01127nas a2200145 4500008004100000245006400041210006200105260001500167490001000182520070300192100001800895700001600913700001500929856003700944 2018 eng d00aPseudorandom States, Non-Cloning Theorems and Quantum Money0 aPseudorandom States NonCloning Theorems and Quantum Money c2017/11/010 v109933 a

We propose the concept of pseudorandom states and study their constructions, properties, and applications. Under the assumption that quantum-secure one-way functions exist, we present concrete and efficient constructions of pseudorandom states. The non-cloning theorem plays a central role in our study—it motivates the proper definition and characterizes one of the important properties of pseudorandom quantum states. Namely, there is no efficient quantum algorithm that can create more copies of the state from a given number of pseudorandom states. As the main application, we prove that any family of pseudorandom states naturally gives rise to a private-key quantum money scheme.

1 aJi, Zhengfeng1 aLiu, Yi-Kai1 aSong, Fang uhttps://arxiv.org/abs/1711.0038501598nas a2200241 4500008004100000245005800041210005800099260001500157300001100172490000800183520093100191100001301122700001401135700001801149700001601167700001801183700001801201700001301219700001601232700001401248700002201262856007201284 2017 eng d00aQuantum state tomography via reduced density matrices0 aQuantum state tomography via reduced density matrices c2017/01/09 a0204010 v1183 a

Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this work we demonstrate for the first time a class of states that are UD by their RDMs under the assumption that the global state is pure, but fail to be UD in the absence of that assumption. This discovery allows us to classify quantum states according to their UD properties, with the requirement that each class be treated distinctly in the practice of simplifying quantum state tomography. Additionally we experimentally test the feasibility and stability of performing quantum state tomography via the measurement of local RDMs for each class. These theoretical and experimental results advance the project of performing efficient and accurate quantum state tomography in practice.

1 aXin, Tao1 aLu, Dawei1 aKlassen, Joel1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aMa, Xian1 aLong, Guilu1 aZeng, Bei1 aLaflamme, Raymond uhttp://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.02040101164nas a2200169 4500008004100000245007500041210006900116260001500185300001100200490000700211520067400218100001800892700001800910700001600928700001400944856003600958 2016 eng d00aDetecting Consistency of Overlapping Quantum Marginals by Separability0 aDetecting Consistency of Overlapping Quantum Marginals by Separa c2016/03/03 a0321050 v933 a The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-known $k$-symmetric extension criterion for separability. 1 aChen, Jianxin1 aJi, Zhengfeng1 aYu, Nengkun1 aZeng, Bei uhttp://arxiv.org/abs/1509.0659101692nas a2200181 4500008004100000245007500041210006900116260001500185520116000200100001801360700001501378700001801393700001901411700001601430700001401446700001401460856003601474 2016 eng d00aJoint product numerical range and geometry of reduced density matrices0 aJoint product numerical range and geometry of reduced density ma c2016/06/233 aThe reduced density matrices of a many-body quantum system form a convex set, whose three-dimensional projection Θ is convex in R3. The boundary ∂Θ of Θ may exhibit nontrivial geometry, in particular ruled surfaces. Two physical mechanisms are known for the origins of ruled surfaces: symmetry breaking and gapless. In this work, we study the emergence of ruled surfaces for systems with local Hamiltonians in infinite spatial dimension, where the reduced density matrices are known to be separable as a consequence of the quantum de Finetti's theorem. This allows us to identify the reduced density matrix geometry with joint product numerical range Π of the Hamiltonian interaction terms. We focus on the case where the interaction terms have certain structures, such that ruled surface emerge naturally when taking a convex hull of Π. We show that, a ruled surface on ∂Θ sitting in Π has a gapless origin, otherwise it has a symmetry breaking origin. As an example, we demonstrate that a famous ruled surface, known as the oloid, is a possible shape of Θ, with two boundary pieces of symmetry breaking origin separated by two gapless lines.1 aChen, Jianxin1 aGuo, Cheng1 aJi, Zhengfeng1 aPoon, Yiu-Tung1 aYu, Nengkun1 aZeng, Bei1 aZhou, Jie uhttp://arxiv.org/abs/1606.0742201933nas a2200277 4500008004100000245007200041210006900113260001500182300001100197490000700208520116900215100001301384700001901397700001401416700001801430700001401448700002501462700002301487700001701510700001701527700002101544700001801565700001401583700002201597856003601619 2016 eng d00aPure-state tomography with the expectation value of Pauli operators0 aPurestate tomography with the expectation value of Pauli operato c2016/03/31 a0321400 v933 a

We examine the problem of finding the minimum number of Pauli measurements needed to uniquely determine an arbitrary n-qubit pure state among all quantum states. We show that only 11 Pauli measurements are needed to determine an arbitrary two-qubit pure state compared to the full quantum state tomography with 16 measurements, and only 31 Pauli measurements are needed to determine an arbitrary three-qubit pure state compared to the full quantum state tomography with 64 measurements. We demonstrate that our protocol is robust under depolarizing error with simulated random pure states. We experimentally test the protocol on two- and three-qubit systems with nuclear magnetic resonance techniques. We show that the pure state tomography protocol saves us a number of measurements without considerable loss of fidelity. We compare our protocol with same-size sets of randomly selected Pauli operators and find that our selected set of Pauli measurements significantly outperforms those random sampling sets. As a direct application, our scheme can also be used to reduce the number of settings needed for pure-state tomography in quantum optical systems.

