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Li-Yi Hsu

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Oleg Yu Vorobyev

Siberian Federal University

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Mariafelicia De Laurentis

Università degli Studi di Napoli "Federico II"

Homi Bhabha National Institute (HBNI, BARC, MUMBAI)

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Papers by Li-Yi Hsu

Any four orthogonal ququad-ququad maximally entangled states are locally markable

arXiv (Cornell University), Sep 2, 2022

In quantum state discrimination, the observers are given a quantum system and aim to verify its s... more In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4 ⊗ 4 systems, N = 4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σ z or σ x simultaneously, and entanglement swapping. It shows that, given arbitrary four 4 ⊗ 4 systems, Alice and Bob can perform the perfect local quantum state marking. In the N = 5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states since Alice and Bob cannot fulfill the task in the simplest case.

Any four orthogonal ququad-ququad maximally entangled states are locally markable

New Journal of Physics

In quantum state discrimination, the observers are given a quantum system and aim to verify its s... more In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4⊗4 systems, N=4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σz or σx simultaneously, and entanglement swapping. It shows that, given arbitrary four 4⊗4 systems, Alice and Bob can perform the perfect local quantum state marking. In the N=5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states si...

Optimal Quantum Detection of Symmetric States

Three equally separated nonorthogonal quantum bits that lie on the same plane are prepared for si... more Three equally separated nonorthogonal quantum bits that lie on the same plane are prepared for signal processing. One of the qubits is randomly picked as the single-qubit signal. The remaining two qubits then form the two-qubit signal. We find that the optimal probability operator measure for the two-qubit signals can be interpreted as the optimal orthogonal measurement in the four-dimensional Hilbert space of the signal states. We also find that the two-qubit signals have a better detection probability than the single-qubit. Possible generalization to the case of N nonorthogonal qubits is also discussed.

Infinite information can be carried using a single quantum particle

arXiv: Quantum Physics, 2020

In the beginning was the photon, and the photon was with information. Theoretically speaking, a p... more In the beginning was the photon, and the photon was with information. Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, which then clicks. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as the extension of that proposed by Del Santo and Dakic. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We prove that, after the photon's travelling through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of...

Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

Physical Review Research, 2021

In practical quantum networks, a variety of multiqubit stabilized states emitted from independent... more In practical quantum networks, a variety of multiqubit stabilized states emitted from independent sources are distributed among the agents, and the correlations across the entire network can be derived from each agent's local measurements on the shared composite quantum systems. To reveal the Bell nonlocality in such cases as a quantum feature, minimal knowledge of the emitted stabilizer state is required. Here, we demonstrate that knowing the stabilizing and logical operators indeed provides a new way of exploring Bell nonlocality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. On the other hand, to violate these inequalities, one can design local incompatible observables using minimal knowledge of the emitted states. The tilted nonlinear Bell inequalities tailored for specific nonmaximal entangled stabilizer states and a way of achieving the maximal violation are also explored.

Quantum Cheshire cats and their elements of reality

Physics Letters A, 2020

Quantum Cheshire cats represent the violation of the product rule in terms of weak values being e... more Quantum Cheshire cats represent the violation of the product rule in terms of weak values being either 0 or 1. We explore the generalized fatter quantum Cheshire cats living in the larger Hilbert spaces. Specifically, two even-dimensional quantum systems are exploited. As for the physical implications, given that no disturbance is made in the weak measurements, quantum Cheshire cats reveal an alternative way of defying EPR elements of reality. In addition, we discuss the inconsistency between the Wigner's friend problem and quantum Cheshire cats.

Exploring Multipartite Steering Effect Using Bell Operators

Entropy, 2019

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification,... more While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are...

Exploring the joint measurability using an information-theoretic approach

Quantum Information Processing, 2016

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening... more We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.

