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Nengkun Yu

Publications and source records attributed to Nengkun Yu.

At least 37 records · Page 2Linked to original sources
arXiv2023

Discrimination of quantum states under locality constraints in the many-copy setting

We study quantum hypothesis testing between orthogonal states under restricted local measurements in the many-copy scenario. For testing arbitrary multipartite entangled pure state against its orthogonal complement state via the local operation and classical communication (LOCC) operation, we prove that the optimal average error probability always decays exponentially in the number of copies. Second, we provide a sufficient condition for the LOCC operations to achieve the same performance as the positive-partial-transpose (PPT) operations. We further show that testing a maximally entangled state against its orthogonal complement and testing extremal Werner states both fulfill the above-mentioned condition. Hence, we determine the explicit expressions for the optimal average error probability, the optimal trade-off between the type-I and type-II errors, and the associated Chernoff, Stein, Hoeffding, and strong converse exponents. Then, we show an infinite asymptotic separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB). The quantum states can be distinguished perfectly by PPT operations, while the optimal error probability, with SEP operations, admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.

quant-ph↗
arXiv2023

Accelerating Voting by Quantum Computation

Studying the computational complexity and designing fast algorithms for determining winners under voting rules are classical and fundamental questions in computational social choice. In this paper, we accelerate voting by leveraging quantum computation: we propose a quantum-accelerated voting algorithm that can be applied to any anonymous voting rule. We show that our algorithm can be quadratically faster than any classical algorithm (based on sampling with replacement) under a wide range of common voting rules, including positional scoring rules, Copeland, and single transferable voting (STV). Precisely, our quantum-accelerated voting algorithm outputs the correct winner with high probability in $Θ\left(\frac{n}{\text{MOV}}\right)$ time, where $n$ is the number of votes and $\text{MOV}$ is {\em margin of victory}, the smallest number of voters to change the winner. In contrast, any classical voting algorithm based on sampling with replacement requires $Ω\left(\frac{n^2}{\text{MOV}^2}\right)$ time under a large class of voting rules. Our theoretical results are supported by experiments under plurality, Borda, Copeland, and STV.

cs.CY↗
arXiv2022

Sample optimal tomography of quantum Markov chains

A state on a tripartite quantum system $\mathcal{H}_{A}\otimes \mathcal{H}_{B}\otimes\mathcal{H}_{C} $ forms a Markov chain, i.e., quantum conditional independence, if it can be reconstructed from its marginal on $\mathcal{H}_{A}\otimes \mathcal{H}_{B}$ by a quantum operation from $\mathcal{H}_{B}$ to $\mathcal{H}_{B}\otimes\mathcal{H}_{C}$ via the famous Petz map: a quantum Markov chain $ρ_{ABC}$ satisfies $ρ_{ABC}=ρ_{BC}^{1/2}(ρ_B^{-1/2}ρ_{AB}ρ_B^{-1/2}\otimes id_C)ρ_{BC}^{1/2}$. In this paper, we study the robustness of the Petz map for different metrics, i.e., the closeness of marginals implies the closeness of the Petz map outcomes. The robustness results are dimension-independent for infidelity $δ$ and trace distance $ε$. The applications of robustness results are The sample complexity of quantum Markov chain tomography, i.e., how many copies of an unknown quantum Markov chain are necessary and sufficient to determine the state, is $\tildeΘ(\frac{(d_A^2+d_C^2)d_B^2}δ)$, and $\tildeΘ(\frac{(d_A^2+d_C^2)d_B^2}{ε^2}) $. The sample complexity of quantum Markov Chain certification, i.e., to certify whether a tripartite state equals a fixed given quantum Markov Chain $σ_{ABC}$ or at least $δ$-far from $σ_{ABC}$, is $Θ(\frac{(d_A+d_C)d_B}δ)$, and $Θ(\frac{(d_A+d_C)d_B}{ε^2})$. $\tilde{O}(\frac{\min\{d_Ad_B^3d_C^3,d_A^3d_B^3d_C\}}{ε^2})$ copies to test whether $ρ_{ABC}$ is a quantum Markov Chain or $ε$-far from its Petz recovery state. We generalized the tomography results into multipartite quantum system by showing $\tilde{O}(\frac{n^2\max_{i} \{d_i^2d_{i+1}^2\}}δ)$ copies for infidelity $δ$ are enough for $n$-partite quantum Markov chain tomography with $d_i$ being the dimension of the $i$-th subsystem.