1 aMa, Xian1 aJackson, Tyler1 aZhou, Hui1 aChen, Jianxin1 aLu, Dawei1 aMazurek, Michael, D.1 aFisher, Kent, A.G.1 aPeng, Xinhua1 aKribs, David1 aResch, Kevin, J.1 aJi, Zhengfeng1 aZeng, Bei1 aLaflamme, Raymond uhttp://arxiv.org/abs/1601.0537901747nas a2200241 4500008004100000245009400041210006900135260001500204300001100219490000800230520106300238100001401301700001301315700001601328700001801344700001801362700001601380700002001396700001701416700001401433700002201447856003601469 2016 eng d00aTomography is necessary for universal entanglement detection with single-copy observables0 aTomography is necessary for universal entanglement detection wit c2016/06/07 a2305010 v1163 aEntanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.1 aLu, Dawei1 aXin, Tao1 aYu, Nengkun1 aJi, Zhengfeng1 aChen, Jianxin1 aLong, Guilu1 aBaugh, Jonathan1 aPeng, Xinhua1 aZeng, Bei1 aLaflamme, Raymond uhttp://arxiv.org/abs/1511.0058101250nas a2200217 4500008004100000245007700041210006900118260001500187300001100202490000700213520064200220100001800862700001800880700001800898700001900916700001300935700001600948700001400964700001700978856003700995 2015 eng d00aDiscontinuity of Maximum Entropy Inference and Quantum Phase Transitions0 aDiscontinuity of Maximum Entropy Inference and Quantum Phase Tra c2015/08/10 a0830190 v173 a In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum entropy inference of local observable measurements signals the non-local type of transitions, where local density matrices of the ground state change smoothly at the transition point. We then propose to use the quantum conditional mutual information of the ground state as an indicator to detect the discontinuity and the non-local type of quantum phase transitions in the thermodynamic limit. 1 aChen, Jianxin1 aJi, Zhengfeng1 aLi, Chi-Kwong1 aPoon, Yiu-Tung1 aShen, Yi1 aYu, Nengkun1 aZeng, Bei1 aZhou, Duanlu uhttp://arxiv.org/abs/1406.5046v201596nas a2200169 4500008004100000245004400041210004300085260001400128490000700142520114800149100001801297700001801315700001701333700002501350700001401375856003701389 2014 eng d00aSymmetric Extension of Two-Qubit States0 aSymmetric Extension of TwoQubit States c2014/9/170 v903 a Quantum key distribution uses public discussion protocols to establish shared secret keys. In the exploration of ultimate limits to such protocols, the property of symmetric extendibility of underlying bipartite states $\rho_{AB}$ plays an important role. A bipartite state $\rho_{AB}$ is symmetric extendible if there exits a tripartite state $\rho_{ABB'}$, such that the $AB$ marginal state is identical to the $AB'$ marginal state, i.e. $\rho_{AB'}=\rho_{AB}$. For a symmetric extendible state $\rho_{AB}$, the first task of the public discussion protocol is to break this symmetric extendibility. Therefore to characterize all bi-partite quantum states that possess symmetric extensions is of vital importance. We prove a simple analytical formula that a two-qubit state $\rho_{AB}$ admits a symmetric extension if and only if $\tr(\rho_B^2)\geq \tr(\rho_{AB}^2)-4\sqrt{\det{\rho_{AB}}}$. Given the intimate relationship between the symmetric extension problem and the quantum marginal problem, our result also provides the first analytical necessary and sufficient condition for the quantum marginal problem with overlapping marginals. 1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David1 aLütkenhaus, Norbert1 aZeng, Bei uhttp://arxiv.org/abs/1310.3530v201999nas a2200193 4500008004100000245005200041210005200093260001500145300001200160490000700172520148600179100001801665700001801683700001901701700001801720700001601738700001401754856003701768 2013 eng d00aSymmetries of Codeword Stabilized Quantum Codes0 aSymmetries of Codeword Stabilized Quantum Codes c2013/03/28 a192-2060 v223 a Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.,e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant. 1 aBeigi, Salman1 aChen, Jianxin1 aGrassl, Markus1 aJi, Zhengfeng1 aWang, Qiang1 aZeng, Bei uhttp://arxiv.org/abs/1303.7020v202008nas a2200193 4500008004100000245007500041210006900116260001400185490000700199520143800206100001801644700002101662700001801683700002401701700001701725700002101742700001401763856003701777 2013 eng d00aUniqueness of Quantum States Compatible with Given Measurement Results0 aUniqueness of Quantum