We provide operational definition of symmetry of entanglement: An entangled state con-tains symmetric entanglement if its subsystems can be exchanged (swapped) by meansof local operations and class...
{"title":"Are quantum correlations symmetric","authors":"HorodeckiKarol, HorodeckiMichał, HorodeckiPaweł","doi":"10.5555/2011451.2011452","DOIUrl":"https://doi.org/10.5555/2011451.2011452","url":null,"abstract":"We provide operational definition of symmetry of entanglement: An entangled state con-tains symmetric entanglement if its subsystems can be exchanged (swapped) by meansof local operations and class...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2010-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71125987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The intrinsic idea of superdense coding is to find as many gates as possible such thatthey can be perfectly discriminated. In this paper, we consider a basic scheme of dis-crimination of quantum ga...
{"title":"Ancilla-assisted discrimination of quantum gates","authors":"Chenjianxin, YingMingsheng","doi":"10.5555/2011438.2011450","DOIUrl":"https://doi.org/10.5555/2011438.2011450","url":null,"abstract":"The intrinsic idea of superdense coding is to find as many gates as possible such thatthey can be perfectly discriminated. In this paper, we consider a basic scheme of dis-crimination of quantum ga...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71125982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discreti...
{"title":"Eigenpath traversal by phase randomization","authors":"BoixoSergio, KnillEmanuel, SommaRolando","doi":"10.5555/2011804.2011811","DOIUrl":"https://doi.org/10.5555/2011804.2011811","url":null,"abstract":"A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discreti...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2009-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71125781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Bera, Stephen A. Fenner, F. Green, Steven Homer
Universal circuits can be viewed as general-purpose simulators for central classes ofcircuits and can be used to capture the computational power of the circuit class beingsimulated. We define and construct quantum universal circuits which are efficient andhave very little overhead in simulation. For depth we construct universal circuits whosedepth is the same order as the circuits being simulated. For size, there is a log factorblow-up in the universal circuits constructed here which is nearly optimal.
{"title":"Efficient universal quantum circuits","authors":"D. Bera, Stephen A. Fenner, F. Green, Steven Homer","doi":"10.26421/QIC10.1-2-2","DOIUrl":"https://doi.org/10.26421/QIC10.1-2-2","url":null,"abstract":"Universal circuits can be viewed as general-purpose simulators for central classes ofcircuits and can be used to capture the computational power of the circuit class beingsimulated. We define and construct quantum universal circuits which are efficient andhave very little overhead in simulation. For depth we construct universal circuits whosedepth is the same order as the circuits being simulated. For size, there is a log factorblow-up in the universal circuits constructed here which is nearly optimal.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"115 1","pages":"418-428"},"PeriodicalIF":1.0,"publicationDate":"2009-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79145960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We construct a family of bipartite states of arbitrary dimension whose eigenvalues of thepartially transposed matrix can be inferred directly from the block structure of the globaldensity matrix. We identify from this several subfamilies in which the PPT criterion isboth necessary and sufficient. A sufficient criterion of separability is obtained, which isfundamental for the discussion. We show how several examples of states known to beclassifiable by the PPT criterion indeed belong to this general set. Possible uses of thesestates in numerical analysis of entanglement and in the search of PPT bound entangledstates are briefly discussed.
