Detection of Macroscopic Entanglement by Correlation of Local Observables

We propose a correlation of local observables on many sites in macroscopic quantum systems. By measuring the correlation one can detect, if any, superposition of macroscopically distinct states, which we call macroscopic entanglement, in arbitrary quantum states that are (effectively) homogeneous. Using this property, we also propose an index of macroscopic entanglement.Comment: Although the index q was proposed for mixed states, it is also applicable to pure states, on which we fix minor bugs (that will be reported in PRL as erratum). The conclusions of the paper remain unchanged. (4 pages, no figures.

Macroscopic entanglement of many-magnon states

We study macroscopic entanglement of various pure states of a one-dimensional N-spin system with N>>1. Here, a quantum state is said to be macroscopically entangled if it is a superposition of macroscopically distinct states. To judge whether such superposition is hidden in a general state, we use an essentially unique index p: A pure state is macroscopically entangled if p=2, whereas it may be entangled but not macroscopically if p<2. This index is directly related to the stability of the state. We calculate the index p for various states in which magnons are excited with various densities and wavenumbers. We find macroscopically entangled states (p=2) as well as states with p=1. The former states are unstable in the sense that they are unstable against some local measurements. On the other hand, the latter states are stable in the senses that they are stable against local measurements and that their decoherence rates never exceed O(N) in any weak classical noises. For comparison, we also calculate the von Neumann entropy S(N) of a subsystem composed of N/2 spins as a measure of bipartite entanglement. We find that S(N) of some states with p=1 is of the same order of magnitude as the maximum value N/2. On the other hand, S(N) of the macroscopically entangled states with p=2 is as small as O(log N)<< N/2. Therefore, larger S(N) does not mean more instability. We also point out that these results are analogous to those for interacting many bosons. Furthermore, the origin of the huge entanglement, as measured either by p or S(N), is discussed to be due to the spatial propagation of magnons.Comment: 30 pages, 5 figures. The manuscript has been shortened and typos have been fixed. Data points of figures have been made larger in order to make them clearly visibl

Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm

We analyze quantum computers which perform Shor's factoring algorithm, paying attention to asymptotic properties as the number L of qubits is increased. Using numerical simulations and a general theory of the stabilities of many-body quantum states, we show the following: Anomalously fluctuating states (AFSs), which have anomalously large fluctuations of additive operators, appear in various stages of the computation. For large L, they decohere at anomalously great rates by weak noises that simulate noises in real systems. Decoherence of some of the AFSs is fatal to the results of the computation, whereas decoherence of some of the other AFSs does not have strong influence on the results of the computation. When such a crucial AFS decoheres, the probability of getting the correct computational result is reduced approximately proportional to L^2. The reduction thus becomes anomalously large with increasing L, even when the coupling constant to the noise is rather small. Therefore, quantum computations should be improved in such a way that all AFSs appearing in the algorithms do not decohere at such great rates in the existing noises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is the SAME as version 2; only errors during the Web-upload were fixed. Version 4 is the publised version, in which several typos are fixed and the reference list is update

Visualization of superposition of macroscopically distinct states

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes non-negative (hence becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.Comment: 12pages, 21figure

Energies and collapse times of symmetric and symmetry-breaking states of finite systems with a U(1) symmetry

We study quantum systems of volume V, which will exhibit the breaking of a U(1) symmetry in the limit of V \to \infty, when V is large but finite. We estimate the energy difference between the `symmetric ground state' (SGS), which is the lowest-energy state that does not breaks the symmetry, and a `pure phase vacuum' (PPV), which approaches a symmetry-breaking vacuum as V \to \infty. Under some natural postulates on the energy of the SGS, it is shown that PPVs always have a higher energy than the SGS, and we derive a lower bound of the excess energy. We argue that the lower bound is O(V^0), which becomes much larger than the excitation energies of low-lying excited states for a large V. We also discuss the collapse time of PPVs for interacting many bosons. It is shown that the wave function collapses in a microscopic time scale, because PPVs are not energy eigenstates. We show, however, that for PPVs the expectation value of any observable, which is a finite polynomial of boson operators and their derivatives, does not collapse for a macroscopic time scale. In this sense, the collapse time of PPVs is macroscopically long.Comment: In the revised manuscript, Eq. (22), Ref. [8], and Notes [13], [15] and [17] have been adde

Characterization of designed, synthetically accessible bryostatin analog HIV latency reversing agents.

