The Royal Swedish Academy of Sciences awarded the Nobel Prize in Physics 2022 jointly to Alain As... more The Royal Swedish Academy of Sciences awarded the Nobel Prize in Physics 2022 jointly to Alain Aspect, John Clauser, and Anton Zeilinger for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. The present article provides a brief overview on the significance of their contributions and practical quantum information applications of Bell inequalities and entanglement.
In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs... more In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs) or symmetric, informationally complete states (SICs), improves the capability of detecting entangled states both theoretically and experimentally. On the theoretical side, we show that measurement in quantum 2-design can detect entangled states twice compared to entanglement witnesses. On the implementation side, we present the scheme of entanglement detection with two detectors only of a Hong-Ou-Mandel interferometer. The experimental scheme applies single-copy level measurement followed by post-processing of measurement outcomes, which is feasible with current technologies.
We study N-dimensional measurement-device-independent quantum-key-distribution protocol where one... more We study N-dimensional measurement-device-independent quantum-key-distribution protocol where one checking state is used. Only assuming that the checking state is a superposition of other N sources, we show that the protocol is secure in zero quantum-bit-error-rate case, suggesting possibility of the protocol. The method may be applied in other quantum information processing. Quantum key distribution (QKD) 1,2 enables two remote users, normally called Alice and Bob, to generate key (private random sequence), which is not a possible task classically. QKD is not only a practically important field but also a theoretically appealing one. After security of QKD for ideal devices was shown 1,3,4 , problems due to imperfect devices protruded. Although a main problem due to imperfect source was resolved 5 , problem due to imperfect detectors still had remained 6,7. Then no-signaling QKD was discovered 8,9. Remarkably, the no-signaling QKD's were found to be immune against the imperfect device problems, because security analysis of the protocol is based only on outcomes of detectors. Soon device-independent (DI) QKD's were found 10. DI QKD has ideal security but not yet feasible. Measurement-device-independent (MDI) QKD was proposed 11 and demonstrated 12-15 in the background. MDI QKD is secure provided that source is ideal, that is, source is exactly in prescribed quantum states. Later protocols 16,17 with more relaxed condition adapt un-characterized source. The only assumption is that the sources are within 2-dimensional subspace. It can be expected that MDI QKD can be generalized to N-dimensional case. However, security of MDI QKD with un-characterized source relies 16,17 on Shor-Preskill proof 4. Thus it is not yet clear that N-dimensional MDI QKD with un-characterized source works. In this paper, we consider the N-dimensional MDI QKD with un-characterized source. The only assumption for security is that the sources are within N-dimensional subspace. In the protocol, a single quantum state is enough for checking eavesdropper, normally called Eve. (It is known that a single checking state is enough 18). We show that the protocol is secure in zero quantum-bit-error-rate (QBER) case. This suggests possibility of N-dimensional MDI QKD with un-characterized source.
We outline a straightforward approach for obtaining a secret key rate using only no-signaling con... more We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed i... more The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
We report the first experimental realization of an approximate partial transpose for photonic two... more We report the first experimental realization of an approximate partial transpose for photonic two-qubit systems. The proposed scheme is based on the local operation on single copies of quantum states and classical communication, and therefore can be easily applied for other quantum information tasks within current technologies. Direct detection of entanglement, i.e., without performing quantum state tomography, using the partial transpose operation, is also demonstrated.
The kernel trick in supervised learning signifies transformations of an inner product by a featur... more The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds to an instance with a Hilbert space of quantum states by fueling quantum resources to machine learning algorithms. In this work, we point out that the quantum state space is specific such that a measurement postulate characterizes an inner product and that manipulation of quantum states prepared from classical data cannot enhance the distinguishability of data points. We present a feature map for quantum data as a probabilistic manipulation of quantum states to improve supervised learning algorithms.
We investigate secrecy properties of bipartite quantum channels when local environment called shi... more We investigate secrecy properties of bipartite quantum channels when local environment called shield system is assisted. Two honest parties apply either the classical distillation such as the standard one-way postprocessing followed by the advantage distillation (AD), or the quantum distillation applying the recurrence protocol. We then identify those entangled states that can be converted to secrecy by either the quantum or the classical distillation. Remarkably much wider range of bound entangled states are shown to be distilled to secrecy.
