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A direct measurement protocol allows reconstructing specific elements of the density matrix of a quantum state without using quantum state tomography. However, the direct measurement protocols to date are primarily based on weak or strong measurements with an ancillary pointer, which interacts with the investigated system to extract information about the specified elements. Here, we present a direct measurement scheme based on phase-shifting operations which do not need ancillary pointers. In this method, estimates of at most six expectation values of projective observables suffice to determine any specific element of an unknown quantum density matrix. A concrete quantum circuit to implement this direct measurement protocol for multiqubit states is provided, which is composed of just single-qubit gates and two multiqubit controlled-phase gates. This scheme is also extended for the direct measurement of the density matrix of continuous-variable quantum states. Our method can be used in quantum information applications where only partial information about the quantum state needs to be extracted, for example, problems such as entanglement witnessing, fidelity estimation of quantum systems, and quantum coherence estimation.

Non-locality sharing for a three-qubit system via multilateral sequential measurements was deeply discussed. Different from 2-qubit case, it is shown that non-locality sharing between $\mathrm{Alice_{1}-Bob_{1}-Charlie_{1}}$ and $\mathrm{Alice_{2}-Bob_{2}-Charlie_{2}}$ in 3-qubit system can be observed, where two Mermin-Ardehali-Belinskii-Klyshko (MABK) inequalities can be violated simultaneously. What's more, a complete non-locality sharing with 8 MABK inequalities violations simultaneously can be also observed. Compared with 2-qubit case, the nonlocal sharing in a three qubit system shows more novel characteristics.

In quantum information science, a major task is to find the quantum models that can outperform their classical counterparts. Automaton is a fundamental computing model that has wide applications in many fields. It has been shown that the quantum version of automaton can solve certain problem using a much smaller state space compared to the classical automaton. Here we report an experimental demonstration of an optical quantum automaton, which is used to solve the promise problems of determining whether the length of an input string can be divided by a prime number P with no remainder or with a remainder of R. Our quantum automaton can solve such problem using a state space with only three orthonormal states, whereas the classical automaton needs no less than P states. Our results demonstrate the quantum benefits of a quantum automaton over its classical counterpart and paves the way for implementing quantum automaton for more complicated and practical applications.

Nonlocality plays a fundamental role in quantum information science. Recently, it has been theoretically predicted and experimentally demonstrated that the nonlocality of an entangled pair may be shared among multiple observers using weak measurements with moderate strength. Here we devise an optimal protocol of nonlocality sharing among three observers and show experimentally that nonlocality sharing may be also achieved using weak measurements with near-maximum strength. Our result sheds light on the interplay between nonlocality and quantum measurements and, may find applications in quantum steering, unbounded randomness certification and quantum communication network., Comment: 6 pages, 4 figures

Quantum mechanics provides a disembodied way to transfer quantum information from one quantum object to another. In theory, this quantum information transfer can occur between quantum objects of any dimension, yet the reported experiments of quantum information transfer to date have mainly focused on the cases where the quantum objects have the same dimension. Here we theoretically propose and experimentally demonstrate a scheme for quantum information transfer between quantum objects of different dimensions.By using an optical qubit-ququart entangling gate, we observe the transfer of quantum information between two photons with different dimensions, including the flow of quantum information from a four-dimensional photon to a two-dimensional photon and vice versa.The fidelities of the quantum information transfer range from 0.700 to 0.917, all above the classical limit of 2/3. Our work sheds light on a new direction for quantum information transfer and demonstrates our ability to implement entangling operations beyond two-level quantum systems., 12 pages, 10 figures

Multiphoton entanglement, as a quantum resource, plays an essential role in linear optical quantum information processing. Krenn et al. (Phys. Rev. Lett. 118, 080401 2017) proposed an innovative scheme that generating entanglement by path identity, in which two-photon interference (called Hong-Ou-Mandel effect) is not necessary in experiment. However, the experiments in this scheme have strict requirements in stability and scalability, which is difficult to be realized in bulk optics. To solve this problem, in this paper we first propose an on-chip scheme to generate multi-photon polarization entangled states, including Greenberger-Horne-Zeilinger (GHZ) states and W states. Moreover, we also present a class of generalized graphs for W states (odd-number-photon) by path identity in theory. The on-chip scheme can be implemented in existing integrated optical technology which is meaningful for multi-party entanglement distribution in quantum communication networks., Comment: 8 pages, 3 figures

