Many previous works on quantum photolithography are based on maximally-entangled states (MES). In this paper, we generalize the MES quantum photolithography to the case where two light beams share a $N$-photon nonmaximally-entangled state. we investigate the correlations between quantum entanglement and quantum photolithography. It is shown that for nonlocal entanglement between the two light beams the amplitude of the deposition rate can be changed through varying the degree of entanglement described by an entanglement angle while the resolution remains unchanged, and found that for local entanglement between the two light beams the effective Rayleigh resolution of quantum photolithography can be resonantly enhanced.
We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via nonmaximally entangled state then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon, i.e., the total probability of successful multiple linear optical teleportation is higher for nonmaximally entangled states than maximally entangled states.
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.
We propose an efficient quantum key distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. They choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that such a refined data analysis guarantees the security of our scheme against a biased eavesdropping strategy.
We show that for pure and mixed states the problem of maximizing the correlation measure in the CHSH inequality reduces to maximizing the perimeter of a parallelogram enclosed by an ellipse characterized by the entanglement contained in the bipartite system. Since our geometrical description is also valid for a non-maximally entangled state we can determine the corresponding optimal measurements.
For carrying out many quantum information protocols entanglement must be established in advance between two distant parties. Practically, inevitable interaction of entangled subsystems with their environments during distribution and storage will result in degradation of entanglement. Here we investigate the decoherence of two-qubit entangled states in the local amplitude noise. We show that there exists a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence, fully entangled fraction, and quan…
We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving LOCC under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension $d\geq3$, one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. We further show that the generalization of the formula that exactly computes one-shot optimal singlet fraction for qubit chan…
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
We study the one-to-two phase-covariant telecloning of a qudit without ancilla. We show that the fidelity of the two clones can reach that of the clones in the optimal ancilla-based one-to-two phase-covariant cloning and telecloning, i.e., the limitation of quantum mechanics. More interestingly, it is a nonmaximally entangled state rather than the maximally entangled state that can be used to realize such a telecloning task.
We discuss some properties of the Knill-Laflamme-Milburn scheme for quantum teleportation with both maximally and nonmaximally entangled states. We derive the error correction scheme when one performs teleportation with nonmaximally entangled states and we find the probability for perfect teleportation. We show that the maximally entangled state is optimal in such a case. We also show how the error correction scheme can be implemented experimentally when one uses polarization encoding.
We investigate the multiple teleportation with some nonmaximally entangled channels. The efficiencies of two multiple teleportation protocols, the separate multiple teleportation protocol (SMTP) and the global multiple teleportation protocol (GMTP), are calculated. We show that GMTP is more efficient than SMTP.
We present a concentration and purification scheme for nonmaximally entangled pure and mixed porization entangled state. We firstly show that two distant parties Alice and Bob first start with two shared but less entangled photon pure states to produce a four photon GHZ state, and then perform a 45 polarization measurement onto one of the two photons at each location such that the remaining two photon are projected onto a maximally entangled state. We further show the scheme also can be used to purify a class of mixed polarization-entangled state.
We propose a scheme for concentrating nonmaximally pure and mixed polarization-entangled state of individual photon pairs. The scheme uses only simple linear optical elements and may be feasible within current optical technology.
We present a proposal for optically implementing the quantum game of the two-player quantum prisoner's dilemma involving nonmaximally entangled states by using beam splitters, phase shifters, cross-Kerr medium, photon detector and the single-photon representation of quantum bits.
We propose a method of the Bell bases decomposition to teleport an arbitrary unknown N-qubit state through a nonmaximally entangled quantum channel, and give the universal decomposition matrix of N-qubit. Using the decomposition matrix, we can easily obtain the collapsed state at the receiver site. The inverse matrix that the decomposition matrix is just the transformation matrix that the receiver can manipulate. The decomposition matrix is a function of the parameters of the quantum channel. After defining the sub-matrix of the quantum channel, we find that the decomposition matrix is a tenso…
We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e., such that the choice of entangled state used in the next teleportation depends on the results of the measurements performed during the previous teleportations. We show that adaptive teleportation enables an increase in the probability of faithful multiple teleportation in the KLM scheme. In particular if a qubit is to be teleported more than once then it is better to use nonmaximally entangled states than maximally entangled ones in order to achieve the highest probability …
We investigate an imbalance between the sensitivity of the common state measures--fidelity, trace distance, concurrence, tangle, von Neumann entropy and linear entropy--when acted on by a depolarizing channel. Further, in this context we explore two classes of two-qubit entangled mixed states. Specifically, we illustrate a sensitivity imbalance between three of these measures for depolarized (i.e., Werner-state like) nonmaximally entangled and maximally entangled mixed states, noting that the size of the imbalance depends on the state's tangle and linear entropy.
