Pure Entangled State Research Articles

Quantifying Causal Influences in the Presence of a Quantum Common Cause.

Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question, we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even postquantum nature of a common cause. In particular, by considering the simplest instrumental scenario-for which violation of Bell inequalities is not possible-we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus, answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.

Optimal extensions of resource measures and their applications

We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e. an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a new technique to extend pure state entanglement measures to mixed bipartite states.

Bell-type inequalities of $$l_1$$-norm of coherence

In this paper, we investigate the Bell-type inequalities of $$l_1$$ -norm of coherence for two- or three-qubit system and establish the relation between the $$l_1$$ -norm of coherence and the degree of coherence. It is found that the upper bounds of the inequalities can be much stronger. The Bell-type inequality of $$l_1$$ -norm of coherence for two-qubit system can be violated by all two-qubit entangled pure states, and thus, it can serve as an entanglement witness. The Bell-type inequalities can also be violated by quantum systems which pass through the uncorrelated or correlated channels. Particularly, the partial correlations among consecutive uses of the correlated channel can enhance the value of the left-hand side of the Bell-type inequalities.

Extremal states of qubit-qutrit system with maximally mixed marginals

We study extremal elements of the convex set of qubit-qutrit states whose marginals are maximally mixed. In the two qubit case, it is known that every extreme state of such a convex set is a maximally entangled pure state. In qubit-qutrit case, pure states do not exist in the convex set. We construct mixed extreme states of ranks 2 and 3. Second rank extremal state is entangled whereas third rank extreme element is separable. Parthasarathy obtained an upper bound on the rank of extreme states of such a convex set of a bipartite system of n and m dimensions as n2+m2−1. Thus for a qubit-qutrit system, the rank of an extreme element should be less than 12. Since Parthasarathy's bound for two qubit system is 7 and all extreme elements are of rank one, Rudolph posed a question about its tightness. We establish that Parthasarathy's upper bound is tight for qubit-qutrit system.

Impossibility of Distinguishing Two Preparations for a Pure State from No-signaling

A pure state of a physical system can be prepared in an infinite number of ways. Quantum theory dictates that given a pure state of a physical system it is impossible to distinguish two preparation procedures. Here, we show that the impossibility of distinguishing two preparation procedures for the same pure state follows from the no-signaling principle. Extending this result for a pure bipartite entangled state entails that the impossibility of distinguishing two preparation procedures for a mixed state follows from the impossibility of distinguishing two preparations for a pure bipartite state.Quanta 2020; 9: 16–21.

Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement

By numerically exact calculations of spin-1/2 antiferromagnetic Heisenberg models on small clusters, we demonstrate that quantum entanglement between subsystems $A$ and $B$ in a pure ground state of a whole system $A+B$ can induce thermal equilibrium in subsystem $A$. Here, the whole system is bipartitoned with the entanglement cut that covers the entire volume of subsystem $A$. Temperature ${\cal T}_{A}$ of subsystem $A$ is not a parameter but can be determined from the entanglement von Neumann entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$ calculated for the ground state of the whole system. We show that temperature ${\cal T}_{A}$ can be derived by minimizing the relative entropy for the reduced density matrix operator of subsystem $A$ and the Gibbs state (i.e., thermodynamic density matrix operator) of subsystem $A$ with respect to the coupling strength between subsystems $A$ and $B$. Temperature ${\cal T}_{A}$ is essentially identical to the thermodynamic temperature, for which the entropy and the internal energy evaluated using the canonical ensemble in statistical mechanics for the isolated subsystem $A$ agree numerically with the entanglement entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$.Fidelity calculations ascertain that the reduced density matrix operator of subsystem $A$ for the pure but entangled ground state of the whole system $A+B$ matches, within a maximally $1.5\%$ error in the finite size clusters studied, the thermodynamic density matrix operator of subsystem $A$ at temperature ${\cal T}_{A}$. We argue that quantum fluctuation in an entangled pure state can mimic thermal fluctuation in a subsystem. We also provide two simple but nontrivial analytical examples of free bosons and free fermions for which these statements are exact. We furthermore discuss implications and possible applications of our finding.

Simultaneous certification of entangled states and measurements in bounded dimensional semiquantum games

Certification of quantum systems and operations is a central task in quantum information processing. Most current schemes rely on a tomography with fully characterized devices, while this may not be met in real experiments. Device characterizations can be removed with device-independent tests, but it is technically challenging at the moment. In this paper, we investigate the problem of certifying entangled states and measurements via semiquantum games, a type of nonlocal quantum games with well characterized quantum inputs, balancing practicality and device independence. We first design a specific bounded-dimensional semiquantum game, with which any pure entangled state and Bell state measurement operators can be simultaneously certified. Afterward via a duality treatment of state and measurement, we interpret the dual form of this game as a source-independent bounded-dimensional entanglement swapping protocol and show the whole process, including any entangled projector and Bell states, can be certified with this protocol. In particular, our results do not require a complete Bell state measurement, which is beneficial for experiments and practical use.Received 11 February 2020Accepted 12 August 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033400Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionNonlocalityQuantum correlations in quantum informationQuantum entanglementQuantum Information

Detecting Topological Order at Finite Temperature Using Entanglement Negativity.