A well-known property of quantum nonlocality is monogamy. However, recent research by Silva et al. shows that multiple observers can share the nonlocality by using weak measurements [Phys. Rev. Lett. 114, 250401 (2015)]. In this paper, we deeply discuss nonlocality sharing for an arbitrary two-qubit state via weak measurements. Two types of nonlocality sharing, passive nonlocality sharing and active nonlocality sharing, which is another type of double violation of Clauser-Horne-Shimony-Holt (CHSH) inequality with many counterintuitive results existing, are fully analyzed. The two types are quite distinct. Active nonlocality sharing can be observed when Bob1 performs strong measurements only except for the ideal strong measurements. Also, a double violation still can be observed in the active nonlocality sharing even using a square pointer type for weak measurements of Bob1, which is impossible in the passive one. As a special example, for a Bell state, a double violation of Clauser-Horne-Shimony-Holt inequality can be always observed in a broad range whether the weak measurement of Bob1 is with an optimal pointer or a square pointer.

The Einstein–Podolsky–Rosen (EPR) paradox is one of the milestones in quantum foundations, arising from the lack of a local realistic description of quantum mechanics. The EPR paradox has stimulated an important concept of “quantum nonlocality,” which manifests itself in three types: quantum entanglement, quantum steering, and Bell’s nonlocality. Although Bell’s nonlocality is more often used to show “quantum nonlocality,” the original EPR paradox is essentially a steering paradox. In this work, we formulate the original EPR steering paradox into a contradiction equality, thus making it amenable to experimental verification. We perform an experimental test of the steering paradox in a two-qubit scenario. Furthermore, by starting from the steering paradox, we generate a generalized linear steering inequality and transform this inequality into a mathematically equivalent form, which is friendlier for experimental implementation, i.e., one may measure the observables only in the x , y , or z axis of the Bloch sphere, rather than other arbitrary directions. We also perform experiments to demonstrate this scheme. Within the experimental errors, the experimental results coincide with theoretical predictions. Our results deepen the understanding of quantum foundations and provide an efficient way to detect the steerability of quantum states.

We consider a simulation problem of a general mechanism by a robot arm. A robot arm can be modeled by a path P, and the target is modeled by a general graph G. Then the problem asks if there is an edge-weighted Eulerian path of G spanned by P. We first show that it is strongly NP-hard even if edge lengths are restricted. Then we consider two different variants of this problem. We first allow the edges in P to be elastic, and minimize the elastic ratio when G is a path. Second, we allow P to cover an edge of G twice or more. The problem is weakly NP-hard even if G is an edge. We thus assume that each edge of G is covered by P exactly twice, and obtain three hardness results and one polynomial-time algorithm when G and edge lengths are restricted.

Quantum computation is a computing model based on quantum theory, which can outperform the classical computation in solving certain problems. With the increase of the complexity of quantum computing tasks, it becomes important to distribute quantum computing resources to multi-parties to cooperatively fulfill the complex tasks. Here in this paper a scheme based on the one-way quantum computing model is proposed to realize collaborative quantum computation. The standard one-way quantum computing model is based on graph states. With graph states used as resources, one can realize a universal quantum computer through using single-qubit measurements and feed-forward. In contrast to the standard one-way computation, the main resource for collaborative quantum computation is a redundant graph state (also a multi-particle highly entangled state). Unlike in the traditional graph state where each particle corresponds to a specific node, in a redundant graph state, several particles correspond to a single node, which means that each node of the graph has several redundant copies. With the help of a redundant graph state, several parties can share a graph state flexibly at will. A redundant graph state is prepared and then distributed to several parties where each of them obtains a full copy of all nodes. By communicating with each other and measuring the particles in different ways, a standard graph state is prepared and distributed among these parties. The collaborative computation then finishes through the common one-way quantum computing operations. Besides the general scheme, a concrete optical implementation of a two-party cooperative single-qubit quantum state preparation based on a six-photon redundant graph state is also put forward. Such a redundant graph state is proposed to be prepared by using the spontaneous parametric down-conversion entangled source and quantum interference. With this redundant graph state, a standard three-node graph state can be shared with the two parties in an arbitrary way. This scheme does not only make the collaborative quantum computation across several parties possible and flexible, but also guarantee the privacy of each party’s operations. This feature would be particularly useful in the case where the computing resource is obtained from an outside provider. This scheme paves the way for realizing quantum computation in more general and complicated applications.