E. Bagan, M. Baig, R. Munoz-Tapia
The communication of directions using quantum states is a useful laboratory test for some basic facts of quantum information. For a system of spin-1/2 particles there are different quantum states that can encode directions. This information can later be decoded by means of a generalized measurement. In this talk we present the optimal strategies under different assumptions.
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It has been recently suggested that the dynamics of a quantum spin system may provide a natural mechanism for transporting quantum information. We show that one dimensional rings of qubits with fixed (time-independent) interactions, constant around the ring, allow high fidelity communication of quantum states. We show that the problem of maximising the fidelity of the quantum communication is related to a classical problem in fourier wave analysis. By making use of this observation we find that if both communicating parties have access to limited numbers of qubits in the ring (a fraction that …
Encoding the information in relative parameters
本文研究无共享参考系下三参数通信问题，提出两种基于自旋相对角度的编码方法，并证明使用三个自旋的方法在单量子比特信息量和粒子效率上均优于三对自旋对方法。
Quantum particles, such as spins, can be used for communicating spatial directions to observers who share no common coordinate frame. We show that if the emitter's signals are the orbit of a group, then the optimal detection method may not be a covariant measurement (contrary to widespread belief). It may be advantageous for the receiver to use a different group and an indirect estimation method: first, an ordinary measurement supplies redundant numerical parameters; the latter are then used for a nonlinear optimal identification of the signal.
An arbitrary qubit can be transmitted through a spin chain by perturbatively coupling both communicating parties to it. Those so-called weak-coupling models rely on effective Rabi oscillations between them, yielding nearly maximum fidelity while offering great resilience against disorder with the cost of having long transfer times. Considering this framework, here we address a 1D non-symmetric channel connecting two spins, one placed at each end of it. Given any pattern of nearest-neighbor coupling strengths, we obtain an analytical expression that accounts for the effective long-range interac…
An unsolved problem in relativistic quantum information research is how to model efficient, directional quantum communication between localised parties in a fully quantum field theoretical framework. We propose a tractable approach to this problem based on solving the Heisenberg evolution of localized field observables. We illustrate our approach by analysing, and obtaining approximate analytical solutions to, the problem of communicating coherent states between an inertial sender, Alice and an accelerated receiver, Rob. We use these results to determine the efficiency with which continuous va…
We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform N identically prepared qubits into a state, which is nontrivial only on the first log(N+1) qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-ef…
We give a first physical model for the quantum measurement of the spin direction. It is an Arthurs-Kelly model that involves a kind of magnetic-dipole interaction of the spin with three modes of radiation. We show that in a limit of infinite squeezing of radiation the optimal POVM for the measurement of the spin direction is achieved for spin 1/2.
For sending unknown direction information, antiparallel spins contains more direction information than parallel spins(Gisin and Popescu, 1999, \textit{Phys. Rev. Lett.} 83, 432).In this paper, the optimal information-disturbance tradeoff bound for antiparallel spins is derived. The quantum measurements which attain the optimal tradeoff bound are obtained. This result can be of practical relevance for posing some general limits on Eve's eavesdropping process. Finally, we also present a comparison between the bound for antiparallel spins and the bound for parallel spins.
We study quantum-state transfer in $XX$ spin-$1/2$ chains where both communicating spins are weakly coupled to a channel featuring disordered on-site magnetic fields. Fluctuations are modelled by long-range correlated sequences with self-similar profile obeying a power-law spectrum. We show that the channel is able to perform an almost perfect quantum-state transfer in most of the samples even in the presence of significant amounts of disorder provided the degree of those correlations is strong enough. In that case, we also show that the lack of mirror symmetry does not affect much the likelih…
We study the existence of jointly measurable POVM approximations to two non-commuting sharp spin observables. We compare two different ways to specify optimal approximations.
"Information is physical", and here we consider the physical directional information of a particle with spin. We ask whether, in the presence of a classical frame of reference, such a particle contains any intrinsic directional information, ie. information above that which can be transmitted by a classical bit. We show that when sending a large number of spins, the answer is asymptotically "no". For finite numbers of spins, N, we do not know the answer. We also show that any frame of reference which we can consider to be classical must use some resource which is exponentially large in N. This …
Total spin eigenstates can be used to intrinsically encode a direction, which can later be decoded by means of a quantum measurement. We study the optimal strategy that can be adopted if, as is likely in practical applications, only product states of $N$-spins are available. We obtain the asymptotic behaviour of the average fidelity which provides a proof that the optimal states must be entangled. We also give a prescription for constructing finite measurements for general encoding eigenstates.
