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Sep 20, 2013
09/13

by
Jon Yard

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The rates at which classical and quantum information can be simultaneously transmitted from two spatially separated senders to a single receiver over an arbitrary quantum channel are characterized. Two main results are proved in detail. The first describes the region of rates at which one sender can send classical information while the other sends quantum information. The second describes those rates at which both senders can send quantum information. For each of these situations, an example of...

Source: http://arxiv.org/abs/quant-ph/0506050v1

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Sep 20, 2013
09/13

by
David Poulin; Jon Yard

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We analyze a quantum mechanical gyroscope which is modeled as a large spin and used as a reference against which to measure the angular momenta of spin-1/2 particles. These measurements induce a back-action on the reference which is the central focus of our study. We begin by deriving explicit expressions for the quantum channel representing the back-action. Then, we analyze the dynamics incurred by the reference when it is used to sequentially measure particles drawn from a fixed ensemble. We...

Source: http://arxiv.org/abs/quant-ph/0612126v2

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Sep 21, 2013
09/13

by
Jon Yard; Igor Devetak

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Consider many instances of an arbitrary quadripartite pure state of four quantum systems ACBR. Alice holds the AC part of each state, Bob holds B, while R represents all other parties correlated with ACB. Alice is required to redistribute the C systems to Bob while asymptotically retaining the purity of the global states. We prove that this is possible using Q qubits of communication and E ebits of shared entanglement between Alice and Bob provided that Q < I(R;C|B)/2 and Q + E < H(C|B)....

Source: http://arxiv.org/abs/0706.2907v1

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Jun 27, 2018
06/18

by
Vadym Kliuchnikov; Jon Yard

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Exact synthesis is a tool used in algorithms for approximating an arbitrary qubit unitary with a sequence of quantum gates from some finite set. These approximation algorithms find asymptotically optimal approximations in probabilistic polynomial time, in some cases even finding the optimal solution in probabilistic polynomial time given access to an oracle for factoring integers. In this paper, we present a common mathematical structure underlying all results related to the exact synthesis of...

Topics: Quantum Physics, Computing Research Repository, Emerging Technologies

Source: http://arxiv.org/abs/1504.04350

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54

Sep 22, 2013
09/13

by
Pawel Wocjan; Jon Yard

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We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the braid group. We use these to provide new quantum algorithms for approximately evaluating a family of specializations of the HOMFLYPT two-variable polynomial of trace closures of braids. We also give algorithms for approximating the Jones polynomial...

Source: http://arxiv.org/abs/quant-ph/0603069v3

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60

Sep 20, 2013
09/13

by
Igor Devetak; Jon Yard

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With a statistical view towards information and noise, information theory derives ultimate limitations on information processing tasks. These limits are generally expressed in terms of entropic measures of information and correlations. Here we answer the quantum information-theoretic question: ``How correlated are two quantum systems from the perspective of a third?" by solving the following `quantum state redistribution' problem. Given an arbitrary quantum state of three systems, where...

Source: http://arxiv.org/abs/quant-ph/0612050v1

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Jul 22, 2013
07/13

by
Graeme Smith; Jon Yard

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Communication over a noisy quantum channel introduces errors in the transmission that must be corrected. A fundamental bound on quantum error correction is the quantum capacity, which quantifies the amount of quantum data that can be protected. We show theoretically that two quantum channels, each with a transmission capacity of zero, can have a nonzero capacity when used together. This unveils a rich structure in the theory of quantum communications, implying that the quantum capacity does not...

Source: http://arxiv.org/abs/0807.4935v2

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Sep 22, 2013
09/13

by
Jon Yard; Igor Devetak; Patrick Hayden

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We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region is comprised of the rates at which it is possible for one sender to send classical information, while the other sends quantum information. The second region consists of the rates at which each sender can send quantum information. For each region, we give an example of a channel for which the...

Source: http://arxiv.org/abs/quant-ph/0501045v3

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Sep 22, 2013
09/13

by
Jon Yard; Patrick Hayden; Igor Devetak

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We consider quantum channels with one sender and two receivers, used in several different ways for the simultaneous transmission of independent messages. We begin by extending the technique of superposition coding to quantum channels with a classical input to give a general achievable region. We also give outer bounds to the capacity regions for various special cases from the classical literature and prove that superposition coding is optimal for a class of channels. We then consider extensions...

Source: http://arxiv.org/abs/quant-ph/0603098v2

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Sep 21, 2013
09/13

by
Jon Yard; Igor Devetak; Patrick Hayden

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We consider quantum channels with two senders and one receiver. For an arbitrary such channel, we give multi-letter characterizations of two different two-dimensional capacity regions. The first region characterizes the rates at which it is possible for one sender to send classical information while the other sends quantum information. The second region gives the rates at which each sender can send quantum information. We give an example of a channel for which each region has a single-letter...

Source: http://arxiv.org/abs/cs/0508031v1

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Sep 18, 2013
09/13

by
Graeme Smith; John A. Smolin; Jon Yard

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As with classical information, error-correcting codes enable reliable transmission of quantum information through noisy or lossy channels. In contrast to the classical theory, imperfect quantum channels exhibit a strong kind of synergy: there exist pairs of discrete memoryless quantum channels, each of zero quantum capacity, which acquire positive quantum capacity when used together. Here we show that this "superactivation" phenomenon also occurs in the more realistic setting of...

Source: http://arxiv.org/abs/1102.4580v1

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Jun 28, 2018
06/18

by
Vadym Kliuchnikov; Alex Bocharov; Martin Roetteler; Jon Yard

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We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+$\pi/12$ [arXiv:1409.3552], running on average in time polynomial in...

Topics: Quantum Physics, Emerging Technologies, Computing Research Repository

Source: http://arxiv.org/abs/1510.03888

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46

Sep 22, 2013
09/13

by
Patrick Hayden; Michal Horodecki; Jon Yard; Andreas Winter

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We give a proof that the coherent information is an achievable rate for the transmission of quantum information through a noisy quantum channel. Our method is to select coding subspaces according to the unitarily invariant measure and then show that provided those subspaces are sufficiently small, any data contained within them will with high probability be decoupled from the noisy channel's environment.

Source: http://arxiv.org/abs/quant-ph/0702005v1

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Jun 29, 2018
06/18

by
Marcus Appleby; Steven Flammia; Gary McConnell; Jon Yard

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Let K be a real quadratic field. For certain K with sufficiently small discriminant we produce explicit unit generators for specific ray class fields of K using a numerical method that arose in the study of complete sets of equiangular lines in $\mathbb{C}^d$ (known in quantum information as symmetric informationally complete measurements or SICs). The construction in low dimensions suggests a general recipe for producing unit generators in infinite towers of ray class fields above arbitrary K...

Topics: Number Theory, Quantum Physics, Mathematics

Source: http://arxiv.org/abs/1604.06098

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Sep 21, 2013
09/13

by
Fernando G. S. L. Brandao; Matthias Christandl; Jon Yard

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We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it is eps-away from the set of the separable states in time exp(O(eps^-2 log |A| log |B|)), where |A| and |B| are the local dimensions, and the distance is measured with either the Euclidean norm, or with the so-called LOCC norm. The latter is an operationally...

Source: http://arxiv.org/abs/1011.2751v2

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Sep 19, 2013
09/13

by
Fernando G. S. L. Brandao; Matthias Christandl; Jon Yard

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Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the...

Source: http://arxiv.org/abs/1010.1750v5