Practical passive decoy state measurement-device-independent quantum key distribution with unstable sources.

Measurement-device-independent quantum key distribution (MDI-QKD) with the active decoy state method can remove all detector loopholes, and resist the imperfections of sources. But it may lead to side channel attacks and break the security of QKD system. In this paper, we apply the passive decoy state method to the MDI-QKD based on polarization encoding mode. Not only all attacks on detectors can be removed, but also the side channel attacks on sources can be overcome. We get that the MDI-QKD with our passive decoy state method can have a performance comparable to the protocol with the active decoy state method. To fit for the demand of practical application, we discuss intensity fluctuation in the security analysis of MDI-QKD protocol using passive decoy state method, and derive the key generation rate for our protocol with intensity fluctuation. It shows that intensity fluctuation has an adverse effect on the key generation rate which is non-negligible, especially in the case of small data size of total transmitting signals and long distance transmission. We give specific simulations on the relationship between intensity fluctuation and the key generation rate. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account.

Bounds for coherence of quantum superpositions in high dimension.

Quantum coherence plays a major role in the promotion for quantum information processing and designing quantum technology. Since coherence is rooted in superposition principle, it is vital to understand the coherence change with respect to superpositions. Here we study the bounds for coherence of quantum superpositions in high dimension. We consider three most frequently used measures of coherence, i.e. the relative entropy of coherence, l 1 norm of coherence and robustness of coherence. For a quantum state (an arbitrary dimension) and its arbitrary decomposition, we give the upper and lower bounds for coherence of the superposition state in terms of the coherence of the states being superposed.

Round-robin differential-phase-shift quantum key distribution with a passive decoy state method.

Recently, a new type of protocol named Round-robin differential-phase-shift quantum key distribution (RRDPS QKD) was proposed, where the security can be guaranteed without monitoring conventional signal disturbances. The active decoy state method can be used in this protocol to overcome the imperfections of the source. But, it may lead to side channel attacks and break the security of QKD systems. In this paper, we apply the passive decoy state method to the RRDPS QKD protocol. Not only can the more environment disturbance be tolerated, but in addition it can overcome side channel attacks on the sources. Importantly, we derive a new key generation rate formula for our RRDPS protocol using passive decoy states and enhance the key generation rate. We also compare the performance of our RRDPS QKD to that using the active decoy state method and the original RRDPS QKD without any decoy states. From numerical simulations, the performance improvement of the RRDPS QKD by our new method can be seen.

Locally indistinguishable orthogonal product bases in arbitrary bipartite quantum system.

As we know, unextendible product basis (UPB) is an incomplete basis whose members cannot be perfectly distinguished by local operations and classical communication. However, very little is known about those incomplete and locally indistinguishable product bases that are not UPBs. In this paper, we first construct a series of orthogonal product bases that are completable but not locally distinguishable in a general m ⊗ n (m ≥ 3 and n ≥ 3) quantum system. In particular, we give so far the smallest number of locally indistinguishable states of a completable orthogonal product basis in arbitrary quantum systems. Furthermore, we construct a series of small and locally indistinguishable orthogonal product bases in m ⊗ n (m ≥ 3 and n ≥ 3). All the results lead to a better understanding of the structures of locally indistinguishable product bases in arbitrary bipartite quantum system.

Entanglement as a resource to distinguish orthogonal product states.

It is known that there are many sets of orthogonal product states which cannot be distinguished perfectly by local operations and classical communication (LOCC). However, these discussions have left the following open question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In m ⊗ n, certain classes of unextendible product bases (UPB) which can be distinguished perfectly using entanglement as a resource, had been presented in 2008. In this paper, we present protocols which use entanglement more efficiently than teleportation to distinguish some classes of orthogonal product states in m ⊗ n, which are not UPB. For the open question, our results offer rather general insight into why entanglement is useful for such tasks, and present a better understanding of the relationship between entanglement and nonlocality.

Minimal number of runs and the sequential scheme for local discrimination between special unitary operations.

It has been shown that any two different multipartite unitary operations are perfectly distinguishable by local operations and classical communication with a finite number of runs. Meanwhile, two open questions were left. One is how to determine the minimal number of runs needed for the local discrimination, and the other is whether a perfect local discrimination can be achieved by merely a sequential scheme. In this paper, we answer the two questions for some unitary operations U1 and U2 with locally unitary equivalent to a diagonal unitary matrix in a product basis. Specifically, we give the minimal number of runs needed for the local discrimination, which is the same with that needed for the global discrimination. In this sense, the local operation works the same with the global one. Moreover, when adding the local property to U1 or U2, we present that the perfect local discrimination can be also realized by merely a sequential scheme with the minimal number of runs. Both results contribute to saving the resources used for the discrimination.

Multipartite entanglement indicators based on monogamy relations of n-qubit symmetric states.