Quantum Dense Coding and Teleportation using Multipartite Graph States

The merging of quantum correlation and information causality boundaries

We analytically derive the criteria of the boundary-merging of quantum correlation and informatio... more

Monogamy of Information Causality

We consider information causality in the multi-receiver random access codes. Therein, no receiver... more We consider information causality in the multi-receiver random access codes. Therein, no receiver can gain any information only from classical communication. We claim the following statement. Information causality still holds with the help of the multi-partite physical non-local resource. That is, the summation of all revivers' information gain cannot be greater than the amount of classical communication. The distributive multi-party physical nonlocal resource can be exploited only for information splitting. It is proved that such trade-off leads to the monogamy of entanglement. Finally the connection between information causality and spin-glass Bethe lattice is discussed.

Cryptanalysis of Quantum Secret Sharing Using Graph States

Quantum secret sharing using product states

Physical Review A, 2005

This study proposes quantum secret sharing protocols using product states. The first two protocol... more This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states ͓Guo et al.Phys. Rev. A 64, 042301 ͑2001͔͒. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.

Carrying an arbitrarily large amount of information using a single quantum particle

Physical Review A, 2020

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, re... more Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting a click. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as an extension of that proposed by Del Santo and Daki\'{c}. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of information. That is, the wave-particle duality makes two-way signal...

Entropic uncertainty relation based on generalized uncertainty principle

Modern Physics Letters A, 2017

We explore the modification of the entropic formulation of uncertainty principle in quantum mecha... more We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

Motivation for online impulse buying: A two-factor theory perspective

International Journal of Information Management, 2016

Impulse buying accounts for a large proportion of consumer shopping behavior in the bricks-and-mo... more Impulse buying accounts for a large proportion of consumer shopping behavior in the bricks-and-mortar retail market. Online retailers also expect to profit from impulse buying. It is therefore interesting and beneficial to investigate the design elements of online stores and the sales promotion stimuli that eretailers can use to either arouse consumers' desire or decrease their self-control to evoke their purchase impulses. This study seeks to explicitly identify the factors associated with online store design and sales promotion stimuli that most affect online impulse buying behavior throughout the consumer decisionmaking process. Drawing on the two-factor theory, it successfully identifies the hygiene and motivation factors that trigger online impulse buying. The questionnaire responses of 239 valid respondents revealed that most of the hygiene factors are associated with the design of online stores, and all of the motivation factors are forms of sales promotion stimuli that effectively facilitate online impulse buying and present utilitarian or hedonic benefits to consumers. This study also identifies the most effective sales promotion stimuli and offers a comprehensive checklist for Web designers. Moreover, the distribution of motivation and hygiene factors for each stage of the EKB model is uneven, and some stages include only hygiene factors. The findings of this study demonstrate that the triggers of consumers' online shopping behavior do not always apply to online impulse buying, and have important implications for impulse buying research and practice.

Faster Database search in Quantum Computing

We propose a new algorithm for quantum database search. Our strategy is to partition the space of... more We propose a new algorithm for quantum database search. Our strategy is to partition the space of all possibilities into subspaces and use a judiciously chosen projection operator as a polarizer in every subspace to filter out the states which have the correct first n-2 qubits. Then we use Grover's algorithm to determine which one of the four survived states is the oracle. This algorithm has three advantages compared to the existing algorithms: It is exponentially fast; it zeros in to the oracle with probability one; and it admits an extra degree of freedom in the choice of the initial state.

Optimal Nonadditive Quantum Error-Detecting Code

In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance... more In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance two. The the numerical simulation shows that, with n being can be 5, 6, 7, 8, 10 and 12, such the n-qubit quantum error-detecting codes with maximal number of codewords can be found. Therein, except the n=7 case, the n-vertex loop graphs help find the optimal quantum codes.

