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We demonstrate that the unitary dynamics of a multi-qubit system can display hypersensitivity to initial state perturbation. This contradicts the common belief that the classical approach based on the exponential divergence of initially neighboring trajectories cannot be applied to identify chaos in quantum systems. To observe hypersensitivity we use quantum state-metric, introduced by Girolami and Anza in [Phys. Rev. Lett. 126 (2021) 170502], which can be interpreted as a quantum Hamming distance. As an example of a quantum system, we take the multi-qubit implementation of the quantum kicked top, a paradigmatic system known to exhibit quantum chaotic behavior. Our findings confirm that the observed hypersensitivity corresponds to commonly used signatures of quantum chaos. Furthermore, we demonstrate that the proposed metric can detect quantum chaos in the same regime and under analogous initial conditions as in the corresponding classical case., Comment: 6 pages, 3 figures

The quantum description of reality is quite different from the classical one. Understanding this difference at a fundamental level is still an interesting topic. Recently, Dragan and Ekert [New J. Phys. 22 (2020) 033038] postulated that considering so-called superluminal observers can be useful in this context. In particular, they claim that the full mathematical structure of the generalized Lorentz transformation may imply the emergence of multiple quantum mechanical trajectories. On the contrary, here we show that the generalized Lorentz transformation, when used in a consistent way, does not provide any correspondence between the classical concept of a definite path and the multiple paths of quantum mechanics., Comment: 4 pages, new section added

Discrete-time quantum walks (DTQWs) provide a convenient platform for a realisation of many topological phases in noninteracting systems. They often offer more possibilities than systems with a static Hamiltonian. Nevertheless, researchers are still looking for DTQW symmetries protecting topological phases and for definitions of appropriate topological invariants. Although majority of DTQW studies on this topic focus on the so called split-step quantum walk, two distinct topological phases can be observed in more basic models. Here we infer topological properties of the basic DTQWs directly from the mapping of the Brillouin zone to the Bloch Hamiltonian. We show that for translation symmetric systems they can be characterized by a homotopy relative to special points. We also propose a new topological invariant corresponding to this concept. This invariant indicates the number of edge states at the interface between two distinct phases., Comment: 6 pages

We study discrete-time quantum walks on $d$-cycles with a position and coin-dependent phase-shift. Such a model simulates a dynamics of a quantum particle moving on a ring with an artificial gauge field. In our case the amplitude of the phase-shift is governed by a single discrete parameter $q$. We solve the model analytically and observe that for prime $d$ there exists a strong complementarity property between the eigenvectors of two quantum walk evolution operators that act in the $2d$-dimensional Hilbert space. Namely, if $d$ is prime the corresponding eigenvectors of the evolution operators obey $|\langle v_q|v'_{q'} \rangle| \leq 1/\sqrt{d}$ for $q\neq q'$ and for all $|v_q\rangle$ and $|v'_{q'}\rangle$. We also discuss dynamical consequences of this complementarity. Finally, we show that the complementarity is still present in the continuous version of this model, which corresponds to a one-dimensional Dirac particle., Comment: 5+7 pages, 2 figures, comments welcome

Recently Dragan and Ekert [New. J. Phys 22, 033038, 2020] presented arguments that probabilistic dynamics inherent in the realm of quantum physics is related to the propagation of superluminal particles. Moreover they argue that existence of such particles is a natural consequence of the principle of relativity. We show that the proposed extension of Lorentz transformation can be interpreted in natural way without invoking superluminal phenomena., Comment: 4 pages

We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is a formulation of a local unitary dynamics describing the action of this barrier. Such dynamics utilises an auxiliary system $\mathcal{A}$ and we study how properties of $\mathcal{A}$ influence the behaviour of particles. An immediate consequence of unitarity is the fact that particles cannot be trapped on one side of the barrier forever, unless $\mathcal{A}$ is infinite. In addition, coherent superpositions and quantum correlations are affected once particles enter the confinement region. Finally, we show that initial superposition of $\mathcal{A}$ allows the barrier to act as a beam splitter., Comment: 11 pages, 3 figures, comments welcome

Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on n-cycle subject to a random coin-dependent phase shift at a single position. This finite system, whose evolution is described by only two Kraus operators, can exhibit all kinds of asymptotic behavior observable in quantum Markov chains: it either evolves towards a maximally mixed state, or partially mixed state, or tends to an oscillatory motion on an asymptotic orbit. We find that the asymptotic orbits do not have a product structure, therefore the corresponding states can manifest entanglement between the position and the coin degrees of freedom, even if the system started in a product state., Comment: 9 pages, 6 figures, comments welcome

