides via nitrogen-centered radicals. This reaction provides a straightforward and efficient preparation method for γ-alkylidene-γ-lactams. Notably, we could controllably synthesize α,β-unsaturated- or α,β-saturated-γ-alkylidene-γ-lactams depending on the reaction conditions.

Inspired by quantum key distribution, we consider wireless communication between Alice and Bob when the noise generated in the intermediate space between Alice and Bob is controlled by Eve. Our model divides the channel noise into two parts, the noise generated during the transmission and the noise generated in the detector. Eve is allowed to control the former, but is not allowed to do the latter. While the latter is assumed to be a Gaussian random variable, the former is not assumed to be a Gaussian random variable. In this situation, using backward reconciliation and random sampling, we propose a protocol to generate secure keys between Alice and Bob under the assumption that Eve’s detector has a Gaussian noise and Eve is not so close to Alice’s transmitting device. In our protocol, the security criteria are quantitatively guaranteed even with finite block-length code based on the evaluation of error of the estimation of the channel.

In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known how to find practical measurements with optimal precisions, even for uncorrelated measurements over probe states. Here, we give a concrete way to find uncorrelated measurement strategies with optimal precisions. We solve this fundamental problem by introducing a framework of conic programming that unifies the theory of precision bounds for multiparameter estimates for uncorrelated and correlated measurement strategies under a common umbrella. Namely, we give precision bounds that arise from linear programs on various cones defined on a tensor product space of matrices, including a particular cone of separable matrices. Subsequently, our theory allows us to develop an efficient algorithm that calculates both upper and lower bounds for the ultimate precision bound for uncorrelated measurement strategies, where these bounds can be tight. In particular, the uncorrelated measurement strategy that arises from our theory saturates the upper bound to the ultimate precision bound. Also, we show numerically that there is a strict gap between the previous efficiently computable bounds and the ultimate precision bound.

The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of relevant information from a large system. The advent of the age of quantum computing calls for efficient methods that work on information regarding quantum systems. Here we address this by proposing a new and general algorithm for the quantum generalisation of information bottleneck. Our algorithm excels in the speed and the definiteness of convergence compared with prior results. It also works for a much broader range of problems, including the quantum extension of deterministic information bottleneck, an important variant of the original information bottleneck problem. Notably, we discover that a quantum system can achieve strictly better performance than a classical system of the same size regarding quantum information bottleneck, providing new vision on justifying the advantage of quantum machine learning.

An experimental verification of the maximally entangled state ensures that the constructed state is close to the maximally entangled state, but it does not guarantee that the state is exactly the same as the maximally entangled state. Further, the entanglement structure is not uniquely determined in general probabilistic theories even if we impose that the local subsystems are fully equal to quantum systems. Therefore, the existence of the maximally entangled state depends on whether the standard entanglement structure (SES) is valid. To examine this issue, we introduce pseudo SES as a structure of quantum composite system under natural assumptions based on the existence of projective measurements and the existence of approximations of all maximally entangled standard states. Surprisingly, there exist infinitely many pseudo SESs different from the SES. In our setting, any maximally entangled state can be arbitrarily approximated by an entangled state that belongs to our obtained pseudo standard entanglement structure. That is, experimental verification does not exclude the possibility of our obtained pseudo standard entanglement structure that is different from the standard entanglement structure. On the other hand, such pseudo structures never possess global unitary symmetry, i.e. global unitary symmetry is essential condition for the SES.

Self-testing is a technology to certify states and measurements using only the statistics of the experiment. Self-testing is possible if some extremal points in the set B_{Q} of quantum correlations for a Bell experiment are achieved, up to isometries, with specific states and measurements. However, B_{Q} is difficult to characterize, so it is also difficult to prove whether or not a given matrix of quantum correlations allows for self-testing. Here, we show how some tools from graph theory can help to address this problem. We observe that B_{Q} is strictly contained in an easy-to-characterize set associated with a graph, Θ(G). Therefore, whenever the optimum over B_{Q} and the optimum over Θ(G) coincide, self-testing can be demonstrated by simply proving self-testability with Θ(G). Interestingly, these maxima coincide for the quantum correlations that maximally violate many families of Bell-like inequalities. Therefore, we can apply this approach to prove the self-testability of many quantum correlations, including some that are not previously known to allow for self-testing. In addition, this approach connects self-testing to some open problems in discrete mathematics. We use this connection to prove a conjecture [M. Araújo et al., Phys. Rev. A, 88, 022118 (2013)] about the closed-form expression of the Lovász theta number for a family of graphs called the Möbius ladders. Although there are a few remaining issues (e.g., in some cases, the proof requires the assumption that measurements are of rank 1), this approach provides an alternative method to self-testing and draws interesting connections between quantum mechanics and discrete mathematics.