Information causality and non-locality swapping are equivalent from emergence of quantum correlations

Is information causality a new physical principle? To answer this question, we first analytically... more Is information causality a new physical principle? To answer this question, we first analytically derive the criteria of emergence of quantum correlations from information causality. Then it is shown that, as emergence criteria of quantum correlations, information causality and uselessness of coupler-based non-locality swapping can be regarded equivalent. Therefore, incapability of non-locality swapping using a coupler is as powerful as information causality in the single-out of quantum physics from generalized non-signalling models.

Informatic error-disturbance relation in the qubit case

In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and... more In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the amount of unavoidable uncertainty in the measuring process. In this paper, we study the error-disturbance relation from the information viewpoint. We ask how much information, rather than how much uncertainty, can be obtained during the two sequential measurements. To achieve optimal information gain, we argue that the strategy for the "intelligent" prior apparatus is to clone the unknown state, and for the posterior one is to perform the swapping operation. We propose the coarse-grained random access code, and therein information causality as a physical principle can be exploited for deriving the upper-bound of information gain. Finally, we conjecture the information gain of measuring the position and momentum of a quantum object in the coarse-grained way.

Any four orthogonal ququad-ququad maximally entangled states are locally markable

arXiv (Cornell University), Sep 2, 2022

In quantum state discrimination, the observers are given a quantum system and aim to verify its s... more In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4 ⊗ 4 systems, N = 4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σ z or σ x simultaneously, and entanglement swapping. It shows that, given arbitrary four 4 ⊗ 4 systems, Alice and Bob can perform the perfect local quantum state marking. In the N = 5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states since Alice and Bob cannot fulfill the task in the simplest case.

Any four orthogonal ququad-ququad maximally entangled states are locally markable

New Journal of Physics

In quantum state discrimination, the observers are given a quantum system and aim to verify its s... more In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4⊗4 systems, N=4, 5, 6, and 7. Therein, Alice and Bob allow for three local operations: measuring the local observable either σz or σx simultaneously, and entanglement swapping. It shows that, given arbitrary four 4⊗4 systems, Alice and Bob can perform the perfect local quantum state marking. In the N=5, 6 cases, they can perform perfect local state marking with specific target states. We conjecture the impossibility of the local quantum state marking given any seven target states si...

Optimal Quantum Detection of Symmetric States

Three equally separated nonorthogonal quantum bits that lie on the same plane are prepared for si... more Three equally separated nonorthogonal quantum bits that lie on the same plane are prepared for signal processing. One of the qubits is randomly picked as the single-qubit signal. The remaining two qubits then form the two-qubit signal. We find that the optimal probability operator measure for the two-qubit signals can be interpreted as the optimal orthogonal measurement in the four-dimensional Hilbert space of the signal states. We also find that the two-qubit signals have a better detection probability than the single-qubit. Possible generalization to the case of N nonorthogonal qubits is also discussed.

Infinite information can be carried using a single quantum particle

arXiv: Quantum Physics, 2020

In the beginning was the photon, and the photon was with information. Theoretically speaking, a p... more In the beginning was the photon, and the photon was with information. Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, which then clicks. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as the extension of that proposed by Del Santo and Dakic. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We prove that, after the photon's travelling through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of...

Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

Physical Review Research, 2021

In practical quantum networks, a variety of multiqubit stabilized states emitted from independent... more In practical quantum networks, a variety of multiqubit stabilized states emitted from independent sources are distributed among the agents, and the correlations across the entire network can be derived from each agent's local measurements on the shared composite quantum systems. To reveal the Bell nonlocality in such cases as a quantum feature, minimal knowledge of the emitted stabilizer state is required. Here, we demonstrate that knowing the stabilizing and logical operators indeed provides a new way of exploring Bell nonlocality in quantum networks. For the qubit distribution in quantum networks, the associated nonlinear Bell inequalities are derived. On the other hand, to violate these inequalities, one can design local incompatible observables using minimal knowledge of the emitted states. The tilted nonlinear Bell inequalities tailored for specific nonmaximal entangled stabilizer states and a way of achieving the maximal violation are also explored.

