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Register a new userSelf-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom
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Usually, the hyperparallel quantum computation can speed up quantum computing, reduce the quantum resource consumed largely, resist to noise, and simplify the storage of quantum information. Here, we present the first scheme for the self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom of photon systems simultaneously. It can prevent bit-flip errors from happening with an imperfect nonlinear interaction in the nearly realistic condition. We give the way to design the universal hyperparallel photonic quantum controlled-NOT (CNOT) gate on a two-photon system, resorting to the nonlinear interaction between the circularly polarized photon and the electron spin in the quantum dot in a double-sided microcavity system, by taking the imperfect interaction in the nearly realistic condition into account. Its self-error-corrected pattern prevents the bit-flip errors from happening in the hyperparallel quantum CNOT gate, guarantees the robust fidelity, and relaxes the requirement for its experiment. Meanwhile, this scheme works in a failure-heralded way. Also, we generalize this approach to achieve the self-error-corrected hyperparallel quantum CNOT$^N$ gate working on a multiple-photon system. These good features make this scheme more useful in the photonic quantum computation and quantum communication in the future.
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We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled N-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom.
We discuss different proposals for the degree of polarization of quantum fields. The simplest approach, namely making a direct analogy with the classical description via the Stokes operators, is known to produce unsatisfactory results. Still, we argue that these operators and their properties should be basic for any measure of polarization. We compare alternative quantum degrees and put forth that they order various states differently. This is to be expected, since, despite being rooted in the Stokes operators, each of these measures only captures certain characteristics. Therefore, it is likely that several quantum degrees of polarization will coexist, each one having its specific domain of usefulness.
I obtain the quantum correction $Delta V_mathrm{eff}= (hbar^2/8m) [(1- 4xi frac{d+1}{d})(mathcal{S})^2 + 2(1-4xi)mathcal{S}]$ that appears in the effective potential whenever a compact $d$-dimensional subspace (of volume $propto exp[mathcal{S}(x)]$) is discarded from the configuration space of a nonrelativistic particle of mass $m$ and curvature coupling parameter $xi$. This correction gives rise to a force $-langleDelta V_mathrm{eff}rangle$ that pushes the expectation value $langle xrangle$ off its classical trajectory. Because $Delta V_mathrm{eff}$ does not depend on the details of the discarded subspace, these results constitute a generic model of the quantum effect of discarded variables with maximum entropy/information capacity $mathcal{S}(x)$.
Whenever variables $phi=(phi^1,phi^2,ldots)$ are discarded from a system, and the discarded information capacity $mathcal{S}(x)$ depends on the value of an observable $x$, a quantum correction $Delta V_mathrm{eff}(x)$ appears in the effective potential [arXiv:1707.05789]. Here I examine the origins and implications of $Delta V_mathrm{eff}$ within the path integral, which I construct using Synges world function. I show that the $phi$ variables can be `integrated out of the path integral, reducing the propagator to a sum of integrals over observable paths $x(t)$ alone. The phase of each path is equal to the semiclassical action (divided by $hbar$) including the same correction $Delta V_mathrm{eff}$ as previously derived. This generalises the prior results beyond the limits of the Schrodinger equation; in particular, it allows us to consider discarded variables with a history-dependent information capacity $mathcal{S}=mathcal{S}(x,int^t f(x(t))mathrm{d} t)$. History dependence does not alter the formula for $Delta V_mathrm{eff}$.
We employ spherical $t$-designs for the systematic construction of solids whose rotational degrees of freedom can be made robust to decoherence due to external fluctuating fields while simultaneously retaining their sensitivity to signals of interest. Specifically, the ratio of signal phase accumulation rate from a nearby source to the decoherence rate caused by fluctuating fields from more distant sources can be incremented to any desired level by using increasingly complex shapes. This allows for the generation of long-lived macroscopic quantum superpositions of rotational degrees of freedom and the robust generation of entanglement between two or more such solids with applications in robust quantum sensing and precision metrology as well as quantum registers.
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