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Runyao Duan

Publications and source records attributed to Runyao Duan.

At least 73 records · Page 4Linked to original sources
arXiv2008

Locally undetermined states, generalized Schmidt decomposition, and an application in distributed computing

Multipartite quantum states that cannot be uniquely determined by their reduced states of all proper subsets of the parties exhibit some inherit `high-order' correlation. This paper elaborates this issue by giving necessary and sufficient conditions for a pure multipartite state to be locally undetermined, and moreover, characterizing precisely all the pure states sharing the same set of reduced states with it. Interestingly, local determinability of pure states is closely related to a generalized notion of Schmidt decomposition. Furthermore, we find that locally undetermined states have some applications to the well-known consensus problem in distributed computation. To be specific, given some physically separated agents, when communication between them, either classical or quantum, is unreliable and they are not allowed to use local ancillary quantum systems, then there exists a totally correct and completely fault-tolerant protocol for them to reach a consensus if and only if they share a priori a locally undetermined quantum state.

quant-ph↗
arXiv2008

Exact Quantum Search by Parallel Unitary Discrimination Schemes

We study the unsorted database search problem with items $N$ from the viewpoint of unitary discrimination. Instead of considering the famous $O(\sqrt{N})$ Grover's the bounded-error algorithm for the original problem, we seek for the results about the exact algorithms, i.e. the ones succeed with certainty. Under the standard oracle model $\sum_j (-1)^{δ_{τj}}|j>< j|$, we demonstrate a tight lower bound ${2/3}N+o(N)$ of the number of queries for any parallel scheme with unentangled input states. With the assistance of entanglement, we obtain a general lower bound ${1/2}(N-\sqrt{N})$. We provide concrete examples to illustrate our results. In particular, we show that the case of N=6 can be solved exactly with only two queries by using a bipartite entangled input state. Our results indicate that in the standard oracle model the complexity of exact quantum search with one unique solution can be strictly less than that of the calculation of OR function.

quant-ph↗
arXiv2008

Tripartite entanglement transformations and tensor rank

Understanding the nature of multipartite entanglement is a central mission of quantum information theory. To this end, we investigate the question of tripartite entanglement convertibility. We find that there exists no easy criterion to determine whether a general tripartite transformation can be performed with a nonzero success probability and in fact, the problem is NP-hard. Our results are based on the connections between multipartite entanglement and tensor rank (also called Schmidt rank), a key concept in algebraic complexity theory. Not only does this relationship allow us to characterize the general difficulty in determining possible entanglement transformations, but it also enables us to observe the previously overlooked fact that {\em the Schmidt rank is not an additive entanglement measure}. As a result, we improve some best known transformation rates between specific tripartite entangled states. In addition, we find obtaining the most efficient algorithm for matrix multiplication to be precisely equivalent to determining the optimal rate of conversion between the Greenberger-Horne-Zeilinger state and a triangular distribution of three Einstein-Podolsky-Rosen states.

quant-ph↗
arXiv2007

Entanglement between Two Uses of a Noisy Multipartite Quantum Channel Enables Perfect Transmission of Classical Information

Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and is enabled by quantum entanglement.

quant-ph↗
arXiv2007

Parameter estimation of quantum channels

The efficiency of parameter estimation of quantum channels is studied in this paper. We introduce the concept of programmable parameters to the theory of estimation. It is found that programmable parameters obey the standard quantum limit strictly; hence no speedup is possible in its estimation. We also construct a class of non-unitary quantum channels whose parameter can be estimated in a way that the standard quantum limit is broken. The study of estimation of general quantum channels also enables an investigation of the effect of noises on quantum estimation.

quant-ph↗
arXiv2007

Local distinguishability of orthogonal 2\otimes3 pure states

We present a complete characterization for the local distinguishability of orthogonal $2\otimes 3$ pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguishable by local projective measurements and classical communication (LPCC) can be perfectly distinguishable by LOCC. That indicates the ability of LOCC for discriminating $2\otimes 3$ states is strictly more powerful than that of LPCC, which is strikingly different from the case of multi-qubit states. We also show that classical communication plays a crucial role for local distinguishability by constructing a class of $m\otimes n$ states which require at least $2\min\{m,n\}-2$ rounds of classical communication in order to achieve a perfect local discrimination.

quant-ph↗
arXiv2007

Distinguishability of Quantum States by Separable Operations

We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of $(D-1)$ pure states, where $D$ is the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of $2\otimes 2$ separable operations not being realizable by local operations and classical communication. Before our work only a class of $3\otimes 3$ nonlocal separable operations was known [Bennett et al, Phys. Rev. A \textbf{59}, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of 1 or 2 orthogonal product states, i.e., has an orthogonal Schmidt number not less than 3, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. \textbf{95}, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp. three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.

quant-ph↗
arXiv2007

Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local Operations and Classical Communication