From a practical perspective it is advantageous to develop methods that verify entanglement in qu... more From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite ( d × d ) -dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses (EWs) composed of MUBs can detect bound entanglement if the number of measurements is greater than d / 2 + 1 . This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of d + 1 MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of EWs. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed i... more The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
Devising efficient communication in a network consisting of multiple transmitters and receivers i... more Devising efficient communication in a network consisting of multiple transmitters and receivers is a problem of immense importance in communication theory. Interestingly, resources in the quantum world have been shown to be very effective in enhancing the performance of communication networks. In this work, we study entanglement-assisted communication over classical network channels. When there is asymmetry such that noise introduced by the channel depends on the input alphabets, non communicating senders may exploit shared entangled states to overcome the noise. We consider multiple access channels, an essential building block for many complex networks, and develop an extensive framework for n-senders and 1-receiver multiple access channels based on nonlocal games. We obtain generic results for computing correlation assisted sum-capacities of these channels. The considered channels introduce less noise on winning and more noise on losing the game, and the correlation assistance is classified as local (L), quantum (Q), or no-signaling (NS). Furthermore, we consider a broad class of multiple access channels such as depolarizing ones that admix a uniform noise with some probability and prove general results on their sum-capacities. Finally, we apply our analysis to three specific depolarizing multiple access channels based on Clauser-Horne-Shimony-Holt, magic square, and Mermin-GHZ nonlocal games. In all three cases we find significant enhancements in sum-capacities on using nonlocal correlations. We obtain either exact expressions for sum-capacities or suitable upper and lower bounds on them. The general framework developed in this work has much wider applicability and the specificity studied in details are some illustrative examples to compare with recent studies in this direction.
Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The fr... more Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin-a mirrored EW-whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.
The universal transpose of quantum states is an antiunitary transformation that is not allowed in... more The universal transpose of quantum states is an antiunitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
In this work, we show the characterization of quantum iterations that would generally construct q... more In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum search algorithms that find a target with certainty and with a quadratic speedup can be composed of sequential applications of QAAO: existing quantum amplitude amplification algorithms thus turn out to be sequences of QAAOs. We show that an optimal and exact quantum amplitude amplification algorithm corresponds to the Grover algorithm together with a single iteration of QAAO. We then realize 3-qubit QAAOs with the current quantum technologies via cloud-based quantum computing services, IBMQ and IonQ. Finally, our results find that fixed-point quantum search algorithms known so far are not a sequence of QAAOs, e.g. the amplitude of a target state may decrease during quantum iterations.
Dynamics of many-qubit systems, that may correspond to computational processing with quantum syst... more Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two-and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated by local resources, without the necessity of creating entanglement repeatedly. It is also shown that the scheme can be applied to estimation of the fraction of noise existing in quantum gates.
It is shown that a fixed measurement setting, e.g., a measurement in the computational basis, can... more It is shown that a fixed measurement setting, e.g., a measurement in the computational basis, can detect all entangled states by preparing multipartite quantum states, called network states. We present network states for both cases to construct decomposable entanglement witnesses (EWs) equivalent to the partial transpose criteria and also non-decomposable EWs that detect undistillable entangled states beyond the partial transpose criteria. Entanglement detection by state preparation can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing. Our results readily apply to a realistic scenario, for instance, an array of superconducting qubits. neutral atoms, or photons, in which the preparation of a multipartite state and a fixed measurement are experimentally feasible.
The Royal Swedish Academy of Sciences awarded the Nobel Prize in Physics 2022 jointly to Alain As... more The Royal Swedish Academy of Sciences awarded the Nobel Prize in Physics 2022 jointly to Alain Aspect, John Clauser, and Anton Zeilinger for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. The present article provides a brief overview on the significance of their contributions and practical quantum information applications of Bell inequalities and entanglement.
In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs... more In this work, we show that measurement in quantum 2-design, such as mutually unbiased bases (MUBs) or symmetric, informationally complete states (SICs), improves the capability of detecting entangled states both theoretically and experimentally. On the theoretical side, we show that measurement in quantum 2-design can detect entangled states twice compared to entanglement witnesses. On the implementation side, we present the scheme of entanglement detection with two detectors only of a Hong-Ou-Mandel interferometer. The experimental scheme applies single-copy level measurement followed by post-processing of measurement outcomes, which is feasible with current technologies.