quant-ph↗
arXiv2022

A Probabilistic Logic for Verifying Continuous-time Markov Chains

A continuous-time Markov chain (CTMC) execution is a continuous class of probability distributions over states. This paper proposes a probabilistic linear-time temporal logic, namely continuous-time linear logic (CLL), to reason about the probability distribution execution of CTMCs. We define the syntax of CLL on the space of probability distributions. The syntax of CLL includes multiphase timed until formulas, and the semantics of CLL allows time reset to study relatively temporal properties. We derive a corresponding model-checking algorithm for CLL formulas. The correctness of the model-checking algorithm depends on Schanuel's conjecture, a central open problem in transcendental number theory. Furthermore, we provide a running example of CTMCs to illustrate our method.

cs.LO↗
arXiv2022

When is the Chernoff Exponent for Quantum Operations finite?

We consider the problem of testing two hypotheses of quantum operations in a setting of many uses where an arbitrary prior probability distribution is given. The Chernoff exponent for quantum operations is investigated to track the minimal average error probability of discriminating two quantum operations asymptotically. We answer the question, "When is the Chernoff exponent for quantum operations finite?" We show that either two quantum operations can be perfectly distinguished with finite uses, or the minimal discrimination error decays exponentially with respect to the number of uses asymptotically. That is, the Chernoff exponent is finite if and only if the quantum operations can not be perfectly distinguished with finite uses. This rules out the possibility of super-exponential decay of error probability. Upper bounds of the Chernoff exponent for quantum operations are provided.

quant-ph↗
arXiv2021

Quantum Max-Flow Min-Cut theorem

The max-flow min-cut theorem is a cornerstone result in combinatorial optimization. Calegari et al. (arXiv:0802.3208) initialized the study of quantum max-flow min-cut conjecture, which connects the rank of a tensor network and the min-cut. Cui et al. (arXiv:1508.04644) showed that this conjecture is false generally. In this paper, we establish a quantum max-flow min-cut theorem for a new definition of quantum maximum flow. In particular, we show that for any quantum tensor network, there are infinitely many $n$, such that quantum max-flow equals quantum min-cut, after attaching dimension $n$ maximally entangled state to each edge as ancilla. Our result implies that the ratio of the quantum max-flow to the quantum min-cut converges to $1$ as the dimension $n$ tends to infinity. As a direct application, we prove the validity of the asymptotical version of the open problem about the quantum max-flow and the min-cut, proposed in Cui et al. (arXiv:1508.04644 ).

quant-ph↗
arXiv2021

Protocols for Packet Quantum Network Intercommunication

A quantum network, which involves multiple parties pinging each other with quantum messages, could revolutionize communication, computing and basic sciences. The future internet will be a global system of various packet switching quantum and classical networks and we call it \emph{quantum internet}. To build a quantum internet, unified protocols that support the distribution of quantum messages within it are necessary. Intuitively one would extend classical internet protocols to handle quantum messages. However, classical network mechanisms, especially those related to error control and reliable connection, implicitly assume that information can be duplicated, which is not true in the quantum world due to the no-cloning theorem and monogamy of entanglement. In this paper, we investigate and propose protocols for packet quantum network intercommunication. To handle the packet loss problem in transport, we propose a quantum retransmission protocol based on the recursive use of a quantum secret sharing scheme. Other internet protocols are also discussed. In particular, the creation of logical process-to-process connections is accomplished by a quantum version of the three-way handshake protocol.