In quantum mechanics, it is often thought that the spin of an object points in a fixed direction at any point in time. For example, after selecting the z-direction as the axis of quantization, a spin-1/2 object (such as an electron) may either point up or down. The spin can also be a linear combination of these two states, in which case, there is an axis in another direction in which the spin points in that direction. In this article, we focus on the spin-spin-1/2 case and point out that spin may not necessarily point in a fixed direction, a phenomenon that we call twisted spin. We argue that …
For a system of N spins 1/2 there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeroes of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in 1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.
In this study we investigate the spin squeezing in superposition of a Biaxial state [1,2] and Bell state. Numerical and analytical solutions for the length of mean spin, mean spin direction and spin squeezing are given. It is shown that both the mean spin direction and spin squeezing parameter are determined by the coefficients of superposition and the relative phase.
The accuracy of a measurement of the spin direction of a spin-s particle is characterised, for arbitrary half-integral s. The disturbance caused by the measurement is also characterised. The approach is based on that taken in several previous papers concerning joint measurements of position and momentum. As in those papers, a distinction is made between the errors of retrodiction and prediction. Retrodictive and predictive error relationships are derived. The POVM describing the outcome of a maximally accurate measurement process is investigated. It is shown that, if the measurement is retrodi…
We study the simulation of a single qubit rotation and Controlled-Not gate in a solid state one-dimensional chain of nuclear spins system interacting weakly through an Ising type of interaction with a modular component of the magnetic field in the z-direction, characterized by $B_z(z,t)=Bo(z)\cosδt$. These qubits are subjected to electromagnetic pulses which determine the transition in the one or two qubits system. We use the fidelity parameter to determine the performance of the Not (N) gate and Controlled-Not (CNOT) gate as a function of the frequency parameter $δ$. We found that for $|δ|\le…
We consider the use of N spin-1/2 particles for indicating a direction in space. If N>2, their optimal state is entangled. For large N, the mean square error decreases as N^{-2} (rather than N^{-1} for parallel spins).
Cylindrically symmetric electron beams in spin polarization are reported for the first time. They are shown to be the eigen states of total angular momentum in the $z$ direction. But they are neither the eigen states of spin nor the eigen states of orbital angular momentum in that direction.
We find that detuning an optical pulse train from electronic transitions in quantum dots controls the direction of nuclear spin flips. The optical pulse train generates electron spins that precess about an applied magnetic field, with a spin component parallel to the field only for detuned pulses. This component leads to asymmetry in the nuclear spin flips, providing a way to produce a stable and precise value of the nuclear spin polarization. This effect is observed using two-color, time-resolved Faraday rotation and ellipticity.
Classification and magic magnetic-field directions for spin-orbit-coupled double quantum dots
该研究将自旋轨道耦合双量子点按g张量分为六类，并预测在魔幻磁场方向下因赝自旋守恒而简化自旋物理，为量子计算实验设计提供指导。
We have generalized our recent results (Arm. J. Phys., 2014) relating to the dynamics, heating and radiation of a small rotating polarizable particle moving in a thermal radiation field in the case of arbitrary spin orientation. General expressions for the tangential force, heating rate and intensity of thermal and nonthermal radiation are given. It is shown that the intensity of nonthermal radiation does not depend on the linear velocity and spin direction of the particle.
We study the impacts of the magnetic field direction on the spin-manipulation and the spin-relaxation in a one-dimensional quantum dot with strong spin-orbit coupling. The energy spectrum and the corresponding eigenfunctions in the quantum dot are obtained exactly. We find that no matter how large the spin-orbit coupling is, the electric-dipole spin transition rate as a function of the magnetic field direction always has a $π$ periodicity. However, the phonon-induced spin relaxation rate as a function of the magnetic field direction has a $π$ periodicity only in the weak spin-orbit coupling re…
We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of 'Two Different Wind Directions'. Data are shown to violate the CHSH version of Bell's inequality with the same magnitude as in typical Bell-test experiments with entangled spins. Wind directions thus appear to be conceptual entities connected through meaning, in human cognition, in a similar way as spins appear to be entangled in experiments conducted in physics laboratories. This is the first part of a two-part article. In the second p…
The arrangement of anisotropic spin couplings can optimize sensitivity of the cryptochrome radical pair to the direction of geomagnetic field
该研究通过优化隐色素自由基中各向异性自旋耦合的排列，提升了对地磁场方向的检测灵敏度。
For a Dirac particle in an Aharonov-Bohm (AB) potential, it is shown that the spin interaction (SI) operator which governs the transitions in the spin sector of the first order S-matrix is related to one of the generators of rotation in the spin space of the particle. This operator, which is given by the projection of the spin operator $\mathbfΣ$ along the direction of the total momentum of the system, and the two operators constructed from the projections of the $\mathbfΣ$ operator along the momentum transfer and the z-directions close the SU(2) algebra.It is suggested, then, that these two d…
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