Quantum Cheshire cats and their elements of reality

Physics Letters A, 2020

Quantum Cheshire cats represent the violation of the product rule in terms of weak values being e... more Quantum Cheshire cats represent the violation of the product rule in terms of weak values being either 0 or 1. We explore the generalized fatter quantum Cheshire cats living in the larger Hilbert spaces. Specifically, two even-dimensional quantum systems are exploited. As for the physical implications, given that no disturbance is made in the weak measurements, quantum Cheshire cats reveal an alternative way of defying EPR elements of reality. In addition, we discuss the inconsistency between the Wigner's friend problem and quantum Cheshire cats.

Exploring Multipartite Steering Effect Using Bell Operators

Entropy, 2019

While Bell operators are exploited in detecting Bell nonlocality and entanglement classification,... more While Bell operators are exploited in detecting Bell nonlocality and entanglement classification, we demonstrate their usefulness in exploring Einstein–Podolsky–Rosen (EPR) steering, which represents the quantum correlation intermediate between entanglement and Bell nonlocality. We propose a task function that detects steerability of multi-qubit states in bipartite scenarios. A novel necessary and sufficient steering criterion is based on the superposition of the recursive Bell operators which are often employed for detecting Bell nonlocality. Utilizing the task function we can (i) reveal the one-to-one mapping relation between joint measurability and unsteerability, (ii) geometrically depict and compare the entanglement classification and the steering criteria and propose a geometrical measure, and (iii) compare the EPR steering with Bell nonlocality using an alternative task function. We extend the result to detect EPR steering for multi-qutrit cases and some numerical results are...

Exploring the joint measurability using an information-theoretic approach

Quantum Information Processing, 2016

We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening... more We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.

Quantum Dense Coding and Teleportation using Multipartite Graph States

The merging of quantum correlation and information causality boundaries

We analytically derive the criteria of the boundary-merging of quantum correlation and informatio... more

Monogamy of Information Causality

We consider information causality in the multi-receiver random access codes. Therein, no receiver... more We consider information causality in the multi-receiver random access codes. Therein, no receiver can gain any information only from classical communication. We claim the following statement. Information causality still holds with the help of the multi-partite physical non-local resource. That is, the summation of all revivers' information gain cannot be greater than the amount of classical communication. The distributive multi-party physical nonlocal resource can be exploited only for information splitting. It is proved that such trade-off leads to the monogamy of entanglement. Finally the connection between information causality and spin-glass Bethe lattice is discussed.

Cryptanalysis of Quantum Secret Sharing Using Graph States

Quantum secret sharing using product states

Physical Review A, 2005

This study proposes quantum secret sharing protocols using product states. The first two protocol... more This study proposes quantum secret sharing protocols using product states. The first two protocols adopt the quantum key distribution protocol using product states ͓Guo et al.Phys. Rev. A 64, 042301 ͑2001͔͒. In these two protocols, the sender does not reveal any information about the qutrits until confirming that each receiver has received a qutrit. This study also considers the security and some possible eavesdropping strategies. In the third proposed protocol, three-level Bell states are exploited for qutrit preparation via nonlocality swapping.

Carrying an arbitrarily large amount of information using a single quantum particle

Physical Review A, 2020

Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, re... more Theoretically speaking, a photon can travel arbitrarily long before it enters into a detector, resulting a click. How much information can a photon carry? We study a bipartite asymmetric "two-way signaling" protocol as an extension of that proposed by Del Santo and Daki\'{c}. Suppose that Alice and Bob are distant from each other and each of them has an $n$-bit string. They are tasked to exchange the information of their local n-bit strings with each other, using only a single photon during the communication. It has been shown that the superposition of different spatial locations in a Mach-Zehnder (MZ) interferometer enables bipartite local encodings. We show that, after the travel of a photon through a cascade of $n$-level MZ interferometers in our protocol, the one of Alice or Bob whose detector clicks can access the other's full information of $n$-bit string, while the other can gain one-bit of information. That is, the wave-particle duality makes two-way signal...

