arXiv subjects
Publications and source records attributed to Dafa Li.
The no-cloning theorem, the no-deleting theorem, the no-hiding theorem, the no-flip theorem, and the no-broadcasting play a crucial role in quantum mechanics and quantum information. In this paper, we propose the no-conjugating theorem which states that it is impossible to conjugate an unknown arbitrary quantum state via a universal physical device or linear/unitary operation.
In [Phy. Rev. Lett., 98, 260501 (2007)] and previous papers, the W-like states were used in many quantum communication schemes, distillation, teleportation and superdense coding. So far, no one has compared the W-like states with the W state. We investigate the properties of three W-like states named as $|\vartheta ^{\prime }\rangle $, $|\eta ^{\prime }\rangle $ and $|\xi ^{\prime }\rangle $. We point out that $|\vartheta ^{\prime }\rangle $ (resp. $|\eta ^{\prime }\rangle $ and $|\xi ^{\prime }\rangle $) has the maximal von Neumann entanglement entropy (vNEE) $S(\rho _{A})=\ln 2$ (resp. $S(\rho _{B})=\ln 2$ and $S(\rho _{C})=\ln 2$) and the maximal tangle $\tau _{A(BC)}=1$ (resp. $\tau _{B(AC)}=1$ and $\tau _{C(AB)}=1$) while the W state does not. We also indicate that if some one of three qubits is traced out, then the remaining two qubits of $|\vartheta ^{\prime }\rangle $ (resp. $|\eta ^{\prime }\rangle $ and $|\xi ^{\prime }\rangle $) are more entangled than the two qubits of the W state by several entanglement measures. It means that the three W-like states have higher robustness against some particle loss than the W state. We show that $|\vartheta ^{\prime }\rangle $, $|\eta ^{\prime }\rangle $ and $|\xi ^{\prime }\rangle $ can be suitable for perfect teleportation and superdense coding but the W state cannot.
Pati and Braunstein defined a deleting machine and showed the impossibility of deleting one of two identical copies of an unknown quantum state. So far, no one has defined two non-identical copies of a quantum state, of course no one has discussed the impossibility of deleting one of two non-identical copies of an unknown quantum state. In this paper, we define $u|{\psi}>$ and $U|{\psi}>$, where $u$ and $U$ are any unitary operators, as two unitary copies of a quantum state $|{\psi}>$, and show that it is impossible to delete one of two unitary copies of an unknown state.
The settling of dust particles plays a critical role in the growth and dynamics of dust grains. We performed a detailed modeling of the ALMA continuum substructures for six highly inclined protoplanetary discs using radiative transfer simulations, to constrain the vertical height of millimetre dust grains and the settling strength. Our modeling results are a very thin millimetre dust disc in T Cha ($\text{h}_{\text{dust}}<$ 0.1 au throughout the disc), a vertically extended dust disc in DoAr 25 ($\text{h}_{\text{dust}}$ of $\sim$ 4.7 au at 140 au) and tentatively a thin disc in MY Lup ($\text{h}_{\text{dust}}<$ 0.5 au at 70 au). From lower resolution observations we found a very thin disc for PDS 111 ($\text{h}_{\text{dust}}<$ 0.1 au throughout the disc) and a more vertically extended millimetre dust disc in V409 Tau ($\text{h}_{\text{dust}}$ of $\sim$ 1.3 au at 35 au). We could not measure the vertical height in the asymmetric disc of RY Lup. We also found that the input dust opacities are a source of degeneracy in our models. Our tentative results, assuming the Ricci dust opacities, point to a diverse settling strength in our sample and possible radial variations. We also compared the models that best fit the ALMA data with the SPHERE data to test if they can reproduce the vertical distribution of small dust grains. This comparison suggests that models that reproduce the dust density distribution in the midplane cannot reproduce the distribution of small dust grains in the upper layers, reinforcing the need for more complex models.
It is known that the classical information like strings of bits can be copied. In 1982, Wootters and Zurek proposed the quantum no-cloning principle. No-cloning principle says that it is impossible to make an identical copy of an arbitrary unknown quantum pure state by using unitary evolution. In this paper, we call U $|\psi>$, where U is any unitary operator, a U-copy of the state $|{\psi}>$ and show it is impossible to make a U-copy of an arbitrary unknown quantum pure state by using unitary evolution.