We study N-dimensional measurement-device-independent quantum-key-distribution protocol where one... more We study N-dimensional measurement-device-independent quantum-key-distribution protocol where one checking state is used. Only assuming that the checking state is a superposition of other N sources, we show that the protocol is secure in zero quantum-bit-error-rate case, suggesting possibility of the protocol. The method may be applied in other quantum information processing. Quantum key distribution (QKD) 1,2 enables two remote users, normally called Alice and Bob, to generate key (private random sequence), which is not a possible task classically. QKD is not only a practically important field but also a theoretically appealing one. After security of QKD for ideal devices was shown 1,3,4 , problems due to imperfect devices protruded. Although a main problem due to imperfect source was resolved 5 , problem due to imperfect detectors still had remained 6,7. Then no-signaling QKD was discovered 8,9. Remarkably, the no-signaling QKD's were found to be immune against the imperfect device problems, because security analysis of the protocol is based only on outcomes of detectors. Soon device-independent (DI) QKD's were found 10. DI QKD has ideal security but not yet feasible. Measurement-device-independent (MDI) QKD was proposed 11 and demonstrated 12-15 in the background. MDI QKD is secure provided that source is ideal, that is, source is exactly in prescribed quantum states. Later protocols 16,17 with more relaxed condition adapt un-characterized source. The only assumption is that the sources are within 2-dimensional subspace. It can be expected that MDI QKD can be generalized to N-dimensional case. However, security of MDI QKD with un-characterized source relies 16,17 on Shor-Preskill proof 4. Thus it is not yet clear that N-dimensional MDI QKD with un-characterized source works. In this paper, we consider the N-dimensional MDI QKD with un-characterized source. The only assumption for security is that the sources are within N-dimensional subspace. In the protocol, a single quantum state is enough for checking eavesdropper, normally called Eve. (It is known that a single checking state is enough 18). We show that the protocol is secure in zero quantum-bit-error-rate (QBER) case. This suggests possibility of N-dimensional MDI QKD with un-characterized source.
We outline a straightforward approach for obtaining a secret key rate using only no-signaling con... more We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed i... more The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
We report the first experimental realization of an approximate partial transpose for photonic two... more We report the first experimental realization of an approximate partial transpose for photonic two-qubit systems. The proposed scheme is based on the local operation on single copies of quantum states and classical communication, and therefore can be easily applied for other quantum information tasks within current technologies. Direct detection of entanglement, i.e., without performing quantum state tomography, using the partial transpose operation, is also demonstrated.
The kernel trick in supervised learning signifies transformations of an inner product by a featur... more The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds to an instance with a Hilbert space of quantum states by fueling quantum resources to machine learning algorithms. In this work, we point out that the quantum state space is specific such that a measurement postulate characterizes an inner product and that manipulation of quantum states prepared from classical data cannot enhance the distinguishability of data points. We present a feature map for quantum data as a probabilistic manipulation of quantum states to improve supervised learning algorithms.
We investigate secrecy properties of bipartite quantum channels when local environment called shi... more We investigate secrecy properties of bipartite quantum channels when local environment called shield system is assisted. Two honest parties apply either the classical distillation such as the standard one-way postprocessing followed by the advantage distillation (AD), or the quantum distillation applying the recurrence protocol. We then identify those entangled states that can be converted to secrecy by either the quantum or the classical distillation. Remarkably much wider range of bound entangled states are shown to be distilled to secrecy.
From a practical perspective it is advantageous to develop methods that verify entanglement in qu... more From a practical perspective it is advantageous to develop methods that verify entanglement in quantum states with as few measurements as possible. In this paper we investigate the minimal number of mutually unbiased bases (MUBs) needed to detect bound entanglement in bipartite ( d × d ) -dimensional states, i.e. entangled states that are positive under partial transposition. In particular, we show that a class of entanglement witnesses (EWs) composed of MUBs can detect bound entanglement if the number of measurements is greater than d / 2 + 1 . This is a substantial improvement over other detection methods, requiring significantly fewer resources than either full quantum state tomography or measuring a complete set of d + 1 MUBs. Our approach is based on a partial characterisation of the (non-)decomposability of EWs. We show that non-decomposability is a universal property of MUBs, which holds regardless of the choice of complementary observables, and we find that both the number of measurements and the structure of the witness play an important role in the detection of bound entanglement.
