Quantum entanglement, a fundamental property ensuring security of key distribution and efficiency of quantum computing, is extremely sensitive to decoherence. Different procedures have been developed in order to recover entanglement after propagation over a noisy channel. However, besides a certain amount of noise, entanglement is completely lost. In this case the channel is called entanglement breaking and any multi-copy distillation methods cannot help to restore even a bit of entanglement. We report the experimental realization of a new method which restores entanglement from a single photon entanglement breaking channel. The method based on measurement of environmental light and quantum feed-forward correction can reveal entanglement even if this one completely disappeared. This protocol provides new elements to overcome decoherence effects.
We experimentally demonstrate that entanglement of bi-photon polarization state can be restored by spectral filters. This restoration procedure can be viewed as a new class of quantum eraser, which retrieves entanglement rather than just interference by manipulating an ancillary degree of freedom.
Generation of polarization-entangled photons from quantum dots via the biexciton-exciton recombination cascade is complicated by the presence of an energy spitting between the intermediate excitonic levels, which severely degrades the quality of the entangled photon source. In this paper we present a novel, conceptually simple and straightforward proposal for restoring the entanglement of said source by applying a cascade of time-dependent operations on the emitted photons. This is in striking contrast with the techniques usually employed, that act on the quantum emitter itself in order to rem…
The distribution of entangled quantum systems among two or more nodes of a network is a key task at the basis of quantum communication, quantum computation and quantum cryptography. Unfortunately the transmission lines used in this procedure can introduce so much perturbations and noise in the transmitted signal that prevent the possibility of restoring quantum correlations in the received messages either by means of encoding optimization or by exploiting local operations and classical communication. In this work we present a procedure which allows one to improve the performance of some of the…
We show the rather counterintuitive result that entangled input states can strictly enhance the distinguishability of two entanglement-breaking channels.
We consider composability of quantum channels from a limited amount of entanglement via local operations and classical communication (LOCC). We show that any $k$-partially entanglement breaking channel can be composed from an entangled state with Schmidt number of $k$ via one-way LOCC. From the entanglement assisted construction we can reach an alternative definition of partially entanglement breaking channels.
Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is of significance to investigate the entanglement dynamics in terms of quantum channels. We study the entanglement-breaking channels and present the necessary and sufficient conditions for a quantum channel to an entanglement-breaking one for qubit systems. Furthermore, a concept of strong entanglement-breaking channel is introduced. The amendment of entangleme…
Entanglement-breaking channels are quantum channels transforming entangled states to separable states. Despite a detailed discussion of their operational structure, to be found in the literature, studies on dynamical characteristics of this type of maps are yet limited. We consider one of the basic questions: for Lindblad-type dynamics, when does a given channel break entanglement? We discuss the finite-dimensional case where the quantification of entanglement via entanglement witnesses is utilized. For the general setup, we use the method of quantum speed limit to derive lower bounds on entan…
Nonclassicality and entanglement are notions fundamental to quantum information processes involving continuous variable systems. That these two notions are intimately related has been intuitively appreciated for quite some time. An aspect of considerable interest is the behaviour of these attributes of a state under the action of a noisy channel. Inspired by the notion of entanglement-breaking channels, we define the concept of nonclassicality-breaking channels in a natural manner. We show that the notion of nonclassicality-breaking is essentially equivalent---in a clearly defined sense of the…
This paper considers the use an entanglement breaking channel in the construction of a secure bit-commitment protocol. It is shown that this can be done via a depolarizing quantum channel.
It is shown that spontaneous symmetry breaking does not modify the ground-state entanglement of two spins, as defined by the concurrence, in the XXZ- and the transverse field Ising-chain. Correlation function inequalities, valid in any dimensions for these models, are presented outlining the regimes where entanglement is unaffected by spontaneous symmetry breaking.