Entropic uncertainty relation based on generalized uncertainty principle

Modern Physics Letters A, 2017

We explore the modification of the entropic formulation of uncertainty principle in quantum mecha... more We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

Motivation for online impulse buying: A two-factor theory perspective

International Journal of Information Management, 2016

Impulse buying accounts for a large proportion of consumer shopping behavior in the bricks-and-mo... more Impulse buying accounts for a large proportion of consumer shopping behavior in the bricks-and-mortar retail market. Online retailers also expect to profit from impulse buying. It is therefore interesting and beneficial to investigate the design elements of online stores and the sales promotion stimuli that eretailers can use to either arouse consumers' desire or decrease their self-control to evoke their purchase impulses. This study seeks to explicitly identify the factors associated with online store design and sales promotion stimuli that most affect online impulse buying behavior throughout the consumer decisionmaking process. Drawing on the two-factor theory, it successfully identifies the hygiene and motivation factors that trigger online impulse buying. The questionnaire responses of 239 valid respondents revealed that most of the hygiene factors are associated with the design of online stores, and all of the motivation factors are forms of sales promotion stimuli that effectively facilitate online impulse buying and present utilitarian or hedonic benefits to consumers. This study also identifies the most effective sales promotion stimuli and offers a comprehensive checklist for Web designers. Moreover, the distribution of motivation and hygiene factors for each stage of the EKB model is uneven, and some stages include only hygiene factors. The findings of this study demonstrate that the triggers of consumers' online shopping behavior do not always apply to online impulse buying, and have important implications for impulse buying research and practice.

Faster Database search in Quantum Computing

We propose a new algorithm for quantum database search. Our strategy is to partition the space of... more We propose a new algorithm for quantum database search. Our strategy is to partition the space of all possibilities into subspaces and use a judiciously chosen projection operator as a polarizer in every subspace to filter out the states which have the correct first n-2 qubits. Then we use Grover's algorithm to determine which one of the four survived states is the oracle. This algorithm has three advantages compared to the existing algorithms: It is exponentially fast; it zeros in to the oracle with probability one; and it admits an extra degree of freedom in the choice of the initial state.

Optimal Nonadditive Quantum Error-Detecting Code

In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance... more In this paper, we investigate the optimal nonadditive quantum error-detecting codes with distance two. The the numerical simulation shows that, with n being can be 5, 6, 7, 8, 10 and 12, such the n-qubit quantum error-detecting codes with maximal number of codewords can be found. Therein, except the n=7 case, the n-vertex loop graphs help find the optimal quantum codes.

Information causality and non-locality swapping are equivalent from emergence of quantum correlations

Is information causality a new physical principle? To answer this question, we first analytically... more Is information causality a new physical principle? To answer this question, we first analytically derive the criteria of emergence of quantum correlations from information causality. Then it is shown that, as emergence criteria of quantum correlations, information causality and uselessness of coupler-based non-locality swapping can be regarded equivalent. Therefore, incapability of non-locality swapping using a coupler is as powerful as information causality in the single-out of quantum physics from generalized non-signalling models.

Informatic error-disturbance relation in the qubit case

In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and... more In 1927, Heisenberg heuristically disclosed the tradeoff between the error in the measurement and the caused disturbance on another complementary observable. In the quantum theory, most of uncertainty relations are proposed to reveal the amount of unavoidable uncertainty in the measuring process. In this paper, we study the error-disturbance relation from the information viewpoint. We ask how much information, rather than how much uncertainty, can be obtained during the two sequential measurements. To achieve optimal information gain, we argue that the strategy for the "intelligent" prior apparatus is to clone the unknown state, and for the posterior one is to perform the swapping operation. We propose the coarse-grained random access code, and therein information causality as a physical principle can be exploited for deriving the upper-bound of information gain. Finally, we conjecture the information gain of measuring the position and momentum of a quantum object in the coarse-grained way.