We propose a diagnostic for finite temperature topological order using "topological entanglement negativity," the long-range component of a mixed-state entanglement measure. As a demonstration, we study the toric code model in d spatial dimensions for d=2,3,4, and find that when topological order survives thermal fluctuations, it possesses a nonzero topological entanglement negativity, whose value is equal to the topological entanglement entropy at zero temperature. Furthermore, we show that the Gibbs state of 2D and 3D toric code at any nonzero temperature, and that of 4D toric code above a certain critical temperature, can be expressed as a convex combination of short-range entangled pure states, consistent with the absence of topological order.

Nonlocality, entanglement, and randomness in different conflicting interest Bayesian games

We analyse different Bayesian games where payoffs of players depend on the types of players involved in a two-player game. The dependence is assumed to commensurate with the CHSH game setting. For this, we consider two different types of each player (Alice and Bob) in the game, thus resulting in four different games clubbed together as one Bayesian game. Considering different combinations of common interest, and conflicting interest coordination and anti-coordination games, we find that quantum strategies are always preferred over classical strategies if the shared resource is a pure non-maximally entangled state. However, when the shared resource is a class of mixed state, then quantum strategies are useful only for a given range of the state parameter. Surprisingly, when all conflicting interest games (Battle of the Sexes game and Chicken game) are merged into the Bayesian game picture, then the best strategy for Alice and Bob is to share a set of non-maximally entangled pure states. We demonstrate that this set not only gives higher payoff than any classical strategy, but also outperforms a maximally entangled pure Bell state, mixed Werner states, and Horodecki states. We further propose the representation of a special class of Bell inequality- tilted Bell inequality, as a common as well as conflicting interest Bayesian game. We thereafter, study the effect of sharing an arbitrary two-qubit pure state and a class of mixed state as quantum resource in those games; thus verifying that non-maximally entangled states with high randomness help attain maximum quantum benefit. Additionally, we propose a general framework of a two-player Bayesian game for d-dimensions Bell-CHSH inequality, with and without the tilt factor.

Quantum entanglement criterion based on extended complex plane

The state space of quantum system is a Hilbert space with complex inner product. The two states quantum system is called a qubit. Its quantum state gives different geometric representations. The density matrix of a quantum state can describe all the information of a quantum system. In particular, the representation of quantum pure states by means of extended complex plane is given. On this basis, combined with the matrix representation of the quantum states of the composite system, the criteria for quantum entanglement and separability are studied. Finally, the measurement method of quantum pure state entanglement is given.

Quantum state sharing with mixing state from six-qubit entangled pure one

In this paper the possibility of using mixing entangled states as quantum channel to accomplish quantum state sharing (QSTS) is considered. As a preliminary study, an efficient tripartite QSTS scheme is put forward by utilizing a mixing entangled state, which is a derivative of a six-qubit entangled pure state under a two-qubit confusion. Some specific discussions about the QSTS scheme are made, including the issues of the scheme determinacy, the sharer symmetry, the scheme security and the essential role of quantum channel as well as the current experimental feasibility.

Arbitrarily Many Independent Observers Can Share the Nonlocality of a Single Maximally Entangled Qubit Pair.

Alice and Bob each have half of a pair of entangled qubits. Bob measures his half and then passes his qubit to a second Bob who measures again and so on. The goal is to maximize the number of Bobs that can have an expected violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality with the single Alice. This scenario was introduced in [R. Silva et al., Phys. Rev. Lett. 114, 250401 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.250401] where the authors mentioned evidence that when the Bobs act independently and with unbiased inputs then at most two of them can expect to violate the CHSH inequality with Alice. Here we show that, contrary to this evidence, arbitrarily many independent Bobs can have an expected CHSH violation with the single Alice. Our proof is constructive and our measurement strategies can be generalized to work with a larger class of two-qubit states that includes all pure entangled two-qubit states. Since violation of a Bell inequality is necessary for device-independent tasks, our work represents a step towards an eventual understanding of the limitations on how much device-independent randomness can be robustly generated from a single pair of qubits.