Eigenstate Thermalization Hypothesis(ETH) has played a pivotal role in understanding ergodicity and its breaking in isolated quantum many-body systems. Recent experiment on 51-atom Rydberg quantum simulator and subsequent theoretical analysis have shown that hardcore kinetic constraint can lead to weak ergodicity breaking. In this work, we demonstrate, using 1d spin-1 PXP chains, that miscellaneous type of ergodicity can be realized by adjusting the hardcore constraints between different components of nearest neighbor spins. This includes ETH violation due to emergent shattering of Hilbert spa…
We discuss the cases where local decoherence selectively degrades one type of entanglement more than other types. A typical case is called state ordering change, in which two input states with different amounts of entanglement undergoes a local decoherence and the state with the larger entanglement results in an output state with less entanglement than the other output state. We are also interested in a special case where the state with the larger entanglement evolves to a separable state while the other output state is still entangled, which we call selective entanglement breaking. For three-…
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.
It shown that when one of the components of a product channel is entanglement breaking, the output state with maximal p-norm is always a product state. This result complements Shor's theorem that both minimal entropy and Holevo capacity are additive for entanglement breaking channels. It is also shown how Shor's results can be recovered from the p-norm results by considering their behavior for p close to one.
We give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank one operators" and use it to describe the complementary channels. We also give necessary and sufficient condition of entanglement-breaking for a general quantum Gaussian channel. Application of this condition to one-mode channels provides several new cases where the additivity conjecture holds in full generality.
In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and some sufficient separability criteria from entanglement-breaking channels are given.
The inevitable interaction between quantum systems and environment induces effects of decoherence which may be so strong as to destroy any initial entanglement between the systems, a phenomenon known as "entanglement breaking". Here we show the simplest examples where the combination of two entanglement-breaking channels into a joint correlated-noise environment reactivates the distribution of entanglement, with classes of entangled states which are perfectly transmitted from a middle station (Charlie) to two remote stations (Alice and Bob). Surprisingly, this reactivation is induced by the pr…
We investigate entanglement breaking times of Markovian evolutions in discrete and continuous time. In continuous time, we characterize which Markovian evolutions are eventually entanglement breaking, that is, evolutions for which there is a finite time after which any entanglement initially present has been destroyed by the noisy evolution. In the discrete time framework, we consider the entanglement breaking index, that is, the number of times a quantum channel has to be composed with itself before it becomes entanglement breaking. The PPT-square conjecture is that every PPT quantum channel …
Entanglement is essential to many quantum information applications, but it is easily destroyed by quantum decoherence arising from interaction with the environment. We report the first experimental demonstration of an entanglement-based protocol that is resilient to loss and noise which destroy entanglement. Specifically, despite channel noise 8.3 dB beyond the threshold for entanglement breaking, eavesdropping-immune communication is achieved between Alice and Bob when an entangled source is used, but no such immunity is obtainable when their source is classical. The results prove that entang…
Originated from the superposition principle in quantum mechanics, coherence has been extensively studied as a kind important resource in quantum information processing. We investigate the distinguishability of coherence-breaking channels with the help of quantum entanglement. By explicitly computing the minimal error probability of channel discrimination, it is shown that entanglement can enhance the capacity of coherence-breaking channel distinguishability with same types for some cases while cannot enhanced for some other cases. For coherence-breaking channels with different types, the chann…
It is known that the minimal output entropy is additive for any product of entanglement breaking (EB) channels. The same is true for the Renyi entropy, where additivity is equivalent to multiplicativity of the $1 \rightarrow q$ norm for all $q \ge 1$. In this paper we consider the related question of multiplicativity of the $2 \rightarrow q$ norm for entanglement breaking channels. We prove that multiplicativity holds in this case for certain classes of EB channels, including both the CQ and QC channels.
