Comment on "Entangled-Photon Imaging of a Pure Phase Object"
M. Bache, A. Gatti, E. Brambilla, D. Magatti, F. Ferri, L. A. Lugiato
备注：
Comment on A.F. Abouraddy, P.R. Stone, A.V. Sergienko, B.E.A. Saleh, and M.C. Teich, ``Entangled-Photon Imaging of a Pure Phase Object,'' Phys. Rev. Lett. 93, 213903 (2004). Unpublished (rejected by Physical Review Letters), but for a publication holding main points see A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L.A. Lugiato "Coherent imaging with pseudo-thermal incoherent light", Journal of Modern Optics 53, 739-760 (2006), quant-ph/0504082. 1 page, 1 figure
Comment on A.F. Abouraddy, P.R. Stone, A.V. Sergienko, B.E.A. Saleh, and M.C. Teich, ``Entangled-Photon Imaging of a Pure Phase Object,'' Phys. Rev. Lett. 93, 213903 (2004). Unpublished (rejected by Physical Review Letters), but for a publication holding main points see A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L.A. Lugiato "Coherent imaging with pseudo-thermal incoherent light", Journal of Modern Optics 53, 739-760 (2006), quant-ph/0504082.
When basic tools of quantum information are applied to the quantum tomography data presented in Nature 439, 179 (2006), none of their devices appears to be a source of entangled photons.
Recently, Li. \emph{et. al.} [Int. J. Theor. Phys., 48, 2777 (2009)] derived a necessary and sufficient condition for LOCC cloning of a set of bipartite orthogonal partially but equally entangled state. We demonstrates that, the result is based on a wrong observation regarding a set of non-maximally entangled states with equal entanglement. We also provide a simple example in favor of our comment.
A discussion on the robustness of continuous-variable entangled states under noisy environment is briefly given in direct relation to Phys. Rev. Lett. 105, 100503 (2010).
Recently Eibl et al. [PRL 92, 077901 (2004)] reported the experimental observation of the three-photon polarization-entangled W state. In this Comment we point out that, actually, the particular measurements involved in the experiment testing Mermin's inequality cannot be used for the verification of the existence of genuinely quantal tripartite correlations in the observed state, and therefore this state cannot conclusively be identified with the W state.
In a recent Brief Report, Lee et al. [L. Lee, D. Ahn, and S.W. Hwang, Phys. Rev. A 66, 024304 (2002)] have claimed that using pairwise entangled qubits gives rise to an exponentially more efficient dense coding when two parties are involved than using maximally entangled qubits shared among N parties. Here, we show that their claim is not true.
A recent theoretical paper [1] proposes a scheme for entanglement swapping utilizing acousto-optic modulators without requiring a Bell-state measurement. In this comment, we show that the proposal is flawed and no entanglement swapping can occur without measurement.
In a recent Brief Report, Zheng [S-B. Zheng, PRA 66, 014103 (2002)] has given a proof of nonlocality without using inequalities for three spin-1/2 particles in the nonmaximally entangled state |psi> = cosθ|+++> + i sinθ|-->. Here we show that Zheng's proof is not correct. Indeed it is the case that, for the experiment considered by Zheng, the only state that admits a nonlocality proof without inequalities is the maximally entangled state.
In the paper [1], authors claim that the scheme for entanglement swapping using an acoustic-optical modulator [2] is flaw. In this reply, we show there is a trivial mistake in the scheme [2], but the main conclusion is still correct, that is, the acoustic-optical modulator can be used to manipulate the frequency-entangled state.
In Xu and Kuang (\textit{J. Phys. A: Math. Gen.} 39 (2006) L191), the authors claim that, for single-mode excited entangled coherent states $| Ψ_{\pm}(α,m)>$, \textquotedblleft the photon excitations lead to the decrease of the concurrence in the strong field regime of $| α| ^{2}$ and the concurrence tends to zero when $| α| ^{2}\to \infty$". This is wrong.
The degree of entanglement between two spins may change due to interaction. About this we find that a wrong result in a recent work by Ge and Wadati [Phys. Rev. A {\bf72}, 052101(2005)] which breach the basic principle.
The ability of parameter recently proposed by Sorensen et al. (Nature, 409, 63 (2001)) to characterize entanglement or inseparability is investigated for a system of two two-level atoms interacting with a single mode of radiation field. For comparison we employ the necessary and sufficient criterion of Peres and Horodecki for inseparability of bipartite states. We show that for diagonal atomic density matrix the parameter of Sorensen et al. fails to show entangled nature of collective atomic state whereas same state is inseparable in accordance with Peres-Horodecki criterion.