We investigate practical dense coding by imposing locality restrictions on decoders and symmetry restrictions on encoders within the resource theory of asymmetry framework. In this task, the sender Alice and the helper Fred preshare an entangled state. Alice encodes a classical message into the quantum state using a symmetric preserving encoder and sends the encoded state to Bob through a noiseless quantum channel. The receiver Bob and helper Fred are limited to performing quantum measurements satisfying certain locality restrictions to decode the classical message. We are interested in the ultimate dense coding capacity under these constraints. Our contributions are summarized as follows. First, we derive both one-shot and asymptotic optimal achievable transmission rates of the dense coding task under different encoder and decoder combinations. Surprisingly, our results reveal that the transmission rate cannot be improved even when the decoder is relaxed from one-way local operations and classical communication (LOCC) to two-way LOCC, separable measurements, and partial transpose positive measurements of the bipartite system. Second, depending on the class of allowed decoders with certain locality restrictions, we relax the class of encoding operations to superquantum encoders in the general probability theory framework and derive dense coding transmission rates under this setting. For example, when the decoder is fixed to a separable measurement, theoretically, a positive operation is allowed as an encoding operation. Remarkably, even under this superquantum relaxation, the transmission rate still cannot be lifted. This fact highlights the universal validity of our analysis on practical dense coding beyond quantum theory.

When a network has relay nodes, there is a risk that a part of the information is leaked to an untrusted relay. Secure network coding (secure NC) is known as a method to resolve this problem, which enables the secrecy of the message when the message is transmitted over a noiseless network and a part of the edges or a part of the intermediate (untrusted) nodes are eavesdropped. If the channels on the network are noisy, the error correction is applied to noisy channels before the application of secure NC on an upper layer. In contrast, secure physical layer network coding (secure PLNC) is a method to securely transmit a message by a combination of coding operation on nodes when the network is composed of set of noisy channels. Since secure NC is a protocol on an upper layer, secure PLNC can be considered as a cross-layer protocol. In this paper, we compare secure PLNC with a simple combination of secure NC and error correction over several typical network models studied in secure NC.

Many quantum computational tasks have inherent symmetries, suggesting a path to enhancing their efficiency and performance. Exploiting this observation, we propose representation matching, a generic probabilistic protocol for reducing the cost of quantum computation in a quantum network. We show that the representation-matching protocol is capable of reducing the communication or memory cost to almost the minimum in various tasks, including remote execution of unitary gate arrays, permutation gates, and unitary conjugation, as well as the storage and retrieval of unitary gates.

The paper (Hayashi M and Tsurumaru T 2012 New J. Phys. https://doi.org/10.1088/1367-2630/14/9/093014 https://doi.org/10.1088/1367-2630/14/9/093014 ) contains an error at the definition of g _t ( x ) in section 5.3 while g _t ( x ) is used for the second order asymptotic expansion for the sacrifice bit. This corrigendum corrects this error and shows its derivation.

We discuss the effect of sequential error injection on information leakage under a network code. We formulate a network code for the single transmission setting and the multiple transmission setting. Under this formulation, we show that the eavesdropper cannot increase the power of eavesdropping by sequential error injection when the operations in the network are linear operations. We demonstrated the usefulness of this reduction theorem by applying a concrete example of network.

Quantum communication over network is particularly appealing in a similar way to classical network communication, but a partially corrupted quantum network has not been sufficiently studied. We discuss quantum state transmission over a partially corrupted quantum network, in which the sender transmits m_{0} qudits, i.e., d-level systems, to the receiver via network, but m_{1} channels are corrupted. As our result, we show that the optimal transmission rate is at least (m_{0}−2m_{1}+1)logd under the following two settings. In the first case, the unitaries on intermediate nodes are arbitrary and the corruptions on the m_{1} channels are individual. In the second case, the unitaries on intermediate nodes are restricted to Clifford operations and the corruptions on the m_{1} channels are adaptive, i.e., they are caused by an attack with a quantum memory. Further, our code in the second case realizes the noiseless communication even with the single-shot setting and is constructed dependently only on the network topology and the places of the m_{1} corrupted channels.

Depolymerization and polymerization of the actin filament are indispensable in eukaryotes. The DNase I binding loop (D-loop), which forms part of the interface between the subunits in the actin filament, is an intrinsically disordered loop with a large degree of conformational freedom. Introduction of the double mutation G42A/G46A to the D-loop of the beta cytoskeletal mammalian actin restricted D-loop conformational freedom, whereas changes to the critical concentration were not large, and no major structural changes were observed. Polymerization and depolymerization rates at both ends of the filament were reduced, and cofilin binding was inhibited by the double mutation. These results indicate that the two glycines at the tip of the D-loop are important for actin dynamics, most likely by contributing to the large degree of conformational freedom.

We derive finite-length bounds for two problems with Markov chains: source coding with side-information where the source and side-information are a joint Markov chain and channel coding for channels with Markovian conditional additive noise. For this purpose, we point out two important aspects of finite-length analysis that must be argued when finite-length bounds are proposed. The first is the asymptotic tightness, and the other is the efficient computability of the bound. Then, we derive finite-length upper and lower bounds for the coding length in both settings such that their computational complexity is low. We argue the first of the above-mentioned aspects by deriving the large deviation bounds, the moderate deviation bounds, and second-order bounds for these two topics and show that these finite-length bounds achieve the asymptotic optimality in these senses. Several kinds of information measures for transition matrices are introduced for the purpose of this discussion.

