Andrzej Grudka

Andrzej Grudka
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Andrzej Grudka

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Quantum Physics (50)
Mathematics - Mathematical Physics (2)
Mathematical Physics (2)
General Relativity and Quantum Cosmology (2)
Physics - Mesoscopic Systems and Quantum Hall Effect (1)
High Energy Physics - Theory (1)

Publications Authored By Andrzej Grudka

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. Read More

Heisenberg uncertainty principle is a trademark of quantum mechanics. In its original form it states that one cannot gain information about a system without disturbing it, which is a core of novel cryptographic techniques based on quantum effects. The principle can be derived from mathematical formalism of quantum theory. Read More

The problem of device-independent randomness amplification against no-signaling adversaries has so far been studied under the assumption that the weak source of randomness is uncorrelated with the (quantum) devices used in the amplification procedure. In this work, we relax this assumption, and reconsider the original protocol of Colbeck and Renner, Nature Physics 8, 450-454 (2012), on randomness amplification using a Santha-Vazirani (SV) source. To do so, we introduce an SV-like condition for devices, namely that any string of SV source bits remains weakly random conditioned upon any other bit string from the same SV source and the outputs obtained when this further string is input into the devices. Read More

The uncertainty principle, which states that certain sets of quantum-mechanical measurements have a minimal joint uncertainty, has many applications in quantum cryptography. But in such applications, it is important to consider the effect of a (sometimes adversarially controlled) memory that can be correlated with the system being measured: The information retained by such a memory can in fact diminish the uncertainty of measurements. Uncertainty conditioned on a memory was considered in the past by Berta et al. Read More

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. Read More

We present a unified axiomatic approach to contextuality and non-locality based on the fact that both are resource theories. In those theories the main objects are consistent boxes, which can be transformed by certain operations to achieve certain tasks. The amount of resource is quantified by appropriate measures of the resource. Read More

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. Read More

We obtain a general connection between a quantum advantage in communication complexity and non-locality. We show that given any protocol offering a (sufficiently large) quantum advantage in communication complexity, there exists a way of obtaining measurement statistics which violate some Bell inequality. Our main tool is port-based teleportation. Read More

In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Read More

We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and Haah 3D code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. Read More

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. Read More

We investigate theoretically the use of non-ideal ferromagnetic contacts as a mean to detect quantum entanglement of electron spins in transport experiments. We use a designated entanglement witness and find a minimal spin polarization of $\eta > 1/\sqrt{3} \approx 58 %$ required to demonstrate spin entanglement. This is significantly less stringent than the ubiquitous tests of Bell's inequality with $\eta > 1/\sqrt[4]{2}\approx 84%$. Read More

Randomness amplification is the task of transforming a source of somewhat random bits into a source of fully random bits. Although it is impossible to amplify randomness from a single source by classical means, the situation is different considering non-local correlations allowed by quantum mechanics. Here we give the first device-independent protocol for randomness amplification using a constant number of devices. Read More

In randomness amplification a slightly random source is used to produce an improved random source. Perhaps surprisingly, a single source of randomness cannot be amplified at all classically. However, the situation is different if one considers correlations allowed by quantum mechanics as an extra resource. Read More

We study a problem of interconvertibility of two supra-quantum resources: one is so called PR-box, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables Bob (receiver) to choose one of two bits of Alice. It has been known, that PR-box supplemented with one bit of communication can be used to simulate RAC. Read More

A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions of bits generated by a Santha-Vazirani source are shown to be mixtures of permutations of Bernoulli distributions with parameter defined by the source. An intuitive proof is provided for the range of partial randomness from which perfect randomness can be extracted using quantum correlations violating the chain inequalities. Read More

We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when one party measures a single observable and the other party measures one of two observables. The uncertainty relation does not follow from Maassen-Uffink uncertainty relation and is much stronger than Hall uncertainty relation derived from the latter. Read More

We consider multiple entanglement swappings performed on a chain of bipartite states. Each state does not violate CHSH inequality. We show that before some critical number of entanglement swappings is achieved the output state does not violate this inequality either. Read More

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. Read More

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. Read More

Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown by Bell [1] and Kochen-Specker [2], quantum mechanics portrays a picture of the world in which reality loses its objectivity and is in fact created by observation. Quantum mechanics predicts phenomena which cannot be explained by any theory with objective realism, although our everyday experience supports the hypothesis that macroscopic objects, despite being made of quantum particles, exist independently of the act of observation; in this paper we identify this behavior as classical. Read More