We correct a mistake in a result reported in [PRA 64, 062106 (2001)], where it is rightfully argued that initial correlations between a system and its environment may render the system reduced dynamics not completely positive. We prove how not only these initial correlations but also the specific joint dynamics does play a significant role in the question of the complete positivy of the reduced dynamics.
In a recent article Giustina et al. [Phys. Rev. Lett. 115, 250401 (2015)] report on an advanced Bell experiment, simultaneously closing loopholes for local hidden-variable theories. The authors claim that 'local realism' has been refuted, unless 'truly exotic hypotheses' are made. Here I argue that a particularly wide and natural class of local hidden-variable theories survives, for instance when the hidden variables describe a background field. Such background-based theories exploit the freedom-of-choice loophole, which cannot be closed for this type of hidden variables. The dynamics of such …
In a recent work (Allegra et al, Phys. Rev. Lett. 105, 100503, 2010) we addressed the evolution of photon-number entangled states in noisy Gaussian channels. Upon exploiting several non equivalent separability criteria we found evidence that entanglement of Gaussian PNES survives longer, and thus we drew a conjecture about the generality of this result. In their Comment to our work, Lee et al. use an additional entanglement criterion (NDPT) which allows them to show some counterexamples to our conjecture, i.e., nonGaussian states whose entanglement survives longer. In this reply, we argue that…
We study the conditions when mixtures of entangled pure states with maximally mixed one-qudit reduced density matrices remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to…
Rydberg atoms traversing a micromaser cavity one after the other can emerge in correlated states, and according to Copenhagen quantum mechanics this may lead to a violation of Bell's inequality, that is, to a Bell sum S>2. S is here calculated in various ideal physical situations including those with (1) different initial states of the atoms, (2) different free adjustable parameters, being either the phase or the turning angle of a classical radiation field put behind the cavity, and (3) either equal or different Rabi angles for successive atoms. The experiments are crucial for a realist inter…
We present two optimal methods of teleporting an unknown qubit using any pure entangled state. We also discuss how such methods can also have succesful application in quantum secret sharing with pure multipartite entangled states.
In a recent paper [quant-ph/0607008] Lapaire and Sipe argue that one can discuss interference experiments using entangled photons in terms of single photon wave functions. Furthermore, they argue that contrary to the claim of the authors of the postponed compensation experiment [2], the single photon wave functions overlap on the beam splitter when interference is observed. In this comment, we show that the claim in [2] is correct and we argue that the idea of single photon wave functions in entangled states is misleading.
We propose a scheme to produce the pure entangled states through type II downconversion. In the scheme, the vacuum states are excluded and the a prori pure entangled states are produced and verified without destroying the state itself. This can help to carry out the many unditional experiments related to quantum entanglement.
A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.
I show that two distant parties can transform pure entangled states to arbitrary pure states by stochastic local operations and classical communication (SLOCC) at the single copy level, if they share bound entangled states. This is the effect of bound entanglement since this entanglement processing is impossible by SLOCC alone. Similar effect of bound entanglement occurs in three qubits where two incomparable entangled states of GHZ and W can be inter-converted. In general multipartite settings composed by $N$ distant parties, all $N$-partite pure entangled states are inter-convertible by SLOC…
We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states.
Recently Yu and Sun [Int. J. Theor. Phys. DOI 10.1007/s10773-014-2360-x] have presented probabilistic teleportation of 3-qubit cat state via 6-qubit cluster state. The success probability depends on absolute value of only two of the coefficients of cluster state i.e. |c|^2 + |d|^2. We have demonstrated the feasibility to teleport 3-qubit cat state via 2-qubit non maximally entangled Bell state instead of a complex state like 6-qubit non maximally entangled cluster state. In this comment we have prescribed an optimal protocol for teleportation of n-qubit state of the form (α|x> + β|\bar{x}>)_n …
Tanabe et al (Phys. Rev. A {\bf 82} 040101(R) 2010) have experimentally demonstrated that the emission properties of unstable atoms in entangled and product states are different. The authors define an apparent decay time as a fitting parameter which falls below the lifetime of the single atom for entangled pairs. We argue that their results about coincidence time spectra are correct, but those concerning lifetimes cannot be considered conclusive because they assume the emission of photons by the two atoms to be independent processes, a doubtful hypothesis for entangled states. We suggest an im…
Any pure entangled state of two particles violates a Bell inequality for two-particle correlation functions (Gisin's theorem). We show that there exist pure entangled N>2 qubit states that do not violate any Bell inequality for N particle correlation functions for experiments involving two dichotomic observables per local measuring station. We also find that Mermin-Ardehali-Belinskii-Klyshko inequalities may not always be optimal for refutation of local realistic description.
We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states.
We show that all pure entangled states of two $d$-dimensional quantum systems (i.e., two qudits) can be generated from an initial separable state via a universal Yang--Baxter matrix if one is assisted by local unitary transformations.