We show that an arbitrary basis of a multipartite quantum state space consisting of $K$ distant parties such that the $k$th party has local dimension $d_k$ always contains at least $N=\sum_{k=1}^K (d_k-1)+1$ members that are unambiguously distinguishable using local operations and classical communication (LOCC). We further show this lower bound is optimal by analytically constructing a special product basis having only $N$ members unambiguously distinguishable by LOCC. Interestingly, such a special product basis not only gives a stronger form of the weird phenomenon ``nonlocality without entanglement", but also implies the existence of locally distinguishable entangled basis.

quant-ph↗
arXiv2007

Existence of Universal Entangler

A gate is called entangler if it transforms some (pure) product states to entangled states. A universal entangler is a gate which transforms all product states to entangled states. In practice, a universal entangler is a very powerful device for generating entanglements, and thus provides important physical resources for accomplishing many tasks in quantum computing and quantum information. This Letter demonstrates that a universal entangler always exists except for a degenerated case. Nevertheless, the problem how to find a universal entangler remains open.

quant-ph↗
arXiv2007

Local Distinguishability of Multipartite Unitary Operations

We show that any two different unitary operations acting on an arbitrary multipartite quantum system can be perfectly distinguishable by local operations and classical communication when a finite number of runs is allowed. We then directly extend this result into the case when the number of unitary operations to be discriminated is more than two. Intuitively, our result means that the lost identity of a nonlocal (entangled) unitary operation can be recovered locally, without any use of entanglement or joint quantum operations.

quant-ph↗
arXiv2007

Entanglement Is Not Necessary for Perfect Discrimination between Unitary Operations

We show that a unitary operation (quantum circuit) secretely chosen from a finite set of unitary operations can be determined with certainty by sequentially applying only a finite amount of runs of the unknown circuit. No entanglement or joint quantum operations is required in our scheme. We further show that our scheme is optimal in the sense that the number of the runs is minimal when discriminating only two unitary operations.

quant-ph↗
arXiv2007

Partial Recovery of Quantum Entanglement

Suppose Alice and Bob try to transform an entangled state shared between them into another one by local operations and classical communications. Then in general a certain amount of entanglement contained in the initial state will decrease in the process of transformation. However, an interesting phenomenon called partial entanglement recovery shows that it is possible to recover some amount of entanglement by adding another entangled state and transforming the two entangled states collectively. In this paper we are mainly concerned with the feasibility of partial entanglement recovery. The basic problem we address is whether a given state is useful in recovering entanglement lost in a specified transformation. In the case where the source and target states of the original transformation satisfy the strict majorization relation, a necessary and sufficient condition for partial entanglement recovery is obtained. For the general case we give two sufficient conditions. We also give an efficient algorithm for the feasibility of partial entanglement recovery in polynomial time. As applications, we establish some interesting connections between partial entanglement recovery and the generation of maximally entangled states, quantum catalysis, mutual catalysis, and multiple-copy entanglement transformation.

quant-ph↗
arXiv2006

Relation Between Catalyst-assisted Entanglement Transformation and Multiple-copy Transformation

We show that in some cases, catalyst-assisted entanglement transformation cannot be implemented by multiple-copy transformation for pure states. This fact, together with the result we obtained in [R. Y. Duan, Y. Feng, X. Li, and M. S. Ying, Phys. Rev. A 71, 042319 (2005)] that the latter can be completely implemented by the former, indicates that catalyst-assisted transformation is strictly more powerful than multiple-copy transformation. For purely probabilistic setting we find, however, these two kinds of transformations are geometrically equivalent in the sense that the sets of pure states which can be converted into a given pure state with maximal probabilities not less than a given value have the same closure, no matter catalyst-assisted transformation or multiple-copy transformation is used.

quant-ph↗
arXiv2006

Optimal dense coding with arbitrary pure entangled states

We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense coding are derived. We also construct the optimal protocol which saturates the upper bound in each case.

quant-ph↗
arXiv2006

Identification and Distance Measures of Measurement Apparatus

We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency significantly. A brief discussion on the problem of how to appropriately define distance measures of measurements is also provided based on the results of identification.

quant-ph↗
arXiv2006

Proof rules for purely quantum programs

We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a purely quantum language fragment which describes the quantum part of a future quantum computer in Knill's architecture. The denotational semantics, weakest precondition semantics, and weakest liberal precondition semantics of this language fragment are introduced. To help reasoning about quantum programs involving quantum loops, we extend proof rules for classical probabilistic programs to our purely quantum programs.

cs.PL↗
arXiv2006

Boundary effect of deterministic dense coding

We present a rigorous proof of an interesting boundary effect of deterministic dense coding first observed by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Namely, it is shown that $d^2-1$ cannot be the maximal alphabet size of any isometric deterministic dense coding schemes utilizing $d$-level partial entanglement.

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