Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are bi-orthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one e-bit more than the average of the entanglement of the two states being superposed. However for more general states, the situation is very different.
We investigate the utility of non classical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection. We find that like squeezed states a superposition of coherent states allows displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single mode superposition states with the same mean photon number.
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a…
For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite $(2\otimes 2\otimes n)$ …
The bounds on concurrence of the superposition state in terms of those of the states being superposed are studied in this paper. The bounds on concurrence are quite different from those on the entanglement measure based on von Neumann entropy (Phys. Rev. Lett. 97, 100502 (2006)). In particular, a nonzero lower bound can be provided if the states being superposed are properly constrained.
The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entangle…
We show how to make quantum networks, both standard and entanglement-based, genuine quantum by providing them with the possibility of handling superposed tasks and superposed addressing. This extension of their functionality relies on a quantum control register, which specifies not only the task of the network, but also the corresponding weights in a coherently superposed fashion. Although adding coherent control to classical tasks, such as sending or measuring -or not doing so-, is in general impossible, we introduce protocols that are able to mimick this behavior under certain conditions. We…
With the aid of the solutions of the Quantum Langevin equations, we have calculated the Q-functions for the two-mode coherent and subharmonic cavity light beams. We have then determined the Q-function for the superposed two-mode coherent and subharmonic cavity light beams. With the help of the pertinent Q-functions for cavity light beams, we determined the photon statistics, quadrature statistics, and entanglement. we have obtained that the superposed two-mode coherent and subharmonic cavity light beams are in a squeezed state and the squeezing occurs in the plus quadrature. Besides, our analy…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
In this paper we use the \textit{concurrence vector}, as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by \textit{I-concurrence}, so that our results can be compared to those given in [Phys. Rev. A {\bf 76}, 042328 (2007)]. We obtain a tighter lower bound in the case that two superposed states are orthogonal. We also show that when the two super…
In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear superposition of states. For example, if we consider two pairs of incomparable states, then their superposition may result into a comparable pair of states. We investigate many such cases and provide some of the results in tabular form. We also investigate the entanglement behavior of such classes of states, specifically their monotone nature. Finally we pro…
A central open problem of quantum physics is to reconcile theory with experience. In this work I present a framework for studying distinct modes of experience in a superposed world. A modes of experience is characterized by how the world, experiences, and options relate to each other by the perceptions, decisions, and actions, as well as by probabilistic rules encoding probabilistic or deterministic correlations among first person experiences. In a toy model, the life expectancies of beings in different candidate modes of experience are compared. It is found that the quantum mode without macro…
We provide an evidence for the validity of strong monogamy inequality of multi-party quantum entanglement using square of convex-roof extended negativity(SCREN). We first consider a large class of multi-qudit mixed state that are in a partially coherent superposition of a generalized W-class state and the vacuum, and provide some useful properties about this class of states. We show that monogamy inequality of multi-qudit entanglement in terms of SCREN holds for this class of states. We further show that SCREN strong monogamy inequality of multi-qudit entanglement also holds for this class of …
Recently, the authors [arXiv quant-ph 1209.3706] studied quantum discord for Werner mixed states based on the four entangled coherent states, which are used for quantum teleportation of single qubit information encoded in superposed coherent state and compared it with entanglement of formation. In the present paper, we consider two more general bipartite superposed coherent states and get two quasi-Werner states. We study quantum discord and entanglement of formation for these states and compare them.
Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\fracπ{2}$ out of phase. The formalism has then been applied to a few physical systems as "harmonious states", "SU(1,1) coherent states" and "the center of mass motion of trapped ion". Finally, the nonclassical properties such as sub-Poissonian statistics, quadrature squeezing, amplitude-squared squeezing and Wigner distribution function of the superposed states have been investigated, numerically. E…
Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to the entanglement. We also study a case of two superposed pair coherent states
An experimental test of quantum effects in gravity has recently been proposed, where the ability of the gravitational field to entangle two masses is used as a witness of its quantum nature. The key idea is that if gravity can generate entanglement between two masses then it must have at least some quantum features (i.e., two non-commuting observables). Here we discuss what existing models for coupled matter and gravity predict for this experiment. Collapse-type models, and also quantum field theory in curved spacetime, as well as various induced gravities, do not predict entanglement generati…
We investigate how the genuine multipartite entanglement is distributed among the components of superposed states. Analytical lower and upper bounds for the usual multipartite negativity and the genuine multipartite entanglement negativity are derived. These bounds are shown to be tight by detailed examples.
We discuss the generation of field-induced entanglement between two objects each in a superposition of two trajectories.The objects have currents coupled to local quantum fields, and the currents are evaluated around each trajectory of the objects.The fields have only dynamical degrees of freedom and satisfy the microcausality condition. We find that the superposed state of trajectories cannot be entangled when the objects are spacelike separated.This means that the quantum fields do not generate spacelike entanglement in the superposition of two trajectories of each object.