It is known that two local unitaries (LU) equivalent states possess the same amount of entanglement and can be used to perform the same tasks in quantum information theory (QIT). For a protocol for a task in QIT, we call a protocol LU invariant if two LU-equivalent states are either both suitable for the protocol or neither is. So far, no one has discussed whether a protocol for a task in QIT is LU invariant. In [Phys. Rev. A, 74, 062320 (2006)], Agrawal and Pati proposed the perfect teleportation protocol (PTP) and the protocol for superdense coding to transmit 2-bit classical information by sending one qubit (PSDC-2) and 3-bit classical information by sending two qubits (PSDC-3). In this paper, we show that PTP and PSDC-2 are LU invariant. That is, two LU equivalent states are suitable for PTP and PSDC-2 or neither of them is. We show that PSDC-3 is not LU invariant. We also indicate that the teleportation proposed in Nielsen is not LU invariant. We give a necessary and sufficient condition for a state to be suitable for PTP, PSDC-2, and PSDC-3, respectively. Via the LU invariance of PTP and PSDC-2, we prove that a state is suitable for PTP and PSDC-2 if and only if it has 1 ebit of shared entanglement, respectively and find all genuine entangled states and separable states which are suitable for PTP and PSDC-2, respectively. So far, no one has indicated that PTP and PSDC-2 do not require genuine entanglement. Agrawal and Pati suggested to study if there are subclasses of W SLOCC class which are suitable for PSDC-3. So far, it still remains an unsolved question. We show that any state of the SLOCC class W is not suitable for PSDC-3.
In [Science 340, 1205, 7 June (2013)], via polytopes Michael Walter et al. proposed a sufficient condition detecting the genuinely entangled pure states. In this paper, assume that a state with six non-zero coefficients is not a trivially separable state. Then the state is separable if and only if its six basis states consist of the three partially complementary pairs and the corresponding coefficient matrix has proportional rows. The contrapositive of this result reads that the state is genuinely entangled if and only if its six basis states do not consist of the three partially complementary pairs or though the six basis states consist of the three partially complementary pairs, the corresponding coefficient matrix does not have proportional rows. We propose four corresponding coefficient 2 by 3 matrices and show that if the four coefficient matrices don't have proportional rows, then the state is genuinely entangled. It is trivial to know if two rows of a 2 by 3 coefficient matrix are proportional. The difference from the previous articles is that the structure of the basis states is used to detect entanglement in this paper. One can see that Osterloh and Siewert's states of five and six qubits are genuinely entangled because two rows for any one of the four corresponding coefficient 2 by 3 matrices are not proportional. These states were distinguished as the maximal entangled states by the complicated filters before. Keywords: entanglement, separability, entangled states, separable states, qubits.
In this paper, we propose the average determinant of reduced density matrices for each qubit as a global entanglement measure. By means of the properties of reduced density matrices, we can investigate the present measure. We propose a decomposition law for the present measure, demonstrate that the present measure just measures the average mixedness for each qubit and the average 1-tangle, and indicate that for n-qubit W state and Dicke states, the average mixedness for each qubit and 1-tangle almost vanish for the large number of qubits. We also point out that for two qubits, the present measure is just the square of the concurrence while for three qubits, the present measure is the sum of the 3-tangle and the twice the average 2-tangle.
In [Phys. Rev. D 54, 6293 (1996)], the black hole entropy was derived by solving the matrix equation obtained from the stabilization equations for the solution of frozen moduli. In this paper, by directly solving the stabilization equations for the solution of frozen moduli without using the matrix equation, we find linear relations between any two of the three complex moduli at the black hole horizon. So far, no one discusses the linear relations. Via the linear relations, we derive the unique solution of frozen moduli and reduce the stabilization equations in three different ways. For example, the eight stabilization equations in [Phys. Rev. D 54, 6293 (1996)] can be replaced equivalently with three equations: the solution of moduli z1 and two linear relations, which are much simpler and more intuitive.