States Compatible with Given Measurement R c2013/7/110 v883 a We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same measurement results and (2) no other state, pure or mixed, is compatible with the same measurement results. For case (1), it is known that for a d-dimensional Hilbert space, there exists a set of 4d-5 observables that uniquely determines any pure state. We show that for case (2), 5d-7 observables suffice to uniquely determine any pure state. Thus there is a gap between the results for (1) and (2), and we give some examples to illustrate this. The case of observables corresponding to reduced density matrices (RDMs) of a multipartite system is also discussed, where we improve known bounds on local dimensions for case (2) in which almost all pure states are uniquely determined by their RDMs. We further discuss circumstances where (1) can imply (2). We use convexity of the numerical range of operators to show that when only two observables are measured, (1) always implies (2). More generally, if there is a compact group of symmetries of the state space which has the span of the observables measured as the set of fixed points, then (1) implies (2). We analyze the possible dimensions for the span of such observables. Our results extend naturally to the case of low rank quantum states. 1 aChen, Jianxin1 aDawkins, Hillary1 aJi, Zhengfeng1 aJohnston, Nathaniel1 aKribs, David1 aShultz, Frederic1 aZeng, Bei uhttp://arxiv.org/abs/1212.3503v201351nas a2200181 4500008004100000245009200041210006900133260001500202300001100217490000700228520080600235100001801041700001801059700002301077700001401100700001801114856003701132 2012 eng d00aComment on some results of Erdahl and the convex structure of reduced density matrices0 aComment on some results of Erdahl and the convex structure of re c2012/05/16 a0722030 v533 a In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-image in both the symmetric and anti-symmetric setting. Moreover, this extends to the quantum marginal setting for a pair of complementary $m$-body and $(N-m)$-body reduced density matrices. 1 aChen, Jianxin1 aJi, Zhengfeng1 aRuskai, Mary, Beth1 aZeng, Bei1 aZhou, Duan-Lu uhttp://arxiv.org/abs/1205.3682v101936nas a2200157 4500008004100000245005700041210005700098260001300155490000700168520149900175100001801674700001801692700001701710700001401727856003701741 2012 eng d00aCorrelations in excited states of local Hamiltonians0 aCorrelations in excited states of local Hamiltonians c2012/4/90 v853 a Physical properties of the ground and excited states of a $k$-local Hamiltonian are largely determined by the $k$-particle reduced density matrices ($k$-RDMs), or simply the $k$-matrix for fermionic systems---they are at least enough for the calculation of the ground state and excited state energies. Moreover, for a non-degenerate ground state of a $k$-local Hamiltonian, even the state itself is completely determined by its $k$-RDMs, and therefore contains no genuine ${>}k$-particle correlations, as they can be inferred from $k$-particle correlation functions. It is natural to ask whether a similar result holds for non-degenerate excited states. In fact, for fermionic systems, it has been conjectured that any non-degenerate excited state of a 2-local Hamiltonian is simultaneously a unique ground state of another 2-local Hamiltonian, hence is uniquely determined by its 2-matrix. And a weaker version of this conjecture states that any non-degenerate excited state of a 2-local Hamiltonian is uniquely determined by its 2-matrix among all the pure $n$-particle states. We construct explicit counterexamples to show that both conjectures are false. It means that correlations in excited states of local Hamiltonians could be dramatically different from those in ground states. We further show that any non-degenerate excited state of a $k$-local Hamiltonian is a unique ground state of another $2k$-local Hamiltonian, hence is uniquely determined by its $2k$-RDMs (or $2k$-matrix). 