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed. After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ansätze, especially to reduce the quantum register size. It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal …
Entangled systems in experiments may be lost or offline in distributed quantum information processing. This inspires a general problem to characterize quantum operations which result in breaking of entanglement or not. Our goal in this work is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled…
We study the ground-state properties of bosons loaded into the $p$-band of a one dimensional optical lattice. We show that the phase diagram of the system is substantially affected by the anharmonicity of the lattice potential. In particular, for a certain range of tunneling strength, the full many-body ground state of the system becomes degenerate. In this region, an additional symmetry of the system, namely the parity of the occupation number of the chosen orbital, is spontaneously broken. The state with nonvanishing staggered angular momentum, which breaks the time-reversal symmetry, become…
We study the entanglement-breaking (EB) space, such that the entanglement of formation (EOF) of a bipartite quantum state is additive when its range is an EB subspace. We systematically construct the EB spaces in the Hilbert space $\bbC^m\otimes\bbC^3$, and the $2$-dimensional EB space in $\bbC^2\otimes\bbC^n$. We characterize the expression of two-qubit states of rank two with nonadditive EOF, if they exist. We further apply our results to construct EB spaces of an arbitrarily given dimensions. We show that the example in [PRL 89,027901(2002)] is a special case of our results. We further work…
A bipartite quantum channel represents the interaction between systems, generally allowing for exchange of information. A special class of bipartite channels are the no-signaling ones, which do not allow communication. In Ref. [1] it has been conjectured that all no-signaling channels are mixtures of entanglement-breaking and localizable channels, which require only local operations and entanglement. Here we provide the general realization scheme, giving a counterexample to the conjecture.
In the paper, we give a characterization of arbitrary $n$-mode Gaussian coherence breaking channels (GCBCs) and show the tensor product of a GCBC and arbitrary a Gaussian channel maps all input states into product states. The inclusion relation among GCBCs, Gaussian positive partial transpose channels (GPPTC), entanglement breaking channels (GEBC) and Gaussian classical-quantum channels (GCQC) is displayed. Finally, we prove that Gaussian classical ($χ$-) capacity for the tensor products of GCBCs and arbitrary Gaussian channels is additive.
Structural approximations to positive, but not completely positive maps are approximate physical realizations of these non-physical maps. They find applications in the design of direct entanglement detection methods. We show that many of these approximations, in the relevant case of optimal positive maps, define an entanglement breaking channel and, consequently, can be implemented via a measurement and state-preparation protocol. We also show how our findings can be useful for the design of better and simpler direct entanglement detection methods.
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for channel capacity) that can occur.
In this paper we give a general integral representation for separable states in the tensor product of infinite dimensional Hilbert spaces and provide the first example of separable states that are not countably decomposable. We also prove the structure theorem for the quantum communication channels that are entanglement-breaking, generalizing the finite-dimensional result of M. Horodecki, Ruskai and Shor. In the finite dimensional case such channels can be characterized as having the Kraus representation with operators of rank 1. The above example implies existence of infinite-dimensional enta…
We study finite-dimensional product Hilbert spaces, coupled spin systems, entanglement and energy level crossing. The Hamilton operators are based on the Pauli group. We show that swapping the interacting term can lead from unentangled eigenstates to entangled eigenstates and from an energy spectrum with energy level crossing to avoided energy level crossing.
Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and …
The occurrence of entanglement sudden death in the evolution of a bipartite system depends on both the initial state and the channel responsible for the evolution. An extreme case is that of entanglement braking channels, which are channels that acting on only one of the subsystems drives them to full disentanglement regardless of the initial state. In general, one can find certain combinations of initial states and channels acting on one or both subsystems that can result in entanglement sudden death or not. Neither the channel nor the initial state, but their combination, is responsible for …
We present a general method to derive entanglement breaking (EB) conditions for continuous-variable quantum gates. We start with an arbitrary entanglement witness, and reach an EB condition. The resultant EB condition is applicable not only for quantum channels but also for general quantum operations, namely, trace-non-increasing class of completely positive maps. We illustrate our method associated with a quantum benchmark based on the input ensemble of Gaussian distributed coherent states. We also exploit our idea for channels acting on finite dimensional systems and present a Schmidt-number…
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. To our knowledge the present effects provide the first qualitative borderline between superadditivities of bipartite and multipartite systems.