HIV latency in resting CD4+ T cell represents a key barrier preventing cure of the infection with antiretroviral drugs alone. Latency reversing agents (LRAs) can activate HIV expression in latently infected cells, potentially leading to their elimination through virus-mediated cytopathic effects, host immune responses, and/or therapeutic strategies targeting cells actively expressing virus. We have recently described several structurally simplified analogs of the PKC modulator LRA bryostatin (termed bryologs) designed to improve synthetic accessibility, tolerability in vivo, and efficacy in inducing HIV latency reversal. Here we report the comparative performance of lead bryologs, including their effects in reducing cell surface expression of HIV entry receptors, inducing proinflammatory cytokines, inhibiting short-term HIV replication, and synergizing with histone deacetylase inhibitors to reverse HIV latency. These data provide unique insights into structure-function relationships between A- and B-ring bryolog modifications and activities in primary cells, and suggest that bryologs represent promising leads for preclinical advancement

Time evolution of condensed state of interacting bosons with reduced number fluctuation in a leaky box

We study the time evolution of the Bose-Einstein condensate of interacting bosons confined in a leaky box, when its number fluctuation is initially (t=0) suppressed. We take account of quantum fluctuations of all modes, including k = 0. We identify a ``natural coordinate'' b_0 of the interacting bosons, by which many physical properties can be simply described. Using b_0, we successfully define the cosine and sine operators for interacting many bosons. The wavefunction, which we call the ``number state of interacting bosons'' (NSIB), of the ground state that has a definite number N of interacting bosons can be represented simply as a number state of b_0. We evaluate the time evolution of the reduced density operator \rho(t) of the bosons in the box with a finite leakage flux J, in the early time stage for which Jt << N. It is shown that \rho(t) evolves from a single NSIB at t = 0, into a classical mixture of NSIBs of various values of N at t > 0. We define a new state called the ``number-phase squeezed state of interacting bosons'' (NPIB). It is shown that \rho(t) for t>0 can be rewritten as the phase-randomized mixture (PRM) of NPIBs. It is also shown that the off-diagonal long-range order (ODLRO) and the order parameter defined by it do not distinguish the NSIB and NPIB. On the other hand, the other order parameter \Psi, defined as the expectation value of the boson operator, has different values among these states. For each element of the PRM of NPIBs, we show that \Psi evolves from zero to a finite value very quickly. Namely, after the leakage of only two or three bosons, each element acquires a full, stable and definite (non-fluctuating) value of \Psi.Comment: 25 pages including 3 figures. To appear in Phys. Rev. A (1999). The title is changed to stress the time evolution. Sections II, III and IV of the previous manuscript have been combined into one section. The introduction and summary of the previous manuscript have been combined into the Introduction and Summary. The names and abbreviations of quantum states are changed to stress that they are for interacting many bosons. More references are cite

Parity Violation in Neutron Resonances in 107,109Ag

Parity nonconservation (PNC) was studied in p-wave resonances in Ag by measuring the helicity dependence of the neutron total cross section. Transmission measurements on natural Ag were performed in the energy range 32 to 422 eV with the time-of-flight method at the Manuel Lujan Neutron Scattering Center at Los Alamos National Laboratory. A total of 15 p-wave neutron resonances were studied in 107Ag and ninep-wave resonances in 109Ag. Statistically significant asymmetries were observed for eight resonances in 107Ag and for four resonances in109Ag. An analysis treating the PNC matrix elements as random variables yields a weak spreading width of Γw=(2.67-1.21+2.65)×10-7 eV for107Ag and Γw=(1.30-0.74+2.49)×10-7 eV for 109Ag

Parity Violation in Neutron Resonances in 115In

Parity nonconservation (PNC) was studied in p-wave resonances in indium by measuring the helicity dependence of the neutron total cross section in the neutron energy range 6.0–316 eV with the time-of-flight method at LANSCE. A total of 36 p-wave neutron resonances were studied in 115In, and statistically significant asymmetries were observed for nine cases. An analysis treating the PNC matrix elements as random variables yields a weak matrix element of M=(0.67-0.12+0.16) meV and a weak spreading width of Γw=(1.30-0.43+0.76)×10-7 eV