Ali Saif M. Hassan, Pramod S. Joag
We show that the quantum discord and the measurement induced non-locality (MiN) in a bipartite quantum state is invariant under the action of a local quantum channel if and only if the channel is invertible. In particular, these quantities are invariant under a local unitary channel.
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We address unitary local (UL) invariance of bipartite pure states. Given a bipartite state $|Ψ>>=\sum_{ij} ψ_{ij}\: |i>_1\otimes |j>_2$ the complete characterization of the class of local unitaries $U_1\otimes U_2$ for which $U_1\otimes U_2 |Ψ>>=|Ψ>>$ is obtained.The two relevant parameters are the rank of the matrix $Ψ$, $[Ψ]_{ij}=ψ_{ij}$, and the number of its equal singular values, {\em i.e.} the degeneracy of the eigenvalues of the partial traces of $|Ψ>>$.
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.
We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show that such a quantifier is deeply connected with the operator Schmidt decomposition of the state. We compute the channel discrimination power exactly for pure states, and provide upper and lower bounds for general mixed states. We show that highly entangled states can outperform any state that passes the realignment criterion for separability. Furthermore, w…
It is well-known that the action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of formation is simply the entropy of the reduced density matrix minus the Holevo capacity. It is natural to ask if every bipartite state can be associated with some channel in this way. We show that the answer is negative.
We first investigate the one-shot static entanglement cost to simulate a bipartite quantum channel under the set of non-entangling channels. The lower bound on the static entanglement cost is given by the generalized robustness of the target channel as well as the robust-generating power of the channel, which implies that the cost necessary to generate a bipartite quantum channel might not be retrievable in general. Next, we conceive a set of quantum channels that extends the set of non-entangling channels. We find out that the one-shot static entanglement cost under the extended set of channe…
We propose a particular encoding for bipartite entangled states derived from multipartite cluster-type entangled coherent states (CTECSs). We investigate the effects of amplitude damping on the entanglement content of this bipartite state, as well as its usefulness as a quantum channel for teleportation. We find interesting relationships among the amplitude of the coherent states constituting the CTECSs, the number of subsystems forming the logical qubits (redundancy), and the extent to which amplitude damping affects the entanglement of the channel. For instance, in the sense of sudden death …
The traditional perspective in quantum resource theories concerns how to use free operations to convert one resourceful quantum state to another one. For example, a fundamental and well known question in entanglement theory is to determine the distillable entanglement of a bipartite state, which is equal to the maximum rate at which fresh Bell states can be distilled from many copies of a given bipartite state by employing local operations and classical communication for free. It is the aim of this paper to take this kind of question to the next level, with the main question being: What is the…
We explore how entanglement of a general bipartite system evolves when one subsystem undergoes the action of an arbitrary noisy channel. It is found that the dynamics of entanglement for general bipartite systems under the influence of such channel is determined by the channel's action on the maximally entangled state, which includes as a special case the results for two-qubit systems [Nature Physics 4, 99 (2008)]. In particular, for multi-qubit or qubit-qudit systems, we get a general factorization law for evolution equation of entanglement with one qubit being subject to a noisy channel. Our…
It is proved that there exist subspaces of bipartite tensor product spaces that have no orthonormal bases that can be perfectly distinguished by means of LOCC protocols. A corollary of this fact is that there exist quantum channels having sub-optimal classical capacity even when the receiver may communicate classically with a third party that represents the channel's environment.
The ability to teleport entanglement through maximally entangled mixed states as defined by concurrence and linear entropy is studied. We show how the teleported entanglement depends on the quality of the quantum channel used, as defined through its entanglement and mixedness, as well as the form of the target state to be teleported. We present new results based on the fidelity of the teleported state as well as an experimental set-up that is immediately implementable with currently available technology.