The instantaneous quantum polynomial time (IQP) model is one of promising models to demonstrate a quantum computational advantage over classical computers. If the IQP model can be efficiently simulated by a classical computer, an unlikely consequence in computer science can be obtained (under some unproven conjectures). In order to experimentally demonstrate the advantage using medium or large-scale IQP circuits, it is inevitable to efficiently verify whether the constructed IQP circuits faithfully work. There exist two types of IQP models, each of which is the sampling on hypergraph states or weighted graph states. For the first-type IQP model, polynomial-time verification protocols have already been proposed. In this paper, we propose verification protocols for the second-type IQP model. To this end, we propose polynomial-time fidelity estimation protocols of weighted graph states for each of the following four situations where a verifier can (i) choose any measurement basis and perform adaptive measurements, (ii) only choose restricted measurement bases and perform adaptive measurements, (iii) choose any measurement basis and only perform non-adaptive measurements, and (iv) only choose restricted measurement bases and only perform non-adaptive measurements. In all of our verification protocols, the verifier’s quantum operations are only single-qubit measurements. Since we assume no independent and identically distributed property on quantum states, our protocols work in any situation.

We have developed a novel imaging cytometry system using a poly(methyl methacrylate (PMMA)) based microfluidic chip. The system was contamination-free, because sample suspensions contacted only with a flammable PMMA chip and no other component of the system. The transparency and low-fluorescence of PMMA was suitable for microscopic imaging of cells flowing through microchannels on the chip. Sample particles flowing through microchannels on the chip were discriminated by an image-recognition unit with a high-speed camera in real time at the rate of 200 event/s, e.g., microparticles 2.5 μm and 3.0 μm in diameter were differentiated with an error rate of less than 2%. Desired cells were separated automatically from other cells by electrophoretic or dielectrophoretic force one by one with a separation efficiency of 90%. Cells in suspension with fluorescent dye were separated using the same kind of microfluidic chip. Sample of 5 μL with 1 × 106 particle/mL was processed within 40 min. Separated cells could be cultured on the microfluidic chip without contamination. The whole operation of sample handling was automated using 3D micropipetting system. These results showed that the novel imaging flow cytometry system is practically applicable for biological research and clinical diagnostics.

A non-destructive method of collecting cultured cells after identifying their in situ functional characteristics is proposed. In this method, cells are cultivated on an alginate layer in a culture dish and released by spot application of a calcium chelate buffer that locally melts the alginate layer and enables the collection of cultured cells at the single-cell level. Primary hippocampal neurons, beating human embryonic stem (hES) cell-derived cardiomyocytes, and beating hES cell-derived cardiomyocyte clusters cultivated on an alginate layer were successfully released and collected with a micropipette. The collected cells were recultured while maintaining their physiological function, including beating, and elongated neurites. These results suggest that the proposed method may eventually facilitate the transplantation of ES- or iPS-derived cardiomyocytes and neurons differentiated in culture.

Type-II DNA topoisomerases resolve DNA entanglements such as supercoils, knots and catenanes by passing one segment of DNA duplex through a transient enzyme-bridged double-stranded break in another segment. The ATP-dependent passage reaction has previously been demonstrated at the single-molecule level, showing apparent processivity at saturating ATP. Here we directly observed the strand passage by human topoisomerase IIα, after winding a pair of fluorescently stained DNA molecules with optical tweezers for 30 turns into an X-shaped braid. On average 0.51 ± 0.33 µm (11 ± 6 turns) of a braid was unlinked in a burst of reactions taking 8 ± 4 s, the unlinked length being essentially independent of the enzyme concentration between 0.25-37 pM. The time elapsed before the start of processive unlinking decreased with the enzyme concentration, being ~100 s at 3.7 pM. These results are consistent with a scenario where the enzyme binds to one DNA for a period of ~10 s, waiting for multiple diffusional encounters with the other DNA to transport it across the break ~10 times, and then dissociates from the binding site without waiting for the exhaustion of transportable DNA segments.

This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett–Brassard 1984 protocol for finite key lengths, when we employ the decoy method. Using the formula, we can guarantee the security parameter for a realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.

We present a tight security analysis of the Bennett–Brassard 1984 protocol taking into account the finite-size effect of key distillation and achieving unconditional security. We begin by presenting a concise analysis utilizing the normal approximation of the hypergeometric function. Next we show that a similar tight bound can also be obtained by a rigorous argument without relying on any approximation. In particular, for the convenience of experimentalists who wish to evaluate the security of their quantum key distribution systems, we also give the explicit procedures of our key distillation and show how to calculate the secret key rate and the security parameter from a given set of experimental parameters. In addition to the exact values of key rates and security parameters, we also describe how to obtain their rough estimates using the normal approximation.