We examine dense coding with an arbitrary pure entangled state sharing between the sender and the receiver. Upper bounds on the average success probability in approximate dense coding and on the probability of conclusive results in unambiguous dense coding are derived. We also construct the optimal protocol which saturates the upper bound in each case.
We prove that a pure entangled state of two subsystems with equal spin is equivalent to a two-mode spin-squeezed state under local operations except for a set of bipartite states with measure zero, and we provide a counterexample to the generalization of this result to two subsystems of unequal spin.
Entangled pure-states, Werner-states and generalized mixed-states of any structure, spanning a 2x2 Hilbert space are created by a novel high-brilliance universal source of polarization-entangled photon pairs. The violation of a Bell inequality has been tested for the first time with a pure-state, indeed a conceptually relevant ideal condition, and with Werner-states. The generalized ''maximally entangled mixed states'' (MEMS) were also synthetized for the first time and their exotic properties investigated by means of a quantum tomographic technique.
The spectral decomposition of all (n,2,2) Bell operators ($2^{2^n}$ in number, $n \ge 2$), as introduced by Werner and Wolf, is done. Its implications on the characterization of Bell operators as probes of entanglement are considered in detail.
We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.
We demonstrate one-sided device-independent self-testing of any pure entangled two-qubit state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable correlations, which certify all pure two-qubit entangled states. Our experimental results identify which particular pure two-qubit entangled state has been self-tested and which measurement operators are used on the untrusted side. Furthermore, we analytically derive the robustness bound of our protocol, enabling our subsequent experimental verification of …
We present a scheme for quantum secure direct communication with quantum encryption. The two authorized users use repeatedly a sequence of the pure entangled pairs (quantum key) shared for encrypting and decrypting the secret message carried by the traveling photons directly. For checking eavesdropping, the two parties perform the single-photon measurements on some decoy particles before each round. This scheme has the advantage that the pure entangled quantum signal source is feasible at present and any eavesdropper cannot steal the message.
We look for local unitary operators $W_1 \otimes W_2$ which would rotate all equally entangled two-qubit pure states by the same but arbitrary amount. It is shown that all two-qubit maximally entangled states can be rotated through the same but arbitrary amount by local unitary operators. But there is no local unitary operator which can rotate all equally entangled non-maximally entangled states by the same amount, unless it is unity. We have found the optimal sets of equally entangled non-maximally entangled states which can be rotated by the same but arbitrary amount via local unitary operat…
Nonlocal correlations as revealed by the violations to Bell inequalities are incompatible with local models without any nonlocal correlations. However some tripartite entangled states, e.g., symmetric pure states, exhibit a stronger nonlocality even incompatible with hybrid local/nonlocal models allowing nonlocal correlations between any two parties. Here we propose a three-particle Hardy-type test without inequality, as illustrated by a gedanken experiment, that is failed by all non-signaling local models while is passed by all tripartite entangled asymmetric pure states. Our result implies t…
In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.
We report on the experimental generation of an entangled state with a spectrally pure heralded single-photon state and a weak coherent state. By choosing group-velocity matching in the nonlinear crystal, our system for producing entangled photons was 60 times brighter than that in the earlier experiment [Phys. Rev. Lett. 90, 240401 (2003)], with no need of bandpass filters. This entanglement system is useful for quantum information protocols that require indistinguishable photons from independent sources.
Suppose two distant observers Alice and Bob share a pure biparticle entangled state secretly chosen from a set, it is shown that Alice (Bob) can probabilistic concentrate the state to a maximally entangled state by applying local operations and classical communication (LQCC) if and only if the states in the set share the same marginal density operator for her (his) subsystem. Applying this result, we present probabilistic superdense coding and show that perfect purification of mixed state is impossible using only LQCC on individual particles.
An entanglement measure for pure-state continuous-variable bi-partite problem, the Schmidt number, is analytically calculated for one simple model of atom-field scattering.
We show that a single Bell's inequality with two dichotomic observables for each observer, which is originated from Hardy's nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin's theorem is proved in its most general form from which it follows that for pure states Bell's nonlocality and quantum entanglement are equivalent.