Dust grains in protoplanetary disks are the building blocks of planets. Investigating the dust composition and size, and their variation over time, is crucial for understanding the planet formation process. The PDS 70 disk is so far the only protoplanetary disk with concrete evidence for the presence of young planets. Mid-infrared spectra were obtained for PDS 70 by the Infrared Spectrograph (IRS) on the Spitzer Space Telescope (SST) and the Mid-Infrared Instrument (MIRI) on the James Webb Space Telescope (JWST) in 2007 and 2022, respectively. In this work, we investigate the dust mineralogy through a detailed decomposition of the observed mid-infrared spectra. The results show that both the dust size and crystallinity increased by a factor of about two during the two epochs of observation, indicating evident dust processing in the terrestrial planet-forming region of the PDS 70 disk. The dust size (~0.8 micron) and crystallinity (~6%) in the PDS 70 disk are similar to those of other disks, which implies that the two nascent planets, PDS 70b and PDS 70c located at radial distances of ~22AU and ~34AU, do not have a significant impact on the dust processing in the inner disk. The flux densities at wavelengths longer than ~16 micron measured by JWST/MIRI are only ~60% of those obtained by Spitzer/IRS. Based on self-consistent radiative transfer modeling, we found that such a strong variability in mid-infrared fluxes can be produced by adjustments to the dust density distribution and structure of the inner disk probably induced by planet-disk interaction.
Investigating the dust grain size and its dependence on substructures in protoplanetary disks is a crucial step in understanding the initial process of planet formation. Spectral indices derived from millimeter observations are used as a common probe for grain size. Converting observed spectral indices into grain sizes is a complex task that involves solving the radiative transfer equation, taking into account the disk structure and dust properties. In this work, we ran reference radiative transfer models with known disk properties, and generated four synthetic images at wavelengths of 0.8, 1.3, 3, and 7.8 mm, representing high-resolution continuum observations. Rings and gaps were considered in the setup. We fit the synthetic images using the analytic solution of the radiative transfer equation to investigate the circumstances under which the input grain sizes can be recovered. The results show that fitting images at only two wavelengths is not sufficient to retrieve the grain size. Fitting three images improves the retrieval of grain size, but the dust surface density is still not well recovered. When taking all of the four images into account, degeneracies between different parameters are highly reduced, and consequently the best-fit grain sizes are consistent with the reference setup at almost all radii. We find that the inclination angle has a significant impact on the fitting results. For disks with low inclinations, the analytic approach works quite well. However, when the disk is tilted above about 60 degree, neither the grain size nor the dust surface density can be constrained, as the inclination effect will smooth out all substructures in the radial intensity profile of the disk.
In \cite{Linde}, Kallosh and Linde discussed the SLOCC classification of black holes. However, the criteria for the SLOCC classification of black holes have not been given. In addition, the LU classification of black holes has not been studied in the past. In this paper we will consider both SLOCC and LU classification of the STU black holes with four integer electric charges $q_{i} $ and four integer magnetic charges $p^{i}$, $i=0,1,2,3$. Two STU black holes with eight charges are considered SLOCC (LU) equivalent if and only if their corresponding states of three qubits are SLOCC (LU) equivalent. Under this definition, we give criteria for the classification of the eight-charge STU black holes under SLOCC and under LU, respectively. We will study the classification of the black holes via the classification of SLOCC and LU entanglement of three qubits. We then identify a set of black holes corresponding to the state W of three qubits, which is of interest since it has the maximal average von Neumann entropy of entanglement. Via von Neumann entanglement entropy, we partition the STU black holes corresponding to pure states of GHZ SLOCC class into five families under LU.
In [M. Walter et al., Science 340, 1205, 7 June (2013)], via polytopes they gave a sufficient condition for genuinely entangled pure states and discussed SLOCC classification. In this paper, we study entanglement classification of pure states of $n$ qubits via the basis state matrix (BSM) whose rows are the basis states. We propose a canonical form of BSM obtained by exchanging columns (i.e. permutation of qubits) and rows of BSM and then a necessary and sufficient condition for a genuinely entangled state of n qubits via a canonical form of BSM. Thus, for any $n$ qubits, the genuinely entangled states can be partitioned into two families. One family includes all states whose BSM cannot be transformed into the canonical form. The states with the BSM are always genuinely entangled no matter what the non-zero coefficients are. GHZ and W states belong to the family. The other includes all states whose BSM can be transformed into the canonical form, but for any canonical form of BSM, some two columns or rows of the corresponding coefficient matrix are not proportional. The cluster state belongs to the family.
Based on an ordering with directed lines and using constructions instead of existential axioms, von Plato proposed a constructive axiomatization of the ordered affine geometry. There are 22 axioms for the ordered affine geometry, of which the axiom I.7 is about the convergence of three lines (ignoring their directions). In this paper, we indicate that the axiom I.7 includes much redundancy, and demonstrate that the complicated axiom I.7 can be replaced equivalently with a simpler and more intuitive new axiom via a theorem prover.
