Quantum Communication Protocol Employing Weak Measurements

We propose a communication protocol exploiting correlations between two events with a definite time-ordering: a) the outcome of a {\em weak measurement} on a spin, and b) the outcome of a subsequent ordinary measurement on the spin. In our protocol, Alice, first generates a "code" by performing weak measurements on a sample of N spins. The sample is sent to Bob, who later performs a post-selection by measuring the spin along either of two certain directions. The results of the post-selection define the "key', which he then broadcasts publicly. Using both her previously generated code and this key, Alice is able to infer the {\em direction} chosen by Bob in the post-selection. Alternatively, if Alice broadcasts publicly her code, Bob is able to infer from the code and the key the direction chosen by Alice for her weak measurement. Two possible experimental realizations of the protocols are briefly mentioned.Comment: 5 pages, Revtex, 1 figure. A second protocol is added, where by a similar set of weak measurement Alice can send, instead of receiving, a message to Bob. The security question for the latter protocol is discusse

Teleportation of Quantum States

Bennett et al. (PRL 70, 1859 (1993)) have shown how to transfer ("teleport") an unknown spin quantum state by using prearranged correlated quantum systems and transmission of classical information. I will show how their results can be obtained in the framework of nonlocal measurements proposed by Aharonov and Albert I will generalize the latter to the teleportation of a quantum state of a system with continuous variables.Comment: 5 page

Security improvement of using modified coherent state for quantum cryptography

Weak coherent states as a photon source for quantum cryptography have limit in secure data rate and transmission distance because of the presence of multi-photon events and loss in transmission line. Two-photon events in a coherent state can be taken out by a two-photon interference scheme. We investigate the security issue of utilizing this modified coherent state in quantum cryptography. A 4 dB improvement in secure data rate or a nearly two-fold increase in transmission distance over the coherent state are found. With a recently proposed and improved encoding strategy, further improvement is possible.Comment: 5 pages, 2 figures, to appear in Physical Review

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

Weak randomness completely trounces the security of QKD

In usual security proofs of quantum protocols the adversary (Eve) is expected to have full control over any quantum communication between any communicating parties (Alice and Bob). Eve is also expected to have full access to an authenticated classical channel between Alice and Bob. Unconditional security against any attack by Eve can be proved even in the realistic setting of device and channel imperfection. In this Letter we show that the security of QKD protocols is ruined if one allows Eve to possess a very limited access to the random sources used by Alice. Such knowledge should always be expected in realistic experimental conditions via different side channels

Neutrino mass matrix suppression by Abelian charges with see-saw mechanism

We have investigated a neutrino mass matrix model without supersymmetry including three see-saw right-handed neutrinos around order $10^{12}$ GeV masses, aiming at a picture with all small numbers explained as being due to approximately conserved gauge charges. The prediction of the solar neutrino mixing angle is given by $\sin^22\theta_{\odot}= 3 {+3\atop -2}\times10^{-2}$; in fact, the solar mixing angle is, apart from detailed order unity corrections, equal to the Cabibbo angle. Furthermore the ratio of the solar neutrino mass square difference to that for the atmospheric neutrino oscillation is predicted to $6 {+11\atop -4}\times10^{-4}$ and is given by the same Cabibbo angle related parameter $\xi$ as $6 \xi^4$.Comment: 20 pages, 1 figure, uses Latex2

“Propositions in Theatre: Theatrical Utterances as Events”

Using William Shakespeare’s Hamlet and the play-within-the play, The Murder of Gonzago, as a case study, this essay argues that theatrical utterances constitute a special case of language usage not previously elucidated: the utterance of a statement with propositional content in theatre functions as an event. In short, the propositional content of a particular p (e.g. p1, p2, p3 …), whether or not it is true, is only understood—and understood to be true—if p1 is uttered in a particular time, place, and situation (i.e. during a theatrical event); otherwise, the propositional content in those theatrical utterances can either be false or contingently true

Measuring Energy, Estimating Hamiltonians, and the Time-Energy Uncertainty Relation

Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine what is the Hamiltonian. We show that in general this requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown Hamiltonian must be estimated. We then apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can in principle be measured in an arbitrarily short time. On the other hand we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time $\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$ where $\Delta E$ is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.Comment: 12pages, revised version with small correction

Polarization correlated photons from a positively charged quantum dot

Polarized cross-correlation spectroscopy on a quantum dot charged with a single hole shows the sequential emission of photons with common circular polarization. This effect is visible without magnetic field, but becomes more pronounced as the field along the quantization axis is increased. We interpret the data in terms of electron dephasing in the X+ state caused by the Overhauser field of nuclei in the dot. We predict the correlation timescale can be increased by accelerating the emission rate with cavity-QED