quant-ph↗
arXiv2021

Model Checking Quantum Continuous-Time Markov Chains

Verifying quantum systems has attracted a lot of interests in the last decades. In this paper, we initialised the model checking of quantum continuous-time Markov chain (QCTMC). As a real-time system, we specify the temporal properties on QCTMC by signal temporal logic (STL). To effectively check the atomic propositions in STL, we develop a state-of-art real root isolation algorithm under Schanuel's conjecture; further, we check the general STL formula by interval operations with a bottom-up fashion, whose query complexity turns out to be linear in the size of the input formula by calling the real root isolation algorithm. A running example of an open quantum walk is provided to demonstrate our method.

quant-ph↗
arXiv2021

A Quantum Interpretation of Bunched Logic for Quantum Separation Logic

We propose a model of the substructural logic of Bunched Implications (BI) that is suitable for reasoning about quantum states. In our model, the separating conjunction of BI describes separable quantum states. We develop a program logic where pre- and post-conditions are BI formulas describing quantum states -- the program logic can be seen as a counterpart of separation logic for imperative quantum programs. We exercise the logic for proving the security of quantum one-time pad and secret sharing, and we show how the program logic can be used to discover a flaw in Google Cirq's tutorial on the Variational Quantum Algorithm (VQA).

cs.LO↗
arXiv2021

Limitations on separable measurements by convex optimization

We prove limitations on LOCC and separable measurements in bipartite state discrimination problems using techniques from convex optimization. Specific results that we prove include: an exact formula for the optimal probability of correctly discriminating any set of either three or four Bell states via LOCC or separable measurements when the parties are given an ancillary partially entangled pair of qubits; an easily checkable characterization of when an unextendable product set is perfectly discriminated by separable measurements, along with the first known example of an unextendable product set that cannot be perfectly discriminated by separable measurements; and an optimal bound on the success probability for any LOCC or separable measurement for the recently proposed state discrimination problem of Yu, Duan, and Ying.

quant-ph↗
arXiv2020

Experimental quantification of coherence of a tunable quantum detector

Quantum coherence is a fundamental resource that quantum technologies exploit to achieve performance beyond that of classical devices. A necessary prerequisite to achieve this advantage is the ability of measurement devices to detect coherence from the measurement statistics. Based on a recently developed resource theory of quantum operations, here we quantify experimentally the ability of a typical quantum-optical detector, the weak-field homodyne detector, to detect coherence. We derive an improved algorithm for quantum detector tomography and apply it to reconstruct the positive-operator-valued measures (POVMs) of the detector in different configurations. The reconstructed POVMs are then employed to evaluate how well the detector can detect coherence using two computable measures. As the first experimental investigation of quantum measurements from a resource theoretical perspective, our work sheds new light on the rigorous evaluation of the performance of a quantum measurement apparatus.

quant-ph↗
arXiv2020

Sample efficient tomography via Pauli Measurements

Pauli Measurements are the most important measurements in both theoretical and experimental aspects of quantum information science. In this paper, we explore the power of Pauli measurements in the state tomography related problems. Firstly, we show that the \textit{quantum state tomography} problem of $n$-qubit system can be accomplished with ${\mathcal{O}}(\frac{10^n}{ε^2})$ copies of the unknown state using Pauli measurements. As a direct application, we studied the \textit{quantum overlapping tomography} problem introduced by Cotler and Wilczek in Ref. \cite{Cotler_2020}. We show that the sample complexity is $\mathcal{O}(\frac{10^k\cdot\log({{n}\choose{k}}/δ))}{ε^{2}})$ for quantum overlapping tomography of $k$-qubit reduced density matrices among $n$ is quantum system, where $1-δ$ is the confidential level, and $ε$ is the trace distance error. This can be achieved using Pauli measurements. Moreover, we prove that $Ω(\frac{\log(n/δ)}{ε^{2}})$ copies are needed. In other words, for constant $k$, joint, highly entangled, measurements are not asymptotically more efficient than Pauli measurements.

