Instytut Podstawowych Problemów Techniki

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The emergence of an objective reality in line with the laws of the microscopic world has been the focus of longstanding debates. Recent approaches seem to have reached a consensus at least with respect to one aspect, namely, that the encoding of information about a given observable in a physical degree freedom is a necessary condition for such an observable to become an element of the physical reality. Taking this as a fundamental premise and inspired by quantum information theory, here we build an axiomatization for quantum realism—a notion of realism compatible with quantum theory. Our strategy consists of listing some physically motivated principles able to characterize quantum realism in a “metric” independent manner. We introduce some criteria defining monotones and measures of realism and then search for potential candidates within some celebrated information theories—those induced by the von Neumann, Rényi, and Tsallis entropies. We explicitly construct some classes of entropic quantifiers, among which some are shown to satisfy all the proposed axioms and hence can be taken as faithful estimates for the degree of reality (or definiteness) of a given physical observable. Hopefully, our framework may offer a formal ground for further discussions on foundational aspects of quantum mechanics.

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We investigate the relation between transport properties and entanglement between the internal (spin) and external (position) degrees of freedom in one-dimensional discrete time quantum walks. We obtain closed-form expressions for the long-time position variance and asymptotic entanglement of quantum walks whose time evolution is given by any balanced quantum coin, starting from any initial qubit and position states following

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That quantum correlations can be generated over time between the spin and the position of a quantum walker is indisputable. The creation of bipartite entanglement has also been reported for two-walker systems. In this scenario, however, since the global state lies in a fourpartite Hilbert space, the question arises as to whether genuine multipartite entanglement may develop in time. Also, since the spatial degrees of freedom can be viewed as a noisy channel for the two-spin part, one may wonder how other nonclassical aspects, such as Bell nonlocality, Einstein-Podolsky-Rosen steering, quantum discord, and symmetrical quantum discord, evolve in time during the walk. The lack of analytical and numerical evidences which would allow one to address these questions is possibly due to the usual computational difficulties associated with the recursive nature of quantum walks. Here, we work around this issue by introducing a simplified Gaussian model which proves to be very accurate within a given domain and powerful for analytical studies. Then, for an instance involving two noninteracting quantum walkers, whose spins start in the singlet state, we quantify the aforementioned nonclassical features as a function of time, and evaluate violations of both realism and related aspects of locality. In addition, we analyze situations in which the initial two-spin state is affected by white noise. The typical scenario found is such that while genuine fourpartite entanglement increases over time, all the investigated nonclassical features vanish (suddenly or asymptotically) except realism-based nonlocality. Moreover, realism is prevented for all finite times. Our findings open perspectives for the understanding of the dynamics of quantum resources in quantum walks.

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We find out a few ways to improve the realization of entanglement between the internal (spin) and external (position) degrees of freedom of a quantum particle, through the insertion of disordered time steps in a one-dimensional discrete time quantum walk in different scenarios. The disorder is introduced by a randomly chosen quantum coin obtained from a uniform distribution among infinite quantum coins or only between Hadamard and Fourier coins for all the time steps (strong disorder). We can also decrease the amount of disorder by alternating disordered and ordered time steps throughout a quantum walk or by establishing a probability p < 0.5 to pick a Fourier coin instead of a Hadamard one for each time step (weak disorder). Our results show that both scenarios lead to maximal entanglement outperforming the ordered quantum walks. However, these last scenarios are more efficient to create entanglement, because they achieve high entanglement rates in fewer time steps than the former ones. In order to compare distinct disordered cases, we perform an average entanglement by averaging over a large set of initial qubits over time starting from one site (local state) or spread over many neighbor positions following a Gaussian distribution. Some transient behaviors from order to disorder in quantum walks are also evaluated and discussed. Experimental remarks based on available experimental platforms from the literature are made.

Słowa kluczowe:

Quantum walks, Entanglement, Gaussian states

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We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.

Słowa kluczowe:

Quantum walks,Quantum entanglement,Entanglement production

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