The universal transpose of quantum states is an anti-unitary transformation that is not allowed i... more The universal transpose of quantum states is an anti-unitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
Devising efficient communication in a network consisting of multiple transmitters and receivers i... more Devising efficient communication in a network consisting of multiple transmitters and receivers is a problem of immense importance in communication theory. Interestingly, resources in the quantum world have been shown to be very effective in enhancing the performance of communication networks. In this work, we study entanglement-assisted communication over classical network channels. When there is asymmetry such that noise introduced by the channel depends on the input alphabets, non communicating senders may exploit shared entangled states to overcome the noise. We consider multiple access channels, an essential building block for many complex networks, and develop an extensive framework for n-senders and 1-receiver multiple access channels based on nonlocal games. We obtain generic results for computing correlation assisted sum-capacities of these channels. The considered channels introduce less noise on winning and more noise on losing the game, and the correlation assistance is classified as local (L), quantum (Q), or no-signaling (NS). Furthermore, we consider a broad class of multiple access channels such as depolarizing ones that admix a uniform noise with some probability and prove general results on their sum-capacities. Finally, we apply our analysis to three specific depolarizing multiple access channels based on Clauser-Horne-Shimony-Holt, magic square, and Mermin-GHZ nonlocal games. In all three cases we find significant enhancements in sum-capacities on using nonlocal correlations. We obtain either exact expressions for sum-capacities or suitable upper and lower bounds on them. The general framework developed in this work has much wider applicability and the specificity studied in details are some illustrative examples to compare with recent studies in this direction.
Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The fr... more Entanglement witnesses (EWs) are a versatile tool in the verification of entangled states. The framework of mirrored EW doubles the power of a given EW by introducing its twin-a mirrored EW-whereby two EWs related by mirroring can bound the set of separable states more efficiently. In this work, we investigate the relation between the EWs and its mirrored ones, and present a conjecture which claims that the mirrored operator obtained from an optimal EW is either a positive operator or a decomposable EW, which implies that positive-partial-transpose entangled states, also known as the bound entangled states, cannot be detected. This conjecture is reached by studying numerous known examples of optimal EWs. However, the mirrored EWs obtained from the non-optimal ones can be non-decomposable as well. We also show that mirrored operators obtained from the extremal decomposable witnesses are positive semi-definite. Interestingly, the witnesses that violate the well known conjecture of Structural Physical Approximation, do satisfy our conjecture. The intricate relation between these two conjectures is discussed and it reveals a novel structure of the separability problem.
The universal transpose of quantum states is an antiunitary transformation that is not allowed in... more The universal transpose of quantum states is an antiunitary transformation that is not allowed in quantum theory. In this work, we investigate approximating the universal transpose of quantum states of two-level systems (qubits) using the method known as the structural physical approximation to positive maps. We also report its experimental implementation in linear optics. The scheme is optimal in that the maximal fidelity is attained and also practical as measurement and preparation of quantum states that are experimentally feasible within current technologies are solely applied.
In this work, we show the characterization of quantum iterations that would generally construct q... more In this work, we show the characterization of quantum iterations that would generally construct quantum amplitude amplification algorithms with a quadratic speedup, namely, quantum amplitude amplification operators (QAAOs). Exact quantum search algorithms that find a target with certainty and with a quadratic speedup can be composed of sequential applications of QAAO: existing quantum amplitude amplification algorithms thus turn out to be sequences of QAAOs. We show that an optimal and exact quantum amplitude amplification algorithm corresponds to the Grover algorithm together with a single iteration of QAAO. We then realize 3-qubit QAAOs with the current quantum technologies via cloud-based quantum computing services, IBMQ and IonQ. Finally, our results find that fixed-point quantum search algorithms known so far are not a sequence of QAAOs, e.g. the amplitude of a target state may decrease during quantum iterations.
Dynamics of many-qubit systems, that may correspond to computational processing with quantum syst... more Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two-and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated by local resources, without the necessity of creating entanglement repeatedly. It is also shown that the scheme can be applied to estimation of the fraction of noise existing in quantum gates.
It is shown that a fixed measurement setting, e.g., a measurement in the computational basis, can... more It is shown that a fixed measurement setting, e.g., a measurement in the computational basis, can detect all entangled states by preparing multipartite quantum states, called network states. We present network states for both cases to construct decomposable entanglement witnesses (EWs) equivalent to the partial transpose criteria and also non-decomposable EWs that detect undistillable entangled states beyond the partial transpose criteria. Entanglement detection by state preparation can be extended to multipartite states such as graph states, a resource for measurement-based quantum computing. Our results readily apply to a realistic scenario, for instance, an array of superconducting qubits. neutral atoms, or photons, in which the preparation of a multipartite state and a fixed measurement are experimentally feasible.
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