Constructed from Bai-Xu-Wang-class monogamy relations, multipartite entanglement indicators can detect the entanglement not stored in pairs of the focus particle and the other subset of particles. We investigate the k-partite entanglement indicators related to the αth power of entanglement of formation (αEoF) for k ≤ n, αϵ and n-qubit symmetric states. We then show that (1) The indicator based on αEoF is a monotonically increasing function of k. (2) When n is large enough, the indicator based on αEoF is a monotonically decreasing function of α, and then the n-partite indicator based on works best. However, the indicator based on 2 EoF works better when n is small enough.

Linear monogamy of entanglement in three-qubit systems.

For any three-qubit quantum systems ABC, Oliveira et al. numerically found that both the concurrence and the entanglement of formation (EoF) obey the linear monogamy relations in pure states. They also conjectured that the linear monogamy relations can be saturated when the focus qubit A is maximally entangled with the joint qubits BC. In this work, we prove analytically that both the concurrence and EoF obey linear monogamy relations in an arbitrary three-qubit state. Furthermore, we verify that all three-qubit pure states are maximally entangled in the bipartition A|BC when they saturate the linear monogamy relations. We also study the distribution of the concurrence and EoF. More specifically, when the amount of entanglement between A and B equals to that of A and C, we show that the sum of EoF itself saturates the linear monogamy relation, while the sum of the squared EoF is minimum. Different from EoF, the concurrence and the squared concurrence both saturate the linear monogamy relations when the entanglement between A and B equals to that of A and C.

Quantum secret sharing via local operations and classical communication.

We investigate the distinguishability of orthogonal multipartite entangled states in d-qudit system by restricted local operations and classical communication. According to these properties, we propose a standard (2, n)-threshold quantum secret sharing scheme (called LOCC-QSS scheme), which solves the open question in [Rahaman et al., Phys. Rev. A, 91, 022330 (2015)]. On the other hand, we find that all the existing (k, n)-threshold LOCC-QSS schemes are imperfect (or "ramp"), i.e., unauthorized groups can obtain some information about the shared secret. Furthermore, we present a (3, 4)-threshold LOCC-QSS scheme which is close to perfect.

Security of Semi-Device-Independent Random Number Expansion Protocols.

Semi-device-independent random number expansion (SDI-RNE) protocols require some truly random numbers to generate fresh ones, with making no assumptions on the internal working of quantum devices except for the dimension of the Hilbert space. The generated randomness is certified by non-classical correlation in the prepare-and-measure test. Until now, the analytical relations between the amount of the generated randomness and the degree of non-classical correlation, which are crucial for evaluating the security of SDI-RNE protocols, are not clear under both the ideal condition and the practical one. In the paper, first, we give the analytical relation between the above two factors under the ideal condition. As well, we derive the analytical relation under the practical conditions, where devices' behavior is not independent and identical in each round and there exists deviation in estimating the non-classical behavior of devices. Furthermore, we choose a different randomness extractor (i.e., two-universal random function) and give the security proof.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Characterizing unextendible product bases in qutrit-ququad system.

Unextendible product bases (UPBs) play an important role in quantum information theory. However, very little is known about UPBs in Hilbert space of local dimension more than three. In this paper, we study the UPBs in qutrit-ququad system and find that there only exist six, seven and eight-state UPBs. We completely characterize the six-state and seven-state UPBs. For eight-state UPBs, seven classes of UPBs are found. As auxiliary results, we study the distinguishability of qutrit-ququad UPBs by separable measurements, and find that there exists a UPB that cannot be distinguished.

Practical quantum private query of blocks based on unbalanced-state Bennett-Brassard-1984 quantum-key-distribution protocol.

Until now, the only kind of practical quantum private query (QPQ), quantum-key-distribution (QKD)-based QPQ, focuses on the retrieval of a single bit. In fact, meaningful message is generally composed of multiple adjacent bits (i.e., a multi-bit block). To obtain a message a1a2···al from database, the user Alice has to query l times to get each ai. In this condition, the server Bob could gain Alice's privacy once he obtains the address she queried in any of the l queries, since each a(i) contributes to the message Alice retrieves. Apparently, the longer the retrieved message is, the worse the user privacy becomes. To solve this problem, via an unbalanced-state technique and based on a variant of multi-level BB84 protocol, we present a protocol for QPQ of blocks, which allows the user to retrieve a multi-bit block from database in one query. Our protocol is somewhat like the high-dimension version of the first QKD-based QPQ protocol proposed by Jacobi et al., but some nontrivial modifications are necessary.

Flexible quantum private queries based on quantum key distribution.

By adding a parameter θ in M. Jakobi et al's protocol [Phys. Rev. A 83, 022301 (2011)], we present a flexible quantum-key-distribution-based protocol for quantum private queries. We show that, by adjusting the value of θ, the average number of the key bits Alice obtains can be located on any fixed value the users wanted for any database size. And the parameter k is generally smaller (even k = 1 can be achieved) when θ < π/4, which implies lower complexity of both quantum and classical communications. Furthermore, the users can choose a smaller θ to get better database security, or a larger θ to obtain a lower probability with which Bob can correctly guess the address of Alice's query.