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Register a new userSeparability and entanglement in the Hilbert space reference frames related through the generic unitary transform for four level system
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Quantum correlations in the state of four-level atom are investigated by using generic unitary transforms of the classical (diagonal) density matrix. Partial cases of pure state, $X$-state, Werner state are studied in details. The geometrical meaning of unitary Hilbert reference-frame rotations generating entanglement in the initially separable state is discussed. Characteristics of the entanglement in terms of concurrence, entropy and negativity are obtained as functions of the unitary matrix rotating the reference frame.
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The practically useful criteria of separable states $rho=sum_{k}w_{k}rho_{k}$ in $d=2times2$ are discussed. The equality $G({bf a},{bf b})= 4[langle psi|P({bf a})otimes P({bf b})|psirangle-langle psi|P({bf a})otimes{bf 1}|psiranglelangle psi|{bf 1}otimes P({bf b})|psirangle]=0$ for any two projection operators $P({bf a})$ and $P({bf b})$ provides a necessary and sufficient separability criterion in the case of a separable pure state $rho=|psiranglelanglepsi|$. We propose the separability criteria of mixed states, which are given by ${rm Tr}rho{{bf a}cdot {bf sigma}otimes {bf b}cdot {bf sigma}}=(1/3)Ccosvarphi$ for two spin $1/2$ systems and $4{rm Tr}rho {P({bf a})otimes P({bf b})}=1+(1/2)Ccos2varphi$ for two photon systems, respectively, after taking a geometrical angular average of ${bf a}$ and ${bf b}$ with fixed $cosvarphi={bf a}cdot{bf b}$. Here $-1leq Cleq 1$, and the difference in the numerical coefficients $1/2$ and $1/3$ arises from the different rotational properties of the spinor and the transverse photon. If one instead takes an average over the states in the $d=2$ Hilbert space, the criterion for two photon systems is replaced by $4{rm Tr}rho {P({bf a})otimes P({bf b})}=1+(1/3)Ccos2varphi$. Those separability criteria are shown to be very efficient using the existing experimental data of Aspect et al. in 1981 and Sakai et al. in 2006. When the Werner state is applied to two photon systems, it is shown that the Hilbert space average can judge its inseparability but not the geometrical angular average.
The quantization of the electromagnetic field has successfully paved the way for the development of the Standard Model of Particle Physics and has established the basis for quantum technologies. Gravity, however, continues to hold out against physicists efforts of including it into the framework of quantum theory. Experimental techniques in quantum optics have only recently reached the precision and maturity required for the investigation of quantum systems under the influence of gravitational fields. Here, we report on experiments in which a genuine quantum state of an entangled photon pair was exposed to a series of different accelerations. We measure an entanglement witness for $g$ values ranging from 30 mg to up to 30 g - under free-fall as well on a spinning centrifuge - and have thus derived an upper bound on the effects of uniform acceleration on photonic entanglement. Our work represents the first quantum optics experiment in which entanglement is systematically tested in geodesic motion as well as in accelerated reference frames with acceleration a>>g = 9.81 m/s^2.
Simply and reliably detecting and quantifying entanglement outside laboratory conditions will be essential for future quantum information technologies. Here we address this issue by proposing a method for generating expressions which can perform this task between two parties who do not share a common reference frame. These reference frame independent expressions only require simple local measurements, which allows us to experimentally test them using an off-the-shelf entangled photon source. We show that the values of these expressions provide bounds on the concurrence of the state, and demonstrate experimentally that these bounds are more reliable than values obtained from state tomography since characterizing experimental errors is easier in our setting. Furthermore, we apply this idea to other quantities, such as the Renyi and von Neumann entropies, which are also more reliably calculated directly from the raw data than from a tomographically reconstructed state. This highlights the relevance of our approach for practical quantum information applications that require entanglement.
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension with the number of particles. For a emph{constant} Hamiltonian system of Hilbert space dimension $n$ whose frequencies range from $f_{min}$ to $f_{max}$, we show via a proper orthogonal decomposition, that for a run-time $T$, the dominant dynamics are compressed in the neighborhood of a subspace whose dimension is the smallest integer larger than the time-bandwidth product $delf=(f_{max}-f_{min})T$. We also show how the distribution of initial states can further compress the system dimension. Under the stated conditions, the time-bandwidth estimate reveals the emph{existence} of an effective compressed model whose dimension is derived solely from system properties and not dependent on the particular implementation of a variational simulator, such as a machine learning system, or quantum device. However, finding an efficient solution procedure emph{is} dependent on the simulator implementation{color{black}, which is not discussed in this paper}. In addition, we show that the compression rendered by the proper orthogonal decomposition encoding method can be further strengthened via a multi-layer autoencoder. Finally, we present numerical illustrations to affirm the compression behavior in time-varying Hamiltonian dynamics in the presence of external fields. We also discuss the potential implications of the findings for machine learning tools to efficiently solve the many-body or other high dimensional Schr{o}dinger equations.
We investigate the entanglement measures of tripartite W-State and GHZ-state in noninertial frame through the coordinate transformation between Minkowski and Rindler. First it is shown that all three qubits undergo in a uniform acceleration $a$ of W-State, we find that the one-tangle, two-tangle, and $pi$-tangle decrease when the acceleration parameter $r$ increases, and the two-tangle cannot arrive to infinity of the acceleration. Next we show that the one qubit goes in a uniform acceleration $a_{1}$ and the other two undergo in a uniform acceleration $a$ of GHZ-state, we find that the two-tangle is equal to zero and $N_{B_I (A_I C_I)} = N_{C_I (A_I B_I)} eq N_{A_I (B_I C_I)}$, but one-tangle and $pi$-tangle never reduce to zero for any acceleration.
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