{"title":"Families of bipartite states classifiable by the positive partial transposition criterion","authors":"F. Steinhoff, M. C. Oliveira","doi":"10.5555/2011362.2011372","DOIUrl":"https://doi.org/10.5555/2011362.2011372","url":null,"abstract":"We construct a family of bipartite states of arbitrary dimension whose eigenvalues of thepartially transposed matrix can be inferred directly from the block structure of the globaldensity matrix. We identify from this several subfamilies in which the PPT criterion isboth necessary and sufficient. A sufficient criterion of separability is obtained, which isfundamental for the discussion. We show how several examples of states known to beclassifiable by the PPT criterion indeed belong to this general set. Possible uses of thesestates in numerical analysis of entanglement and in the search of PPT bound entangledstates are briefly discussed.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"10 1","pages":"525-538"},"PeriodicalIF":1.0,"publicationDate":"2009-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71125681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M. Kaplan, Sophie Laplante, Iordanis Kerenidis, J. Roland
A non-local box is an abstract device into which Alice and Bob input bits x and yrespectively and receive outputs a and b, where a, b are uniformly distributed and a+b =x∧y. Such boxes have been central to the study of quantum or generalized non-locality, aswell as the simulation of non-signaling distributions. In this paper, we start by studyinghow many non-local boxes Alice and Bob need in order to compute a Boolean functionf. We provide tight upper and lower bounds in terms of the communication complexityof the function both in the deterministic and randomized case. We show that non-localbox complexity has interesting applications to classical cryptography, in particular tosecure function evaluation, and study the question posed by Beimel and Malkin [1] ofhow many Oblivious Transfer calls Alice and Bob need in order to securely compute afunction f. We show that this question is related to the non-local box complexity of thefunction and conclude by greatly improving their bounds. Finally, another consequenceof our results is that traceless two-outcome measurements on maximally entangled statescan be simulated with 3 non-local boxes, while no finite bound was previously known.
{"title":"Non-local box complexity and secure function evaluation","authors":"M. Kaplan, Sophie Laplante, Iordanis Kerenidis, J. Roland","doi":"10.26421/QIC11.1-2-4","DOIUrl":"https://doi.org/10.26421/QIC11.1-2-4","url":null,"abstract":"A non-local box is an abstract device into which Alice and Bob input bits x and yrespectively and receive outputs a and b, where a, b are uniformly distributed and a+b =x∧y. Such boxes have been central to the study of quantum or generalized non-locality, aswell as the simulation of non-signaling distributions. In this paper, we start by studyinghow many non-local boxes Alice and Bob need in order to compute a Boolean functionf. We provide tight upper and lower bounds in terms of the communication complexityof the function both in the deterministic and randomized case. We show that non-localbox complexity has interesting applications to classical cryptography, in particular tosecure function evaluation, and study the question posed by Beimel and Malkin [1] ofhow many Oblivious Transfer calls Alice and Bob need in order to securely compute afunction f. We show that this question is related to the non-local box complexity of thefunction and conclude by greatly improving their bounds. Finally, another consequenceof our results is that traceless two-outcome measurements on maximally entangled statescan be simulated with 3 non-local boxes, while no finite bound was previously known.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"129 17 1","pages":"239-250"},"PeriodicalIF":1.0,"publicationDate":"2009-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85039296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of local search on a graph. Given a real-valued black-box functionf on the graph's vertices, this is the problem of determining a local minimum of f--a vertex v for which f(v) is no more than f evaluated at any of v's neighbors. In1983, Aldous gave the first strong lower bounds for the problem, showing that anyrandomized algorithm requires Ω(2n/2-o(n)) queries to determine a local minimum onthe n-dimensional hypercube. The next major step forward was not until 2004 whenAaronson, introducing a new method for query complexity bounds, both strengthened thislower bound to Ω(2n/2/n2) and gave an analogous lower bound on the quantum querycomplexity. While these bounds are very strong, they are known only for narrow familiesof graphs (hypercubes and grids). We show how to generalize Aaronson's techniques inorder to give randomized (and quantum) lower bounds on the query complexity of localsearch for the family of vertex-transitive graphs. In particular, we show that for anyvertex-transitive graph G of N vertices and diameter d, the randomized and quantumquery complexities for local search on G are Ω (√N/dlogN) and (4√N / √dlogN),respectively.