Entangling power and fidelity diagnostic for bipartite quantum channels
研究双向量子信道的保真度保持和纠缠生成能力，引入基于并发度和负性的纠缠能力度量，证明其凸性和局部后处理单调性，并推广到非乘积输入。
Controlling nonlocality of bipartite qubit states via quantum channels
本文分析了从X态导出的量子信道，刻画了破坏Bell CHSH条件的逆Choi-Jamiolkowski映射（非定域性生成），发现稳态偏离最大混合态时该信道区域收缩，并证明特殊情况仅需单参数即可简化非定域性分析。
Classical communication cost of a bipartite quantum channel assisted by non-signalling correlations
本文研究非信号关联辅助下双体量子信道的双向经典模拟成本，通过非信号超信道给出 one-shot 与渐近界、SDP表述及 seesaw 算法，并验证界的有效性与紧致性。
Entanglement cost of bipartite quantum channel discrimination under positive partial transpose operations
本研究提出双分量量子通道鉴别的纠缠成本理论，通过k-可注入PPT测试器分析最优成功概率，并利用SDP方法计算纠缠成本。
This thesis explores ways in which quantum channels and correlations (of both classical and quantum types) manifest themselves, and also studies the interplay between these two aspects in various physical settings. Quantum channels represent all possible evolutions of states allowed by quantum mechanics while correlations are intrinsic (nonlocal) properties of composite systems. There are four main problems that are addressed (i) the role played by initial system-bath correlations on the subsystem dynamics of an open quantum system, (ii) computation of correlations for two-qubit X-states, (iii…
We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.
The teleportation channel associated with an arbitrary bipartite state denotes the map that represents the change suffered by a teleported state when the bipartite state is used instead of the ideal maximally entangled state for teleportation. This work presents and proves an explicit expression of the teleportation channel for the teleportation using Weyl's projective unitary representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1, n>0, which has been known for n=1. This formula allows any correlation among the n bipartite mixed states, and an application shows the exis…
Subtle quantum properties offer exciting new prospects in optical communications. Quantum entanglement enables the secure exchange of cryptographic keys and the distribution of quantum information by teleportation. Entangled bright beams of light attract increasing interest for such tasks, since they enable the employment of well-established classical communications techniques. However, quantum resources are fragile and undergo decoherence by interaction with the environment. The unavoidable losses in the communication channel can lead to a complete destruction of useful quantum properties -- …
Diagrammatic representation and manipulation of tensor networks has proven to be a useful tool in mathematics, physics, and computer science. Here we present several important and mostly well-known theorems regarding the dualities between linear maps and bipartite pure quantum states, and the dualities between quantum channels and bipartite mixed quantum states, in diagrammatic form. The graphical presentation makes the proofs very compact and in some cases even intuitive.
Quantum discord is a measure based on local projective measurements which captures quantum correlations that may not be fully captured by entanglement. A change in the measurement process, achieved by replacing rank-one projectors with a weak positive operator-valued measure (POVM), allows one to define weak variants of quantum discord. In this work, we experimentally simulate the effect of a weak POVM on a nuclear magnetic resonance quantum information processor. The two-qubit system under investigation is part of a three-qubit system, where one of the qubits is used as an ancillary to implem…
Bounding the forward classical capacity of bipartite quantum channels
本文为二部量子信道提出多种前向经典通信度量，证明其可作为前向经典容量及经典反馈辅助点到点容量的上界，且部分度量可由半定规划计算。
The most general quantum object that can be shared between two distant parties is a bipartite channel, as it is the basic element to construct all quantum circuits. In general, bipartite channels can produce entangled states, and can be used to simulate quantum operations that are not local. While much effort over the last two decades has been devoted to the study of entanglement of bipartite states, very little is known about the entanglement of bipartite channels. In this work, we rigorously study the entanglement of bipartite channels as a resource theory of quantum processes. We present an…
We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free su…
Exact and local compression of quantum bipartite states
本文研究量子二分态的精确局域压缩，通过最小化特定纯态的施密特秩给出最小可实现维度的闭式表达式，并应用于量子信道的输出降维后处理。
We develop a framework which unifies seemingly different extension (or "joinability") problems for bipartite quantum states and channels. This includes well known extension problems such as optimal quantum cloning and quantum marginal problems as special instances. Central to our generalization is a variant of the Choi-Jamiolkowski isomorphism between bipartite states and dynamical maps which we term the "homocorrelation map": while the former emphasizes the preservation of the positivity constraint, the latter is designed to preserve statistical correlations, allowing direct contact with enta…
The high degree of control available over individual atoms enables precision tests of fundamental physical concepts. In this Letter, we experimentally study how precision measurements can be improved by preparing entangled states immune to the dominant source of decoherence. Using \Ca ions, we explicitly demonstrate the advantage from entanglement on a precision test of local Lorentz invariance for the electron. Reaching the quantum projection noise limit set by quantum mechanics, we observe for bipartite entangled states the expected gain of a factor of two in the precision. Under specific co…
Motivated by the recent studies on post-quantum steering, we generalize the notion of bipartite channel steering by introducing the concept of multipartite no-signaling channel assemblages. We first show that beyond the bipartite case, the no-signaling and quantum descriptions of channel assemblages do not coincide. Using the Choi-Jamiołkowski isomorphism, we present a complete characterization of these classes of assemblages and use this characterization to provide sufficient conditions for extremality of quantum channel assemblages within the set of all no-signaling channel assemblages. Fina…
We provide a method for witnessing nonseparability of quantum processes on shared systems, which uses the channel-state duality. The method uses a maximally entangled state as a resource. We show that using the resource provides significant advantage over the corresponding protocol for nonseparability detection without the resource.