quant-ph↗
arXiv2020

The QQUIC Transport Protocol: Quantum assisted UDP Internet Connections

Quantum key distribution, initialized in 1984, is a commercialized secure communication method which enables two parties to produce shared random secret key by the nature of quantum mechanics. We propose QQUIC (Quantum assisted Quick UDP Internet Connections) transport protocol, which modifies the famous QUIC transport protocol by employing the quantum key distribution instead of the original classical algorithms in the key exchanging stage. Thanks to the provable security of quantum key distribution, the security of QQUIC key does not depend on computational assumptions. Maybe surprisingly, QQUIC can reduce the network latency in some circumstance even comparing with QUIC. To achieve this, the attached quantum connections are used as the dedicated lines for key generation.

cs.CR↗
arXiv2020

Proq: Projection-based Runtime Assertions for Debugging on a Quantum Computer

In this paper, we propose Proq, a runtime assertion scheme for testing and debugging quantum programs on a quantum computer. The predicates in Proq are represented by projections (or equivalently, closed subspaces of the state space), following Birkhoff-von Neumann quantum logic. The satisfaction of a projection by a quantum state can be directly checked upon a small number of projective measurements rather than a large number of repeated executions. On the theory side, we rigorously prove that checking projection-based assertions can help locate bugs or statistically assure that the semantic function of the tested program is close to what we expect, for both exact and approximate quantum programs. On the practice side, we consider hardware constraints and introduce several techniques to transform the assertions, making them directly executable on the measurement-restricted quantum computers. We also propose to achieve simplified assertion implementation using local projection technique with soundness guaranteed. We compare Proq with existing quantum program assertions and demonstrate the effectiveness and efficiency of Proq by its applications to assert two ingenious quantum algorithms, the Harrow-Hassidim-Lloyd algorithm and Shor's algorithm.

cs.PL↗
arXiv2020

Quantum Closeness Testing: A Streaming Algorithm and Applications

One of the main subjects of this paper is to study quantum property testing with local measurement. In particular, we establish a novel $\ell_2$ norm connection between quantum property testing problems and the corresponding distribution testing problems. This connection opens up the potential to derive efficient testing algorithms using techniques developed for classical property testing. As the first demonstration of these possibilities, we designed two streaming algorithms: one for quantum state tomography, the other for quantum closeness testing. By using the idea of our tomography algorithm, we obtain a streaming algorithm which provide good estimations for each $k$-qubit reduced density matrice of $m$-qubit state using only $\log m$ copies for constant $k$. This is tight and exponential speedup compare with optimal tomography for each $k$-qubit reduced density matrice. To the best of our knowledge, no streaming algorithm has yet been used for quantum property testing. So, to illustrate their usefulness, we achieve the following: independence testing for quantum states; identity and independence testing for quantum state collections; and conditional independence for classical-quantum-quantum states. Additionally, with a dimension splitting technique, we derive matching lower bound up to log factor for independence testing with joint measurement.

quant-ph↗
arXiv2020

Capacity Approaching Coding for Low Noise Interactive Quantum Communication, Part I: Large Alphabets

We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages, designed for a noiseless qudit channel over a $\mathrm{poly}(n)$ size alphabet, our main result is a simulation method that fails with probability less than $2^{-Θ(nε)}$ and uses a qudit channel over the same alphabet $n\left(1+Θ\left(\sqrtε\right)\right)$ times, of which an $ε$ fraction can be corrupted adversarially. The simulation is thus capacity achieving to leading order, and we conjecture that it is optimal up to a constant factor in the $\sqrtε$ term. Furthermore, the simulation is in a model that does not require pre-shared resources such as randomness or entanglement between the communicating parties. Our work improves over the best previously known quantum result where the overhead is a non-explicit large constant [Brassard et al., FOCS'14] for low $ε$.

quant-ph↗
arXiv2019

Relational Proofs for Quantum Programs

Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a quantum analogue of probabilistic couplings. We use our logic to verify non-trivial relational properties of quantum programs, including uniformity for samples generated by the quantum Bernoulli factory, reliability of quantum teleportation against noise (bit and phase flip), security of quantum one-time pad and equivalence of quantum walks.

cs.LO↗