Compression and R-wave detection of ECG/VCG data

Application of information theory to eliminate redundant part of electrocardiogram or vectorcardiogram is described. Operation of medical equipment to obtain three dimensional study of patient is discussed. Use of fast Fourier transform to accomplish data compression is explained

When only two thirds of the entanglement can be distilled

We provide an example of distillable bipartite mixed state such that, even in the asymptotic limit, more pure-state entanglement is required to create it than can be distilled from it. Thus, we show that the irreversibility in the processes of formation and distillation of bipartite states, recently proved in [G. Vidal, J.I. Cirac, Phys. Rev. Lett. 86, (2001) 5803-5806], is not limited to bound-entangled states.Comment: 4 pages, revtex, 1 figur

A method of enciphering quantum states

In this paper, we propose a method of enciphering quantum states of two-state systems (qubits) for sending them in secrecy without entangled qubits shared by two legitimate users (Alice and Bob). This method has the following two properties. First, even if an eavesdropper (Eve) steals qubits, she can extract information from them with certain probability at most. Second, Alice and Bob can confirm that the qubits are transmitted between them correctly by measuring a signature. If Eve measures m qubits one by one from n enciphered qubits and sends alternative ones (the Intercept/Resend attack), a probability that Alice and Bob do not notice Eve's action is equal to (3/4)^m or less. Passwords for decryption and the signature are given by classical binary strings and they are disclosed through a public channel. Enciphering classical information by this method is equivalent to the one-time pad method with distributing a classical key (random binary string) by the BB84 protocol. If Eve takes away qubits, Alice and Bob lose the original quantum information. If we apply our method to a state in iteration, Eve's success probability decreases exponentially. We cannot examine security against the case that Eve makes an attack with using entanglement. This remains to be solved in the future.Comment: 21 pages, Latex2e, 10 epsf figures. v2: 22 pages, added two references, several clarifying sentences are added in Sec. 5, typos corrected, a new proof is provided in Appendix A and it is shorter than the old one. v3: 23 pages, one section is adde

Activating bound entanglement in multi-particle systems

We analyze the existence of activable bound entangled states in multi-particle systems. We first give a series of examples which illustrate some different ways in which bound entangled states can be activated by letting some of the parties to share maximally entangled states. Then, we derive necessary conditions for a state to be distillable as well as to be activable. These conditions turn out to be also sufficient for a certain family of multi-qubit states. We use these results to explicitely to construct states displaying novel properties related to bound entanglement and its activation.Comment: 8 pages, 3 figure

Factoring in a Dissipative Quantum Computer

We describe an array of quantum gates implementing Shor's algorithm for prime factorization in a quantum computer. The array includes a circuit for modular exponentiation with several subcomponents (such as controlled multipliers, adders, etc) which are described in terms of elementary Toffoli gates. We present a simple analysis of the impact of losses and decoherence on the performance of this quantum factoring circuit. For that purpose, we simulate a quantum computer which is running the program to factor N = 15 while interacting with a dissipative environment. As a consequence of this interaction randomly selected qubits may spontaneously decay. Using the results of our numerical simulations we analyze the efficiency of some simple error correction techniques.Comment: plain tex, 18 pages, 8 postscript figure

Helicoidal surfaces with constant anisotropic mean curvature

We study surfaces with constant anisotropic mean curvature which are invariant under a helicoidal motion. For functionals with axially symmetric Wulff shapes, we generalize the recently developed twizzler representation of Perdomo to the anisotropic case and show how all helicoidal constant anisotropic mean curvature surfaces can be obtained by quadratures

Irreversibility in asymptotic manipulations of entanglement

We show that the process of entanglement distillation is irreversible by showing that the entanglement cost of a bound entangled state is finite. Such irreversibility remains even if extra pure entanglement is loaned to assist the distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states under pure entanglement catalytic LOCC adde

A Comparison of Quantum Oracles

A standard quantum oracle $S_f$ for a general function $f: Z_N \to Z_N$ is defined to act on two input states and return two outputs, with inputs $\ket{i}$ and $\ket{j}$ ($i,j \in Z_N$) returning outputs $\ket{i}$ and $\ket{j \oplus f(i)}$. However, if $f$ is known to be a one-to-one function, a simpler oracle, $M_f$, which returns $\ket{f(i)}$ given $\ket{i}$, can also be defined. We consider the relative strengths of these oracles. We define a simple promise problem which minimal quantum oracles can solve exponentially faster than classical oracles, via an algorithm which cannot be naively adapted to standard quantum oracles. We show that $S_f$ can be constructed by invoking $M_f$ and $(M_f)^{-1}$ once each, while $\Theta(\sqrt{N})$ invocations of $S_f$ and/or $(S_f)^{-1}$ are required to construct $M_f$.Comment: 4 pages, 1 figure; Final version, with an extended discussion of oracle inverses. To appear in Phys Rev

Remote State Preparation

Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown quantum state. Remote state preparation (RSP) has the same goal, but the sender knows classically what state is to be transmitted. We show that the asymptotic classical communication cost of RSP is one bit per qubit - half that of teleportation - and becomes even less when transmitting part of a known entangled state. We explore the tradeoff between entanglement and classical communication required for RSP, and discuss RSP capacities of general quantum channels.Comment: 4 pages including 1 epsf figure; v3 has an additional author and discusses relation to work of Devetak and Berger (quant-ph/0102123); v4 improves low-entanglement protocols without back communication to perform as well as low-entanglement protocols with back communication; v5 (journal version) has a few small change