We propose a probabilistic two-party communication complexity scenario with a prior nonmaximally entangled state, which results in less communication than that is required with only classical random correlations. A simple all-optical implementation of this protocol is presented and demonstrates our conclusion.
The ladder proof of nonlocality without inequalities for two spin half particles proposed by Hardy et al. (Phys. Rev. Lett. 79 (1997) 2755) works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-1 particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-s particles (with s equal or greater than 1).
We show that bipartite entanglements involving non-orthogonal states are {\it necessarily nonmaximally} entangled, however {\it small} the non-orthogonality may be. How the deviation from maximal entanglement is related to nonorthogonality is quantified by using two independent measures of entanglement corresponding to the violation of Bell's inequality and the entropy measure respectively. This result is true even if one of the subsystems has orthogonal states. An application of this is that a maximal violation of Bell's inequality in entangled neutral kaons is not possible in the presence of…
We present an entanglement swapping process for unknown nonmaximally entangled photonic states, where the standard Bell-state measurement is replaced by a three-step quantum walk-like state discrimination process, i.e., the practically nontrivial coupling element of two photons is replaced by manipulating their trajectories, which will greatly enrich the dynamics of the coupling between photons in realizing quantum computation, and reduce the integration complexity of optical quantum processing. In addition, the output state can be maximally entangled, which allows for entanglement concentrati…
We perform numerical tests on quantum nonlocality of two-level quantum systems (qubits) observed by a uniformly moving observer. Under a suitable momentum setting, the quantum nonlocality of two-qubit nonmaximally entangled states could be weakened drastically by the Lorentz transformation allowing for the existence of local-hidden-variable models, whereas three-qubit genuinely entangled states are robust. In particular, the generalized GHZ state remains nonlocal under arbitrary Wigner rotation and the generalized W state could admit local-hidden-variable models within a rather narrow range of…
We propose a linear optical scheme for the teleportation of unknown ionic states, the entanglement concentration for nonmaximally entangled states for ions via entanglement swapping and the remote preparation for ionic entangled states. The unique advantage of the scheme is that the joint Bell-state measurement needed in the previous schemes is not needed in the current scheme, i.e. the joint Bell-state measurement has been converted into the product of separate measurements on single ions and photons. In addition, the current scheme can realize the quantum information processes for ions by us…
We propose an experimentally feasible scheme to generate nonmaximal entanglement between two atomic ensembles. The degree of entanglement is readily tunable. The scheme involves laser manipulation of atomic ensembles, adjustable quarter- and half-wave plates, beam splitter, polarizing beam splitters, and single-photon detectors, and well fits the status of the current experimental technology. Finally we use the nonmaximally entangled state of ensembles to demonstrate quantum nonlocality by detecting the Clauser-Horne-Shimony-Holt inequality.
I derive a tight bound between the quality of estimating the state of a single copy of a $d$-level system, and the degree the initial state has to be altered in course of this procedure. This result provides a complete analytical description of the quantum mechanical trade-off between the information gain and the quantum state disturbance expressed in terms of mean fidelities. I also discuss consequences of this bound for quantum teleportation using nonmaximally entangled states.
Recently, Harrow et al. [Phys. Rev. Lett. 92, 187901 (2004)] gave a method for preparing an arbitrary quantum state with high success probability by physically transmitting some qubits, and by consuming a maximally entangled state, together with exhausting some shared random bits. In this paper, we discover that some states are impossible to be perfectly prepared by Alice and Bob initially sharing those entangled states that are superposed by the ground states, as the states to be prepared. In particular, we present a sufficient and necessary condition for the states being enabled to be exactl…
We show two experimental realizations of Hardy ladder test of quantum nonlocality using energy-time correlated photons, following the scheme proposed by A. Cabello \emph{et al.} [Phys. Rev. Lett. \textbf{102}, 040401 (2009)]. Unlike, previous energy-time Bell experiments, these tests require precise tailored nonmaximally entangled states. One of them is equivalent to the two-setting two-outcome Bell test requiring a minimum detection efficiency. The reported experiments are still affected by the locality and detection loopholes, but are free of the post-selection loophole of previous energy-ti…
In this paper we show a Clauser-Horne (CH) inequality for two three-level quantum systems or qutrits, alternative to the CH inequality given by Kaszlikowski et al. [PRA 65, 032118 (2002)]. In contrast to this latter CH inequality, the new one is shown to be equivalent to the Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins et al. [PRL 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the strongest resistance to noise for a nonmaximally entangled state for the case of two von Neumann measurements per site, as first shown by Acin et al. [PRA 65, 052325 (2…