The black-hole--qubit correspondence has been proven to be ``useful for obtaining additional insight into one of the string black hole theory and quantum information theory by exploiting approaches of the other"[Phys. Rev. D 82, 026003 (2010)]. Though different classes of stringy black holes can be related to the well-known stochastic local operations and classical communication (SLOCC) entanglement classes of pure states, the string theory requires a more detailed classification than the SLOCC classification of three qubits. In this paper, we derive the entanglement family of three qubits under local unitary operations (LU), and use the black-hole--qubit correspondence to classify \textquotedblleft large\textquotedblright\ black holes into seven inequivalent families. In particular, we show that two black holes with 4 non-vanishing charges ($q_{0}$, $p^{1}$, $p^{2}$, and $p^{3}$) are LU equivalent if their difference is only in the signs of charges. Thus, the classification of black holes is independent of the signs of charges and is only related to the ratio of the absolute values of charges. This observation simplifies the classification task, as one would only need to consider either the classification of non-BPS black holes or the classification of BPS black holes, but not both. Moreover, through the LU classification, the physical basis for this black-hole--qubit correspondence can be observed, and a relation between the black-hole entropy and the von Neumann entanglement entropy is revealed. Therefore, the LU classification offers a more straightforward physical connection than the SLOCC classification. Based on the LU classification, we further study the properties of von Neumann entanglement entropy for each of the seven families, and find the black holes with the maximal von Neumann entanglement entropy.
How do dust grains in protoplanetary disks overcome rapid radial drift and grow from micron size particles to planets is not well understood. The key is to search for evidence of dust accumulation and growth as a function of radius in the disk. We investigate the radial profile of grain size in the DS Tau disk by fitting multi-band ALMA observations with self-consistent radiative transfer models. The best-fit grain sizes range from centimeters in the inner disk down to 30 micron in the outer regions. Such an inside-out decreasing tendency is consistent with theories of dust evolution. Based on the best-fit model, we find that dust of 2 Jupiter masses has been depleted within the gap. By taking the gas-to-dust mass ratio into account, the lost mass is enough to form the 3.5 Jupiter mass planet inferred by literature hydrodynamic simulations. Moreover, our modeling also indicates that at the interface region between the gap and the ring, the grain size profile shows a discontinuity, with its amplitude dependent on the dust model adopted in the radiative transfer analysis. Future multi-wavelength observations at higher angular resolutions are required to better constrain the grain size and its variation in the vicinity of disk substructures.
The total amount of dust grains in protoplanetary disks is one of the key properties that characterize the potential for planet formation. With (sub-)millimeter flux measurements, literature studies usually derive the dust mass using an analytic form under the assumption of optically thin emission, which may lead to substantial underestimation. In this work, we conduct a parameter study with the goal of investigating the effects of disk structure and dust properties on the underestimation through self-consistent radiative transfer models. Different dust models, scattering modes and approaches for dust settling are considered and compared. The influences of disk substructures, such as rings and crescents, on the mass derivation are investigated as well. The results indicate that the traditional analytic method can underestimate the mass by a factor of a few to hundreds, depending on the optical depth along the line of sight set mainly by the true dust mass, disk size and inclination. As an application, we perform a detailed radiative transfer modeling of the spectral energy distribution of DoAr 33, one of the observed DSHARP disks. When the DSHARP dust opacities are adopted, the most probable dust mass returned from the Bayesian analysis is roughly 7 times higher than the value given by the analytic calculation. Our study demonstrates that estimating disk dust masses from radiative transfer modeling is one solution for alleviating the problem of insufficient mass for planet formation raised in the ALMA era.
Based on an ordering with directed lines and using constructions instead of existential axioms, von Plato proposed a constructive axiomatization of ordered affine geometry. There are 22 axioms for the ordered affine geometry, of which the axiom I.7 is about the convergence of three lines (ignoring their directions). In this paper, we indicate that the axiom I.7 includes much redundancy, and demonstrate that the complicated axiom I.7 can be replaced with a simpler and more intuitive new axiom (called ODO) which describes the properties of oppositely and equally directed lines. We also investigate a possibility to replace the axiom I.6 with ODO.