The dynamics of entanglement and quantum discord for qubit-qutrit systems are studied in the presence of phase damping and amplitude damping noises. Both one way and two couplings of the marginal systems with the environments are considered. Entanglement sudden death is unavoidable under any setup, however, the required time span depends on the way of coupling. On the other hand, the dynamics of quantum discord strongly depends both on the nature of environment and on the number of dimensions of the Hilbert space of the coupled marginal system. We show that freezing and invariance of quantum d…
We introduce the entanglement gauge describing the combined effects of local operations and nonlocal unitary transformations on bipartite quantum systems. The entanglement gauge exploits the invariance of nonlocal properties for bipartite systems under local (gauge) transformations. This new formalism yields observable effects arising from the gauge geometry of the bipartite system. In particular, we propose a non-Abelian gauge theory realized via two separated spatial modes of the quantized electromagnetic field manipulated by linear optics. In this linear optical realization, a bi-partite st…
We investigate unitary operators acting on a tensor product space, with the property that the quantum channels they generate, via the Stinespring dilation theorem, are of a particular type, independently of the state of the ancilla system in the Stinespring relation. The types of quantum channels we consider are those of interest in quantum information theory: unitary conjugations, constant channels, unital channels, mixed unitary channels, PPT channels, and entanglement breaking channels. For some of the classes of bipartite unitary operators corresponding to the above types of channels, we p…
Milz and Strunz ({\it J. Phys. A}: {\bf{48}} [2015] 035306) recently studied the probabilities that two-qubit and qubit-qutrit states, randomly generated with respect to Hilbert-Schmidt (Euclidean/flat) measure, are separable. They concluded that in both cases, the separability probabilities (apparently exactly $\frac{8}{33}$ in the two-qubit scenario) hold {\it constant} over the Bloch radii ($r$) of the single-qubit subsystems, jumping to 1 at the pure state boundaries ($r=1$). Here, firstly, we present evidence that in the qubit-qutrit case, the separability probability is uniformly distrib…
Given a quantum channel it is possible to define the non-commutative operator graph whose properties determine a possibility of error-free transmission of information via this channel. The corresponding graph has a straight definition through Kraus operators determining quantum errors. We are discussing the opposite problem of a proper definition of errors that some graph corresponds to. Taking into account that any graph is generated by some POVM we give a solution to such a problem by means of the Naimark dilatation theorem. Using our approach we construct errors corresponding to the graphs …
Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses, such as those introduced by a realistic quantum communication channel, e.g. by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situa- tion reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement…
We study the entanglement dynamics of two qubits, each of which is embedded into its local amplitude-damping reservoir, and the entanglement distribution among all the bipartite subsystems including qubit-qubit, qubit-reservoir, and reservoir-reservoir. It is found that the entanglement can be stably distributed among all components, which is much different to the result obtained under the Born-Markovian approximation by C. E. López {\it et al.} [Phys. Rev. Lett. \textbf{101}, 080503 (2008)], and particularly it also satisfies an identity. Our unified treatment includes the previous results as…
We introduce a 3-parameter class of maps acting on a bipartite system that are a natural generalisation of the depolarizing channel (and include it as a special case). Then, we find the exact regions of the parameter space that alternatively determine a positive, completely positive, entanglement-breaking or entanglement-annihilating map. This model displays a much richer behaviour than the one shown by a simple depolarizing channel, yet it stays exactly solvable. As an example of this richness, PPT but not entanglement-breaking maps are found. A simple example of a positive yet indecomposable…
Discord, originally notable as a signature of bipartite quantum correlation,in fact can be nonzero classically, i.e., arising from noisy measurements by one of the two parties. Here we redefine classical discord to quantify channel distortion,in contrast to the previous restriction of classical discord to a state,and we then show a monotonic relationship between classical (channel) discord and channel distortion. We show that classical discord is equivalent to (doubly stochastic) channel distortion by numerically discovering a monotonic relation between discord and total-variation distance for…
A class of quantum protocols to teleport bipartite (entangled) states of two qubits is suggested. Our schemes require a single entangled pair shared by the two parties and the transmission of three bits of classical information, as well as a two-qubit gate with an additional qubit at the receiver' location. Noisy quantum channels are considered and the effects on both the teleportation fidelity and the entanglement of the replica are evaluated.