1 aChen, Jianxin1 aJi, Zhengfeng1 aWei, Zhaohui1 aZeng, Bei uhttp://arxiv.org/abs/1106.1373v201702nas a2200157 4500008004100000245004500041210004500086260001400131490000700145520128800152100001801440700001801458700001401476700001701490856003701507 2012 eng d00aFrom Ground States to Local Hamiltonians0 aFrom Ground States to Local Hamiltonians c2012/8/300 v863 a Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be mainly interested in local Hamiltonians with certain interaction patterns, such as nearest neighbour interactions on some type of lattices. A necessary condition for a space $V$ to be the ground-state space of some local Hamiltonian with a given interaction pattern, is that the maximally mixed state supported on $V$ is uniquely determined by its reduced density matrices associated with the given pattern, based on the principle of maximum entropy. However, it is unclear whether this condition is in general also sufficient. We examine the situations for the existence of such a local Hamiltonian to have $V$ satisfying the necessary condition mentioned above as its ground-state space, by linking to faces of the convex body of the local reduced states. We further discuss some methods for constructing the corresponding local Hamiltonians with given interaction patterns, mainly from physical points of view, including constructions related to perturbation methods, local frustration-free Hamiltonians, as well as thermodynamical ensembles. 1 aChen, Jianxin1 aJi, Zhengfeng1 aZeng, Bei1 aZhou, D., L. uhttp://arxiv.org/abs/1110.6583v401607nas a2200181 4500008004100000245005700041210005500098260001500153300001100168490000700179520111800186100001801304700001801322700001701340700001701357700001401374856003701388 2012 eng d00aGround-State Spaces of Frustration-Free Hamiltonians0 aGroundState Spaces of FrustrationFree Hamiltonians c2012/01/01 a1022010 v533 a We study the ground-state space properties for frustration-free Hamiltonians. We introduce a concept of `reduced spaces' to characterize local structures of ground-state spaces. For a many-body system, we characterize mathematical structures for the set $\Theta_k$ of all the $k$-particle reduced spaces, which with a binary operation called join forms a semilattice that can be interpreted as an abstract convex structure. The smallest nonzero elements in $\Theta_k$, called atoms, are analogs of extreme points. We study the properties of atoms in $\Theta_k$ and discuss its relationship with ground states of $k$-local frustration-free Hamiltonians. For spin-1/2 systems, we show that all the atoms in $\Theta_2$ are unique ground states of some 2-local frustration-free Hamiltonians. Moreover, we show that the elements in $\Theta_k$ may not be the join of atoms, indicating a richer structure for $\Theta_k$ beyond the convex structure. Our study of $\Theta_k$ deepens the understanding of ground-state space properties for frustration-free Hamiltonians, from a new angle of reduced spaces. 1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David1 aWei, Zhaohui1 aZeng, Bei uhttp://arxiv.org/abs/1112.0762v101508nas a2200145 4500008004100000245005300041210005300094260001500147520109300162100001801255700001801273700002001291700001401311856003701325 2012 eng d00aMinimum Entangling Power is Close to Its Maximum0 aMinimum Entangling Power is Close to Its Maximum c2012/10/043 a Given a quantum gate $U$ acting on a bipartite quantum system, its maximum (average, minimum) entangling power is the maximum (average, minimum) entanglement generation with respect to certain entanglement measure when the inputs are restricted to be product states. In this paper, we mainly focus on the 'weakest' one, i.e., the minimum entangling power, among all these entangling powers. We show that, by choosing von Neumann entropy of reduced density operator or Schmidt rank as entanglement measure, even the 'weakest' entangling power is generically very close to its maximal possible entanglement generation. In other words, maximum, average and minimum entangling powers are generically close. We then study minimum entangling power with respect to other Lipschitiz-continuous entanglement measures and generalize our results to multipartite quantum systems. As a straightforward application, a random quantum gate will almost surely be an intrinsically fault-tolerant entangling device that will always transform every low-entangled state to near-maximally entangled state. 