Violations of Bell inequalities have been an incontestable indicator of non-classicality since the seminal paper by John Bell. However, recent claims of Bell inequalities violations with classical light have cast some doubts on their significance as hallmarks of non-classicality. Here, we challenge those claims. The crux of the problem is that such classical experiments simulate quantum probabilities with intensities of classical fields. However, fields intensities measurements are radically different from single-photon detections, which are primitives of any genuine Bell experiment. We show that this fundamental difference between field intensities measurements and single photon detections shifts the classical bound of relevant Bell inequalities to its algebraic limit, leaving no place for their violations., Comment: 11 pages, 4 figures

The superposition principle is one of the landmarks of quantum mechanics. The importance of quantum superpositions provokes questions about the limitations that quantum mechanics itself imposes on the possibility of their generation. In this work we systematically study the problem of creation of superpositions of unknown quantum states. First, we prove a no-go theorem that forbids the existence of a universal probabilistic quantum protocol producing a superposition of two unknown quantum states. Secondly, we provide an explicit probabilistic protocol generating a superposition of two unknown states, each having a fixed overlap with the known referential pure state. The protocol is proven to be unique and optimal. Moreover, it can be implemented on arbitrary Hilbert spaces. In the context of quantum optics it can be used to efficiently generate highly nonclassical or nongaussian states., Comment: 4.5 pages + 4.5 pages of Appandix, 4 figures, updated discussion on the Alvarez-Rodriguez et. al. article arxiv:1411.4534, updated references, accepted for publication in PRL

A well known cryptographic primitive is so called random access code. Namely, Alice is to send to Bob one of two bits, so that Bob has the choice which bit he wants to learn about. However at any time Alice should not learn Bob's choice, and Bob should learn only the bit of his choice. The task is impossible to accomplish by means of either classical or quantum communication. On the other hand, a concept of correlations stronger than quantum ones, exhibited by so called Popescu- Rohrlich box, was introduced and widely studied. In particular, it is known that Popescu-Rohrlich box enables simulation of the random access code with the support of one bit of communication. Here, we propose a quantum analogue of this phenomenon. Namely, we define an analogue of a random access code, where instead of classical bits, one encodes qubits. We provide a quantum non-signaling box that if supported with two classical bits, allows to simulate a quantum version of random access code. We point out that two bits are necessary. We also show that a quantum random access code cannot be fully quantum: when Bob inputs superposition of two choices, the output will be in a mixed state rather than in a superposition of required states.

We show that a one-dimensional discrete time quantum walk can be used to implement a generalized measurement in terms of positive operator value measure (POVM) on a single qubit. More precisely, we show that for a single qubit any set of rank 1 and rank 2 POVM elements can be generated by a properly engineered quantum walk. In such a scenario the measurement of particle at position x=i corresponds to a measurement of a POVM element E_i on a qubit. We explicitly construct quantum walks implementing unambiguous state discrimination and SIC-POVM., Comment: 6 pages, 1 figure

We observe that changing a phase at a single point in a discrete quantum walk results in a rather surprising localization effect. For certain values of this phase change the possibility of localization strongly depends on the internal coin-state of the walker., Comment: 5 pages, 4 figures

We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to additional degrees of freedom, discrete time quantum walks allow to observe effects which cannot be observed in the corresponding continuous time case. First, we study a discrete time version of the engineered coupling protocol due to Christandl et. al. [Phys. Rev. Lett. 92, 187902 (2004)] and then discuss the general idea of conversion between continuous time quantum walks and discrete time quantum walks., Comment: 9 pages, 6 figures, comments welcome

We show that recent results on the interaction of causality-respecting particles with particles on closed timelike curves derived in [Phys. Rev. A 82, 062330 (2010)] depend on ambiguous assumption about the form of the state which is inputted into the proposed equivalent circuit. Choosing different form of this state leads to opposite conclusion on the power of closed timelike curves.

We consider violation of CHSH inequality for states before and after entanglement swapping. We present a pair of initial states which do not violate CHSH inequality however the final state violates CHSH inequality for some results of Bell measurements performed in order to swap entanglement., Comment: 3 pages, 2 figures

We present an entanglement purification protocol for a mixture of a pure entangled state and a pure product state, which are orthogonal to each other. The protocol is combination of bisection method and one-way hashing protocol. We give recursive formula for the rate of the protocol for different states, i.e. the number of maximally entangled two-qubit pairs obtained with the protocol per a single copy of the initial state. We also calculate numerically the rate for some states., Comment: 4 pages, 1 figure