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. W…
Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a det…
The influence of gravitational field on entanglement of bipartite states is investigated based on the recent idea of superposition states of gravitational field. Different from earlier considerations, we study the case where the gravitational field cannot be separated unitarily from the bipartite system in the final stage of the interaction. When the different gravitational field states are orthogonal, entanglement cannot be generated for an initial product state. If the different gravitational field states are non-orthogonal, entanglement can be generated and the amount of generated entanglem…
Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as $|i_1 i_2 ... i_n\ket$ with $i_j$ being either 0 or 1, but is a non-trivial task to construct an {\it arbitrary} superposed quantum state. In this Paper, we present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate operations, {\it without introducing additional quantum bits}. Applicat…
The quantum state of Schroedinger's cat is usually incorrectly described as a superposition of "dead" and "alive," despite an argument by Rinner and Werner that, locally, the cat should be considered to be in a mixture of non-superposed states. Here, it is rigorously proven that the cat is not in a superposition. This is central to the measurement problem. Nonlocal two-photon interferometry experiments throw further light on the measurement state by probing the effect of a variable phase factor inserted between its superposed terms. These experiments demonstrate that both subsystems really are…
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition state which can be expressed according to entanglements of its component states. Especially, if the component states are mutually bi-orthogonal, the entanglement of the superposition state can be exactly given in terms of the entanglements of the states being superposed.
We consider an entanglement harvesting protocol between two Unruh-deWitt detectors in quantum superpositions of static trajectories in the static de Sitter and thermal Minkowski spacetimes. We demonstrate for the first time that the spatial superposition of each detector's path allows entanglement to be harvested from the quantum field in regimes where it would be otherwise impossible for detectors on classical trajectories. Surprisingly, for detectors on sufficiently delocalised trajectories in a thermal bath, the amount of harvested entanglement grows with the temperature of the field, viola…
We study a coherent superposition of field annihilation and creation operator acting on continuous variable systems and propose its application for quantum state engineering. Specifically, it is investigated how the superposed operation transforms a classical state to a nonclassical one, together with emerging nonclassical effects. We also propose an experimental scheme to implement this elementary coherent operation and discuss its usefulness to produce an arbitrary superposition of number states involving up to two photons.
We show how macroscopically distinct quantum superposition states (Schroedinger cat states) may be used as logical qubit encodings for the correction of spontaneous emission errors. Spontaneous emission causes a bit flip error which is easily corrected by a standard error correction circuit. The method works arbitrarily well as the distance between the amplitudes of the superposed coherent states increases.
B92-type and BB84-type quantum cryptography schemes using superposed states of the vacuum and single particle states which are robust against PNS attacks are studied. The number of securely transferred classical bits per particle (not per qubit) sent in these schemes is calculated and found to have upper bounds. Possible experimental realizations using the cavity QED or linear optics are suggested.
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed states and the superposition coefficients. This bound is proven to be tight for a class of states composed by an arbitrary number of qubits. We also extend the result to a large family of quantifiers which includes the negativity, the robustness of entanglement, and the best separable approximation measure.
We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.
We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions "fragile" if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition evolve under the internal thermalization dynamics of the system, followed by a time reversal manipulation known as Loschmidt echo. The thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure. We validate the metho…
We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized su…
We investigate upper and lower bounds on the entropy of entanglement of a superposition of bipartite states as a function of the individual states in the superposition. In particular, we extend the results in [G. Gour, arxiv.org:0704.1521 (2007)] to superpositions of several states rather than just two. We then investigate the entanglement in a subspace as a function of its basis states: we find upper bounds for the largest entanglement in a subspace and demonstrate that no such lower bound for the smallest entanglement exists. Finally, we consider entanglement of superpositions using measures…
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub…
Particle detector in a position-superposed black hole spacetime
University of York（约克大学）；International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术国际实验室）；University of Vienna（维也纳大学）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）
We find tight lower and upper bounds on the entanglement of a superposition of two bipartite states in terms of the entanglement of the two states constituting the superposition. Our upper bound is dramatically tighter than the one presented in Phys. Rev. Lett 97, 100502 (2006) and our lower bound can be used to provide lower bounds on different measures of entanglement such as the entanglement of formation and the entanglement of subspaces. We also find that in the case in which the two states are one-sided orthogonal, the entanglement of the superposition state can be expressed explicitly in…
Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but despite their longstanding central role we know very little about how to extract the number of coherently superposed amplitudes from a general interference pattern. A fundamental issue is that performing a phase-sensitive measurement is as challenging as creating a coherent superposition, so that assuming a perfectly implemented measurement for verification of qua…
Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.
We show relations between superposition of macroscopically distinct states and entanglement. These relations lead to the important conclusion that if a state contains superposition of macroscopically distinct states, the state also contains large multipartite entanglement in terms of several measures. Such multipartite entanglement property also suggests that if a state contains superposition of macroscopically distinct states, a measurement on a single particle drastically changes the state of macroscopically many other particles, as in the case of the N-qubit GHZ state.
This work discuss the entanglement and quantum polarization of superpositions of two-mode coherent states. We use the concurrence to measure their entanglements and the quantum Stokes parameters and the Q function in order to analyze their polarization and degree of polarization.
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We propose a simple scheme to generate deterministic entanglement between two movable end mirrors in a Fabry-Perot cavity using a single photon superposition state. We derive analytically the expressions of the generated entangled states and the degree of entanglement for each state. We show that strong entanglement can be obtained either in the single-photon strong coupling regime deterministically or in the single-photon weak coupling regime conditionally.