1 aChen, Jianxin1 aJi, Zhengfeng1 aKribs, David, W1 aZeng, Bei uhttp://arxiv.org/abs/1210.1296v101124nas a2200181 4500008004100000245005300041210005300094260001500147300001100162490000700173520063000180100001800810700001800828700002400846700002100870700001400891856003700905 2012 eng d00aRank Reduction for the Local Consistency Problem0 aRank Reduction for the Local Consistency Problem c2012/02/09 a0222020 v533 a We address the problem of how simple a solution can be for a given quantum local consistency instance. More specifically, we investigate how small the rank of the global density operator can be if the local constraints are known to be compatible. We prove that any compatible local density operators can be satisfied by a low rank global density operator. Then we study both fermionic and bosonic versions of the N-representability problem as applications. After applying the channel-state duality, we prove that any compatible local channels can be obtained through a global quantum channel with small Kraus rank. 1 aChen, Jianxin1 aJi, Zhengfeng1 aKlyachko, Alexander1 aKribs, David, W.1 aZeng, Bei uhttp://arxiv.org/abs/1106.3235v202114nas a2200169 4500008004100000245009200041210006900133260001300202490000700215520160400222100001801826700001401844700001701858700001801875700001401893856003701907 2011 eng d00aNo-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems 0 aNogo Theorem for Oneway Quantum Computing on Naturally Occurring c2011/5/90 v833 a One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measurements in the course of the computation leave the remaining particles in the ground space. Recently, significant efforts have been made to the search of resource states that appear naturally as ground states in spin lattice systems. The approach is proved to be successful in spin-5/2 and spin-3/2 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin-1/2, i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin-1/2 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit states, a stronger result that is interesting independent of the context of one-way quantum computing. 1 aChen, Jianxin1 aChen, Xie1 aDuan, Runyao1 aJi, Zhengfeng1 aZeng, Bei uhttp://arxiv.org/abs/1004.3787v101132nas a2200157 4500008004100000245007300041210006900114260001500183520064900198100001800847700001800865700002300883700001400906700001700920856003700937 2010 eng d00aPrinciple of Maximum Entropy and Ground Spaces of Local Hamiltonians0 aPrinciple of Maximum Entropy and Ground Spaces of Local Hamilton c2010/10/133 a The structure of the ground spaces of quantum systems consisting of local interactions is of fundamental importance to different areas of physics. In this Letter, we present a necessary and sufficient condition for a subspace to be the ground space of a k-local Hamiltonian. Our analysis are motivated by the concept of irreducible correlations studied by [Linden et al., PRL 89, 277906] and [Zhou, PRL 101, 180505], which is in turn based on the principle of maximum entropy. It establishes a better understanding of the ground spaces of local Hamiltonians and builds an intimate link of ground spaces to the correlations of quantum states. 1 aChen, Jianxin1 aJi, Zhengfeng1 aRuskai, Mary, Beth1 aZeng, Bei1 aZhou, Duanlu uhttp://arxiv.org/abs/1010.2739v401032nas a2200181 4500008004100000245003700041210003700078260001500115300001100130490000700141520058000148100001800728700001700746700001800763700002000781700001200801856003700813 2008 eng d00aExistence of Universal Entangler0 aExistence of Universal Entangler c2008/01/01 a0121030 v493 a 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. 1 aChen, Jianxin1 aDuan, Runyao1 aJi, Zhengfeng1 aYing, Mingsheng1 aYu, Jun uhttp://arxiv.org/abs/0704.1473v200857nas a2200145 4500008004100000245003400041210002900075260001500104520048200119100001800601700001800619700001700637700002000654856003700674 2007 eng d00aThe LU-LC conjecture is false0 aLULC conjecture is false c2007/09/093 a The LU-LC conjecture is an important open problem concerning the structure of entanglement of states described in the stabilizer formalism. It states that two local unitary equivalent stabilizer states are also local Clifford equivalent. If this conjecture were true, the local equivalence of stabilizer states would be extremely easy to characterize. Unfortunately, however, based on the recent progress made by Gross and Van den Nest, we find that the conjecture is false. 1 aJi, Zhengfeng1 aChen, Jianxin1 aWei, Zhaohui1 aYing, Mingsheng uhttp://arxiv.org/abs/0709.1266v2