{"title":"Quantum and randomized lower bounds for local search on vertex-transitive graphs","authors":"Hang T. Dinh, A. Russell","doi":"10.26421/QIC10.7-8-5","DOIUrl":"https://doi.org/10.26421/QIC10.7-8-5","url":null,"abstract":"We study the problem of local search on a graph. Given a real-valued black-box functionf on the graph's vertices, this is the problem of determining a local minimum of f--a vertex v for which f(v) is no more than f evaluated at any of v's neighbors. In1983, Aldous gave the first strong lower bounds for the problem, showing that anyrandomized algorithm requires Ω(2n/2-o(n)) queries to determine a local minimum onthe n-dimensional hypercube. The next major step forward was not until 2004 whenAaronson, introducing a new method for query complexity bounds, both strengthened thislower bound to Ω(2n/2/n2) and gave an analogous lower bound on the quantum querycomplexity. While these bounds are very strong, they are known only for narrow familiesof graphs (hypercubes and grids). We show how to generalize Aaronson's techniques inorder to give randomized (and quantum) lower bounds on the query complexity of localsearch for the family of vertex-transitive graphs. In particular, we show that for anyvertex-transitive graph G of N vertices and diameter d, the randomized and quantumquery complexities for local search on G are Ω (√N/dlogN) and (4√N / √dlogN),respectively.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"33 1","pages":"385-401"},"PeriodicalIF":1.0,"publicationDate":"2008-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88695068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We address the problem of generation and detection of the four mutually unbiased biphoton polarization-qutrit bases by linear optics. First, the generation of the bases is studied. Our numeric resu...
{"title":"Generation and detection of photonic qutrit states by linear optics","authors":"ChenYuntian, BjorkGunnar","doi":"10.5555/2011772.2011774","DOIUrl":"https://doi.org/10.5555/2011772.2011774","url":null,"abstract":"We address the problem of generation and detection of the four mutually unbiased biphoton polarization-qutrit bases by linear optics. First, the generation of the bases is studied. Our numeric resu...","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"113 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2008-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71125755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove new upper bounds on the tolerable level of noise in a quantum circuit. Weconsider circuits consisting of unitary k-qubit gates each of whose input wires is subject todepolarizing noise of strength p, as well as arbitrary one-qubit gates that are essentiallynoise-free. We assume that the output of the circuit is the result of measuring somedesignated qubit in the final state. Our main result is that for p > 1 - Θ(1/√k), theoutput of any such circuit of large enough depth is essentially independent of its input,thereby making the circuit useless. For the important special case of k = 2, our bound isp > 35.7%. Moreover, if the only allowed gate on more than one qubit is the two-qubitCNOT gate, then our bound becomes 29.3%. These bounds on p are numerically betterthan previous bounds, yet are incomparable because of the somewhat different circuitmodel that we are using. Our main technique is the use of a Pauli basis decomposition,in which the effects of depolarizing noise are very easy to describe.
{"title":"Upper bounds on the noise threshold for fault-tolerant quantum computing","authors":"J. Kempe, O. Regev, Falk Unger, R. D. Wolf","doi":"10.26421/QIC10.5-6-1","DOIUrl":"https://doi.org/10.26421/QIC10.5-6-1","url":null,"abstract":"We prove new upper bounds on the tolerable level of noise in a quantum circuit. Weconsider circuits consisting of unitary k-qubit gates each of whose input wires is subject todepolarizing noise of strength p, as well as arbitrary one-qubit gates that are essentiallynoise-free. We assume that the output of the circuit is the result of measuring somedesignated qubit in the final state. Our main result is that for p > 1 - Θ(1/√k), theoutput of any such circuit of large enough depth is essentially independent of its input,thereby making the circuit useless. For the important special case of k = 2, our bound isp > 35.7%. Moreover, if the only allowed gate on more than one qubit is the two-qubitCNOT gate, then our bound becomes 29.3%. These bounds on p are numerically betterthan previous bounds, yet are incomparable because of the somewhat different circuitmodel that we are using. Our main technique is the use of a Pauli basis decomposition,in which the effects of depolarizing noise are very easy to describe.","PeriodicalId":54524,"journal":{"name":"Quantum Information & Computation","volume":"45 1","pages":"845-856"},"PeriodicalIF":1.0,"publicationDate":"2008-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76057405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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