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen $\textit{et al}$, J. Phys. A 53, 125302 (2020)]. We apply our …
Entanglement breaking channels play a significant role in quantum information theory. In this work we investigate qubit channels through their property of `non-locality breaking', defined in a natural way but within the purview of CHSH nonlocality. This also provides a different perspective on the relationship between entanglement and nonlocality through the dual picture of quantum channels instead of through states. For a channel to be entanglement breaking it is sufficient to `break' the entanglement of maximally entangled states. We provide examples to show that for CHSH nonlocality breakin…
We report a bulk optics experiment demonstrating the possibility of restoring the entanglement distribution through noisy quantum channels by inserting a suitable unitary operation (filter) in the middle of the transmission process. We focus on two relevant classes of single-qubit channels consisting in repeated applications of rotated phase damping or rotated amplitude damping maps, both modeling the combined Hamiltonian and dissipative dynamics of the polarization state of single photons. Our results show that interposing a unitary filter between two noisy channels can significantly improve …
A simple scheme is presented for achieving effectively maximal pure-state entanglement between non-interacting atoms through purely collective decay and controlled symmetry breaking. The scheme requires no measurements or feedback or even knowledge of the initial states of the atoms. It relies on breaking the symmetry of the system Hamiltonian to ensure the existence of a unique attractive steady state and minimal control to achieve almost perfect overlap of this steady state with the maximally entangled singlet state. We demonstrate how our scheme can be implemented for two qubits encoded in …
We investigate the nullspace structures of entanglement breaking channels, and related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.
Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum channels, and optimal ensemble length with entanglement breaking rank. The multiplicative domain is an important operator structure in the theory of completely positive maps. We introduce a new technique to determine if a channel is entanglement breaking and to evaluate entanglement breaking rank, based on an analysis of multiplicative domains determined by comple…
We introduce and study the entanglement breaking rank of an entanglement breaking channel. We show that the entanglement breaking rank of the channel $\mathfrak Z: M_d \to M_d$ defined by \begin{align*} \mathfrak Z(X) = \frac{1}{d+1}(X+\text{Tr}(X)\mathbb I_d) \end{align*} is $d^2$ if and only if there exists a symmetric informationally-complete POVM in dimension $d$.
We consider the important class of quantum operations (completely positive trace-preserving maps) called entanglement breaking channels. We show how every such channel induces stochastic matrix representations that have the same non-zero spectrum as the channel. We then use this to investigate when entanglement breaking channels are primitive, and prove this depends on primitivity of the matrix representations. This in turn leads to tight bounds on the primitivity index of entanglement breaking channels in terms of the primitivity index of the associated stochastic matrices. We also present ex…
Ergodicity breaking is observed in the blockade regime of Rydberg atoms arrays, in the form of low entanglement eigenstates known as scars, which fail to thermalize. The signature of these states persists in periodically driven systems, where they coexist with an extensive number of chaotic states. Here we investigate a quantum cellular automaton based on the classical rule that updates a site if its two neighbors are in the lower state. We show that the breaking of ergodicity extends to chaotic states. The dynamical breaking of ergodicity is controlled by chiral quasiparticle excitations whic…
We study the effect of symmetry breaking in a quantum phase transition on pairwise entanglement in spin-1/2 models. We give a set of conditions on correlation functions a model has to meet in order to keep the pairwise entanglement unchanged by a parity symmetry breaking. It turns out that all mean-field solvable models do meet this requirement, whereas the presence of strong correlations leads to a violation of this condition. This results in an order-induced enhancement of entanglement, and we report on two examples where this takes place.
We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipart…
In \cite{CMW19}, the authors introduced $k$-entanglement breaking linear maps to understand the entanglement breaking property of completely positive maps on taking composition. In this article, we do a systematic study of $k$-entanglement breaking maps. We prove many equivalent conditions for a $k$-positive linear map to be $k$-entanglement breaking, thereby study the mapping cone structure of $k$-entanglement breaking maps. We discuss examples of $k$-entanglement breaking maps and some of their significance. As an application of our study, we characterize completely positive maps that reduce…
This paper continues the study of stochastic maps, or channels, which break entanglement. We give a detailed description of entanglement-breaking qubit channels, and show that such maps are precisely the convex hull of those known as classical-quantum channels. We also review the complete positivity conditions in a canonical parameterization and show how they lead to entanglement-breaking conditions.
We introduce and investigate a family of entanglement-annihilating channels. These channels are capable of destroying any quantum entanglement within the system they act on. We show that they are not necessarily entanglement breaking. In order to achieve this result we analyze the subset of locally entanglement-annihilating channels. In this case, the same local noise applied on each subsystem individually is less entanglement annihilating (with respect to multi-partite entanglement) as the number of subsystems is increasing. Therefore, the bipartite case provides restrictions on the set of lo…