We extend the definition of the conditional min-entropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an operational interpretation as a guessing probability when one of the subsystems is classical. We then show that the extended conditional min-entropy can be used to fully characterize when two bipartite quantum channels are related to each other via a superchannel (also known as supermap or a comb) that is acting on one of the subsystems. This relation is a pre-orde…
After realising qutrit in the form of bipartite system we estimate from below the entropy gain under the action of the amplitude damping channel.
The ability to distribute entanglement over complex quantum networks is an important step towards a quantum internet. Recently, there has been significant theoretical effort, mainly focusing on the distribution of bipartite entanglement via a simple quantum network composed only of bipartite quantum channels. There are, however, a number of quantum information processing protocols based on multipartite rather than bipartite entanglement. Whereas multipartite entanglement can be distributed by means of a network of bipartite channels, a more natural way is to use a more general network, that is…
We analyze different aspects of multiparty communication over quantum memoryless channels and generalize some of key results known from bipartite channels to that of multiparty scenario. In particular, we introduce multiparty versions of minimal subspace transmission fidelity and entanglement transmission fidelity. We also provide alternative, local, versions of fidelities and show their equivalence to the global ones in context of capacity regions defined. The equivalence of two different capacity notions with respect to two types of the fidelities is proven. In analogy to bipartite case it i…
On super quantum discord for high-dimensional bipartite state
本文针对高维两体量子态，给出了有或无相位阻尼通道时超量子失谐的有效界限，并证明超量子失谐始终大于通常的量子失谐。
A bipartite quantum interaction corresponds to the most general quantum interaction that can occur between two quantum systems in the presence of a bath. In this work, we determine bounds on the capacities of bipartite interactions for entanglement generation and secret key agreement between two quantum systems. Our upper bound on the entanglement generation capacity of a bipartite quantum interaction is given by a quantity called the bidirectional max-Rains information. Our upper bound on the secret-key-agreement capacity of a bipartite quantum interaction is given by a related quantity calle…
We fully characterize bipartite entanglement-annihilating (EA) channels that destroy entanglement of any state shared by subsystems and, thus, should be avoided in any entanglement-enabled experiment. Our approach relies on extending the problem to EA positive maps, the cone of which remains invariant under concatenation with partially positive maps. Due to this invariancy, positive EA maps adopt a well characterization and their intersection with completely positive trace-preserving maps results in the set of EA channels. In addition to a general description, we also provide sufficient operat…
Inspired by the `computable cross norm' or `realignment' criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator. The corresponding Schmidt coefficients, or the associated symmetric polynomials, are regarded as quantities that can be used to characterize bipartite quantum states. In particular, starting from the realignment criterion, a family of necessary conditions for the separability of bipartite quantum states is derived. We conjecture that these conditions, which a…
The realism-based nonlocality (RBN) is a recently introduced measure that differs from the well-known Bell's nonlocality. For bipartite states, the RBN concerns how much an element of reality associated with a given observable is affected upon local measurements on a subsystem. Here, we present an analytical proof for the unitary invariance of the RBN and that it presents a monotonous behavior upon the action of unital and non-unital local quantum noise. We illustrate our results by employing the two-qubits Werner state and thermal quantum correlated states. We show how the RBN is limited by t…
Invariance of separability probability over reduced states in 4x4 bipartite systems
该研究针对4x4双量子系统的可分概率问题，利用Peres-Horodecki判据证明了rebit-rebit态可分概率为29/64，验证了Milz和Strunz关于可分概率仅依赖Bloch半径且恒定的猜想，还给出了不同测度下的积分公式。
We present a mathematical formulation of old teleportation protocol (original teleportation protocol introduced by Bennett et.al.) for mixed states and study in detail the role of mixedness of the two qubit quantum channel in a teleportation protocol. We show that maximally entangled mixed state described by the density matrix of rank-4 will be useful as a two qubit teleportation channel to teleport a single qubit mixed state when the teleportation channel parameter p1 greater than 0.5. Also we discuss the case when p1 less than equal to 0.5.