We present an analysis of the entanglement characteristics in the Majumdar-Ghosh (MG) or $J_{1}$-$J_{2}$ Heisenberg model. For a system consisting of up to 28 spins, there is a deviation from the scaling behaviour of the entanglement entropy characterizing the unfrustrated Heisenberg chain as soon as $J_{2} >0.25$. This feature can be used as an indicator of the dimer phase transition that occurs at $J_{2} = J_{2}^{*} \approx 0.2411 J_{1}$. Additionally, we also consider entanglement at the MG point $J_{2}=0.5 J_{1}$., Comment: 7 figures

We discuss properties of probabilistic coding of two qubits to one qutrit and generalize the scheme to higher dimensions. We show that the protocol preservers entanglement between qubits to be encoded and environment and can be also applied to mixed states. We present the protocol which enables encoding of n qudits to one qudit of dimension smaller than the Hilbert space of the original system and then probabilistically but error-free decode any subset of k qudits. We give a formula for the probability of successful decoding.

In a recent Letter (Phys. Rev. Lett. 95 (2005) 010503) Barrett, Hardy and Kent (BHK) considered a very interesting question which of the fundamental laws of physics ensure security of quantum cryptographic protocols. In particular, they presented quantum key distribution protocol and claimed its security in a very general framework, which allows - what they call - postquantum eavesdropping strategies i.e. which "allows for eavesdroppers who can break the laws of quantum mechanics, as long as nothing they can do implies the possibility of superluminal signaling". In this Comment, however, we show that it is still possible to construct a strategy, which although consistent with all asumptions explicitely stated in BHK paper, enables perfect eavesdropping in their protocol.

We study a quantum state transfer between two qubits interacting with the ends of a quantum wire consisting of linearly arranged spins coupled by an excitation conserving, time-independent Hamiltonian. We show that if we control the coupling between the source and the destination qubits and the ends of the wire, the evolution of the system can lead to an almost perfect transfer even in the case in which all nearest-neighbour couplings between the internal spins of the wire are equal., Comment: 4 pages, 5 figures

Quantum computers are believed to surpass the classical ones. Moreover, it is claimed that this belief reaches the level of a mathematically proven fact within the oracle model of computation. Here we impair the whole class of the so-called rigorist proofs of quantum speed-up obtained within this model.

In this Comment we question the security of recently proposed by Degiovanni et al. [Phys. Rev. A 69 (2004) 032310] scheme of quantum dense key distribution.

In the note we show how the choice of the initial states can influence the evolution of time-averaged probability distribution of the quantum walk on even cycles.

We clarify the connections between the erasure scheme of probabilistic CNOT gate implementation recently proposed by Pittman, Jacobs and Franson [Phys. Rev. A 64, 062311 (2001)] and quantum teleportation.

We consider asymptotic behaviour of a Hadamard walk on a cycle. For a walk which starts with a state in which all the probability is concentrated on one node, we find the explicit formula for the limiting distribution and discuss its asymptotic behaviour when the length of the cycle tends to infinity. We also demonstrate that for a carefully chosen initial state, the limiting distribution of a quantum walk on cycle can lie further away from the uniform distribution than its initial state.

A new scheme of quantum coding is presented. The scheme concerns the quantum states to which Schumacher's compression does not apply. It is shown that two qubits can be encoded in a single qutrit in such a way that one can faithfully reconstruct the state of one qubit. Decision on which of these two qubits is to be reconstructed can be made long after the encoding took place. The scheme succeeds with the average probability of 2/3., Comment: 7 pages

The proposed eavesdropping scheme reveals that the quantum communication protocol recently presented by Bostrom and Felbinger [Phys. Rev. Lett. 89, 187902 (2002)] is not secure as far as quantum channel losses are taken into account.

We will show how to measure the overlap between photon polarization states with the use of linear optics and postselection only. Our scheme is based on quantum teleportation and succeeds with the probability of 1/8., Comment: 10 pages, 3 figures

We will present a method of implementation of general projective measurement of two-photon polarization state with the use of linear optics elements only. The scheme presented succeeds with a probability of at least 1/16. For some specific measurements, (e.g. parity measurement) this probability reaches 1/4., Comment: 8 pages

Generalization of quantum information splitting protocol from qubits to qudits (quantum d-dimensional systems) is presented., Comment: 7 pages

Recently Liu, Long, Tong and Li [Phys. Rev. A 65, 022304 (2002)] have proposed a scheme for superdense coding between multiparties. This scheme seems to be highly asymmetric in the sense that only one sender effectively exploits entanglement. We show that this scheme can be modified in order to allow more senders to benefit of the entanglement enhanced information transmission., Comment: 6 pages