Analysis of quantum coherence for localized fermionic systems in an accelerated motion

Although quantum coherence is a well known phenomenon in quantum information theory and quantum optics, it has been investigated from the resource theory perspective only recently. Furthermore, quantum coherence has important implications in relativistic quantum information where the degradation of entanglement can be attributed to decoherence. In this paper, we investigate the quantum coherence of 1+1 Dirac field modes localized in a cavity as observed by two relatively accelerated observers. The acceleration is assigned very small values and its effects are investigated in a perturbative regime. For this purpose, we use α parameterized two-qubit pure entangled state and a Werner state. We find that coherence shows a periodic degradation due to accelerated motion. However, this degradation can be balanced by adjusting the durations of uniform and accelerated motion. Moreover, it is found that dynamics of quantum coherence closely resembles that of entanglement under the same settings. This similarity confirms the recent attempts to relate the resource theories of coherence and entanglement in a relativistic regime.

Independence of work and entropy for equal-energetic finite quantum systems: Passive-state energy as an entanglement quantifier.

Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detailed investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPOs) as free, to compare the amount of extractable work from two different quantum states. Under the EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive-state energy is a concave function, and, for EE states, it becomes proportional to the ergotropy in absolute sense. Invariance of the passive-state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states. Furthermore, due to the nonadditivity of passive-state energy for the different system Hamiltonians, one can generate Vidal^{'}s monotones which would give the optimal probability for pure entangled state transformation. This measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three-qubit pure entangled states.

Protecting the entanglement of two-qubit over quantum channels with memory via weak measurement and quantum measurement reversal* *Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2017MF040).

Based on the quantum technique of the weak measurement and quantum measurement reversal (WMR), we propose a scheme to protect entanglement for an entangled two-qubit pure state from four typical quantum noise channels with memory, i.e., the amplitude damping channel, the phase damping channel, the bit flip channel, and the depolarizing channel. For a given initial state | ψ 〉 = a| 00 〉 + d| 11 〉, it is found that the WMR operation indeed helps to protect entanglement from the above four quantum channels with memory, and the protection effect of WMR scheme is better when the coefficient a is small. For the other initial state | ϕ 〉 = b| 01 〉 + c| 10 〉, the effect of the protection scheme is the same regardless of the coefficient b and the WMR operation can protect entanglement in the amplitude damping channel with memory. Moreover, the protection of entanglement in quantum noise channels without memory in contrast to the results of the channels with memory is more effective. For | ψ 〉 or | ϕ 〉, we also find that the memory parameters play a significant role in the suppression of entanglement sudden death and the initial entanglement can be drastically amplified. Another more important result is that the relationship between the concurrence, the memory parameter, the weak measurement strength, and quantum measurement reversal strength is found through calculation and discussion. It provides a strong basis for the system to maintain maximum entanglement in the nosie channel.

Activating Hidden Metrological Usefulness.

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian for which a given quantum state performs the best compared to separable states. We obtain analytically the optimal Hamiltonian for some quantum states with a high symmetry. We show that all bipartite entangled pure states outperform separable states in metrology. Some potential applications of the results are also suggested.

Locally distinguishing quantum states with limited classical communication

We consider different settings of the task to distinguish pure orthogonal quantum states under local operations and a limited amount of classical communication. In the first setting, the spatially separated parties are allowed to perform only local projective measurements without any classical communication during the measurements. Under such a restricted class of operations, if the states are indistinguishable, then within a second group of settings, the parties are allowed to use an additional resource for the distinguishing. The additional resource is either a pure entangled state or multiple identical copies of the given states. Comparisons between these two types of resources are also done in certain cases. Both probabilistic and perfect discrimination of the states are considered for the second group of settings. Within a third setting, the parties perform local projective measurements with a restriction on the availability of classical communication during the measurements. But in this setting the parties are allowed to use a maximally entangled state as a resource.

Z-eigenvalue inclusion theorem of tensors and the geometric measure of entanglement of multipartite pure states

In our paper, we concentrate on the Z-eigenvalue inclusion theorem and its application in the geometric measure of entanglement of multipartite pure states. We present a new Z-eigenvalue inclusion theorem by virtue of the division and classification of tensor elements, and tighter bounds of Z-spectral radius of weakly symmetric nonnegative tensors are obtained. As applications, we present some theoretical upper and lower bounds of entanglement for symmetric pure state with nonnegative amplitudes for two kinds of geometric measures with different definitions, respectively.

The QBIT Theory of Consciousness.

A quale is a superdense pack of quantum information encoded in maximally entangled pure states. Question 2: How are qualia generated? When a pack of quantum information is compressed beyond a certain threshold, a quale is generated. Question 3: Why are qualia subjective? A quale is subjective because a pack of information encoded in maximally entangled pure states are essentially private and unshareable. Question 4: Why does a quale have a particular meaning? A pack of information within a cognitive system gradually obtains a particular meaning as it undergoes a progressive process of interpretation performed by an internal model installed in the system. This paper introduces the QBIT theory of consciousness, and explains its basic assumptions and conjectures.

Fidelity deviation in quantum teleportation with a two-qubit state

Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.