We demonstrate the existence of general constraints on distributed quantum correlations, which impose a trade-off on bipartite and multipartite entanglement at once. For all N-mode Gaussian states under permutation invariance, we establish exactly a monogamy inequality, stronger than the traditional one, that by recursion defines a proper measure of genuine N-partite entanglement. Strong monogamy holds as well for subsystems of arbitrary size, and the emerging multipartite entanglement measure is found to be scale invariant. We unveil its operational connection with the optimal fidelity of con…
Certifying bipartite entangled states with few local measurements: from separable stabilizers to applications
通过少量本地测量认证双粒子纠缠态，提供了一种简单有效的方法来确定量子态的保真度和纠缠特性。
Protecting Classical-Quantum Signals in Free Space Optical Channels
本文提出一种利用辅助纠缠二分态编码的纠错协议，可在自由空间光信道损耗与擦除条件下同时保护经典和量子信号，并提升相干态传输保真度。
We establish strict upper bounds on local quantum uncertainty (LQU) and skew information associated with state conversion via certain quantum channels. Specifically, we obtain a bound on the achievable LQU for bipartite channels whose Kraus operators commute with nondegenerate von Neumann measurements on the first subsystem, and this LQU bound is expressed in terms of the skew information for the first subsystem. Furthermore, we establish a bound on the skew information of one subsystem obtained from any initial bipartite state subject to any quantum steering channel, and this bound is express…
The concept of entanglement splitting is introduced by asking whether it is possible for a party possessing half of a pure bipartite quantum state to transfer some of his entanglement with the other party to a third party. We describe the unitary local transformation for symmetric and isotropic splitting of a singlet into two branches that leads to the highest entanglement of the output. The capacity of the resulting quantum channels is discussed. Using the same transformation for less than maximally entangled pure states, the entanglement of the resulting states is found. We discuss whether t…
We consider the standard quantum teleportation protocol where a general bipartite state is used as entanglement resource. We use the entanglement fidelity to describe how well the standard quantum teleportation channel transmits quantum entanglement and give a simple expression for the entanglement fidelity when it is averaged on all input states.
In this paper we find, for a class of bipartite quantum states, a nontrivial lower bound on the entropy gain resulting from the action of a tensor product of identity channel with an arbitrary channel. By means of that we then estimate (from below) the output entropy of the tensor product of dephasing channel with an arbitrary channel. Finally, we provide a characterization of all phase-damping channels resulting as particular cases of dephasing channels.
A system-ancilla bipartite state capable of containing the complete information of an unknown quantum channel acting on the system is called faithful. The equivalence between faithfulness of state and invertibility of the corresponding Jamiolkowski map proved by D'Ariano and Presti has been a useful characterization for ancilla-assisted process tomography albeit the proof was incomplete as they assumed trace nonincreasing quantum operations, not quantum channels. We complete the proof of the equivalence and introduce the generalization of faithfulness to various classes of quantum channels. We…
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a new bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.
Assume the quantum state of a bipartite system is known. The result of local von Neumann measurements can be described by maps from one subsystem to the other one. Main properties of these antilinear ''EPR-channel'' maps are shortly discussed. Talk in honour of Jan Lopuszanski.
Unlike the entanglement of quantum states, very little is known about the entanglement of bipartite channels, called dynamical entanglement. Here we work with the partial transpose of a superchannel, and use it to define computable measures of dynamical entanglement, such as the negativity. We show that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost. We discover a family of dynamical entanglement measures that provide necessary and sufficient conditions for bipartite channel simulation under local operations and classical communicat…
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