In this paper, we propose a novel scheme to generate two-ion maximally entangled states from either pure product states or mixed states using linear optics. Our new scheme is mainly based on the ionic interference. Because the proposed scheme can generate pure maximally entangled states from mixed states, we denote it as purification-like generation scheme. The scheme does not need a Bell state analyzer as the existing entanglement generation schemes do, it also avoids the difficulty of synchronizing the arrival time of the two scattered photons faced by the existing schemes, thus the proposed…
While it has recently been demonstrated how to certify the maximal amount of randomness from any pure two-qubit entangled state in a device-independent way [E. Woodhead et al., Phys. Rev. Research 2, 042028(R)(2020)], the problem of optimal randomness certification from entangled states of higher local dimension remains open. Here we introduce a method for device-independent certification of the maximal possible amount of $2\log_23$ random bits using pure bipartite entangled two-qutrit states and extremal nine-outcome general non-projective measurements. To this aim, we exploit the extended Be…
We consider the problem of $1$-sided device-independent self-testing of any pure entangled two-qubit state based on steering inequalities which certify the presence of quantum steering. In particular, we note that in the $2-2-2$ steering scenario (involving $2$ parties, $2$ measurement settings per party, $2$ outcomes per measurement setting), the maximal violation of a fine-grained steering inequality can be used to witness certain extremal steerable correlations, which certify all pure two-qubit entangled states. We demonstrate that the violation of analogous CHSH inequality of steering or n…
We study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement, exclude the existence of maximally mixed entangled states. In the multipartite scenario, our conclusions allow us to generalize the idea of monogamy of entanglement: we establish the \textit{polygamy of entanglement}, expressing that if a general state is maximally entangled with respect to some kind of multipartite entanglement, then it is necessarily factori…
We study the feasibility of extracting a pure entangled state of non-complementary, and potentially well separated, regions of a quantum many-body system. It is shown that this can indeed be accomplished in non-equilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as magnetization in separated blocks of spins. A general procedure is presented, which can search for the optimal way to extract a pure entangled state through local projections. Our results indicate a connection of the projective extraction of entanglement to…
The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Recently it was shown by Coladangelo et. al. (Nat Commun 8, 15485 (2017)) that all pure bipartite entangled states can be self tested in the device independent scenario by employing subspace methods introduced by Yang et. al. (Phys. Rev. A 87, 050102(R)). Here, we have adapted their method to show that any bipartite pure entangled state can be certified in the semi-device independent scen…
We present a quantum secure direct communication protocol where the channels are not maximally entangled states. The communication parties utilize decoy photons to check eavesdropping. After ensuring the security of the quantum channel, the sender encodes the secret message and transmits it to the receiver by using Controlled-NOT operation and von Neumann measurement. The protocol is simple and realizable with present technology. We also show the protocol is secure for noisy quantum channel.
Employing the general BXOR operation and local state discrimination, the mixed state of the form ρ^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|ϕ_{mn}><ϕ_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|ϕ_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.
The nature of quantum correlations in networks featuring independent sources of entanglement remains poorly understood. Here, focusing on the simplest network of entanglement swapping, we start a systematic characterization of the set of quantum states leading to violation of the so-called "bilocality" inequality. First, we show that all possible pairs of entangled pure states can violate the inequality. Next, we derive a general criterion for violation for arbitrary pairs of mixed two-qubit states. Notably, this reveals a strong connection between the CHSH Bell inequality and the bilocality i…
We present a scheme for multiparty quantum secret sharing of a private key with pure entangled states and decoy photons. The boss, say Alice uses the decoy photons, which are randomly in one of the four nonorthogonal single-photon states, to prevent a potentially dishonest agent from eavesdropping freely. This scheme requires the parties of communication to have neither an ideal single-photon quantum source nor a maximally entangled one, which makes this scheme more convenient than others in a practical application. Moreover, it has the advantage of having high intrinsic efficiency for qubits …
We derive lower limits on the inefficiency and classical communication costs of dilution between two-term bipartite pure states that are partially entangled. We first calculate explicit relations between the allowable error and classical communication costs of entanglement dilution using the protocol of Lo-Popescu and then consider a two-stage dilution from singlets with this protocol followed by some unknown protocol for conversion between partially entangled states. Applying the lower bounds on classical communication and inefficiency of Harrow-Lo and Hayden-Winter to this two-stage protocol…
Almost all pure entangled states enable unbounded nonlocality sharing
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学与技术研究院）；Physics Department and NanoLund, Lund University（隆德大学物理系与纳米实验室）
We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition nor by the realignment criterion, i.e. by any permutational criterion i…
Complete complementarity relations, as e.g. $P(ρ_{A})^{2} + C(ρ_{A})^{2} + E(|Ψ\rangle_{AB})^{2}=1$, constrain the local predictability, $P$, and local coherence, $C$, and the entanglement, $E$, of bipartite pure states. For pairs of qubits prepared initially in a particular class of partially entangled pure states with null local coherence, these relations were used in Ref. [Phys. Lett. A, 451, 128414 (2022)] to provide an operational connection between local predictability of the pre-measurement states with the probability of the maximally entangled components of the states after the Bell-ba…
In this paper, we propose a novel scheme that can generate two-atom maximally entangled states from pure product states and mixed states using linear optics. Because the scheme can generate pure maximally entangled states from mixed states, we denote it as purification-like generation scheme.