We consider distillation of entanglement from two qubit states which are mixtures of three mutually orthogonal states: two pure entangled states and one pure product state. We distill entanglement from such states by projecting n copies of the state on permutationally invariant subspace and then applying one-way hashing protocol. We find analytical expressions for the rate of the protocol. Read More

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. Read More

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. Read More

We present a constructive example of violation of additivity of minimum output R\'enyi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels. Read More

We analyze quantum network primitives which are entanglement-breaking. We show superadditivity of quantum and classical capacity regions for quantum multiple-access channel and quantum butterfly network. Since the effects are especially visible at high noise they suggest that quantum information effects may be particularly helpful in the case of the networks with occasional high noise rates. Read More

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. Read More

We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e. Read More

We establish a framework to study the classical-communication properties of primitive local operations assisted by classical communication which realize various redistributions of entanglement, like, e.g., entanglement swapping. Read More

A lot of research has been done on multipartite correlations. However, it seems strange that there is no definition of so called genuine multipartite correlations. In this paper we propose three reasonable postulates which each measure or indicator of genuine multipartite correlations (or genuine multipartite entanglement) should satisfy. Read More

We consider entanglement swapping for certain mixed states. We assume that the initial states have the same singlet fraction and show that the final state can have singlet fraction greater than the initial states. We also consider two quantum teleportations and show that entanglement swapping can increase teleportation fidelity. Read More

We discuss the problem of coexistence of genuine quantum multipartite correlations and classical multipartite correlations. We introduce a postulate which any measure of genuine multipartite classical correlations should satisfy. We show that covariance does not satisfy this postulate. Read More

We investigate multiple linear optical teleportation in the Knill-Laflamme-Milburn scheme with both maximally and nonmaximally entangled states. We show that if the qubit is teleported several times via nonmaximally entangled state then the errors introduced in the previous teleportations can be corrected by the errors introduced in the following teleportations. This effect is so strong that it leads to another interesting phenomenon, i. Read More

We discuss some properties of the Knill-Laflamme-Milburn scheme for quantum teleportation with both maximally and nonmaximally entangled states. We derive the error correction scheme when one performs teleportation with nonmaximally entangled states and we find the probability for perfect teleportation. We show that the maximally entangled state is optimal in such a case. Read More

It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Read More

We pose the fundamental question of communication properties of primitives irrespectively of their implementation. To illustrate the idea we introduce the concept of entanglement-swapping boxes, i.e. Read More

We present graphical representation for genaralized quantum measurements (POVM). We represent POVM elements as Bloch vectors and find the conditions these vectors should satisfy in order to describe realizable physical measurements. We show how to find probability of measurement outcome in a graphical way. Read More

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. Read More

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. Read More

The problem of ordering of two-qubit states imposed by relative entropy of entanglement (E) in comparison to concurrence (C) and negativity (N) is studied. Analytical examples of states consistently and inconsistently ordered by the entanglement measures are given. In particular, the states for which any of the three measures imposes order opposite to that given by the other two measures are described. Read More

It is well known that for two qubits the upper bounds of the relative entropy of entanglement (REE) for a given concurrence as well as the negativity for a given concurrence are reached by pure states. We show that, by contrast, there are two-qubit mixed states for which the REE for some range of a fixed negativity is higher than that for pure states. Moreover, we demonstrate that a mixture of a pure entangled state and pure separable state orthogonal to it is likely to give the maximal REE. Read More

We study the ordering of two-qubit states with respect to the degree of bipartite entanglement using the Wootters concurrence -- a measure of the entanglement of formation, and the negativity -- a measure of the entanglement cost under the positive-partial-transpose-preserving operations. For two-qubit pure states, the negativity is the same as the concurrence. However, we demonstrate analytically on simple examples of various mixtures of Bell and separable states that the entanglement measures can impose different orderings on the states. Read More

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. Read More

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. Read More

A protocol for teleporting two qudits simultaneously in opposite directions using a single pair of maximally entangled qudits is presented. This procedure works provided that the product of dimensions of the two qudits to be teleported does not exceed the dimension of the individual qudits in the maximally entangled pair. Read More

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. Read More

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. Read More

The paper presents general protocols for quantum teleportation between multiparties. It is shown how N parties can teleport N unknown quantum states to M other parties with the use of N+M qudits in the maximally entangled state. It is also shown that a single pair of qudits in the maximally entangled state can be used to teleport two qudits in opposite directions simultaneously. Read More

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. Read More

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. Read More