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Register a new userQuantum superposition of the order of parties as a communication resource
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In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared entanglement can increase the probability for the parties to arrive at the correct value of the function, compared to classical resources. Here we show that quantum superpositions of the direction of communication between parties can also serve as a resource to improve the probability of success. We present a tripartite task for which such a superposition provides an advantage compared to the case where the parties communicate in a fixed order. In a more general context, our result also provides the first semi-device-independent certification of the absence of a definite order of communication.
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We propose a novel approach to qubit thermometry using a quantum switch, that introduces an indefinite causal order in the probe-bath interaction, to significantly enhance the thermometric precision. The resulting qubit probe shows improved precision in both low and high temperature regimes when compared to optimal qubit probes studied previously. It even performs better than a Harmonic oscillator probe, in spite of having only two energy levels rather than an infinite number of energy levels as that in a harmonic oscillator. We thereby show unambiguously that quantum resources such as the quantum switch can significantly improve equilibrium thermometry. We also derive a new form of thermodynamic uncertainty relation that is tighter and depends on the energy gap of the probe. The present work may pave the way for using indefinite causal order as a metrological resource.
In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.
A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition state transformations. These conditions strictly depend on the scalar products of the basis states and reduce to the well-known majorization condition for quantum coherence in the limit of orthonormal basis. To further superposition-free transformations of $d$-dimensional systems, we provide superposition-free operators for a deterministic transformation of superposition states. The linear independence of a finite number of basis states requires a relation between the scalar products of these states. With this information in hand, we determine the maximal superposition states which are valid over a certain range of scalar products. Notably, we show that, for $dgeq3$, scalar products of the pure superposition-free states have a greater place in seeking maximally resourceful states. Various explicit examples illustrate our findings.
Just recently, complementarity relations (CRs) have been derived from the basic rules of Quantum Mechanics. The complete CRs are equalities involving quantum coherence, $C$, quantum entanglement, and predictability, $P$. While the first two are already quantified in the resource theory framework, such a characterization lacks for the last. In this article, we start showing that, for a system prepared in a state $rho$, $P$ of $rho$, with reference to an observable $X$, is equal to $C$, with reference to observables mutually unbiased (MU) to $X$, of the state $Phi_{X}(rho)$, which is obtained from a non-revealing von Neumann measurement (NRvNM) of $X$. We also show that $P^X(rho)>C^{Y}(Phi_{X}(rho))$ for observables not MU. Afterwards, we provide quantum circuits for implementing NRvNMs and use these circuits to experimentally test these (in)equalities using the IBMs quantum computers. Furthermore, we give a resource theory for predictability, identifying its free quantum states and free quantum operations and discussing some predictability monotones. Besides, after applying one of these predictability monotones to study bipartite systems, we discuss the relation among the resource theories of quantum coherence, predictability, and purity.
The characterization of quantum correlations in terms of information-theoretic resource has been a fruitful approach to understand the power of quantum correlations as a resource. While bipartite entanglement and Bell inequality violation in this setting have been extensively studied, relatively little is known about their multipartite counterpart. In this paper, we apply and adapt the recently proposed definitions of multipartite nonlocality [Phys. Rev. A 88, 014102] to the three- and four-partite scenario to gain new insight on the resource aspect of multipartite nonlocal quantum correlations. Specifically, we show that reproducing certain tripartite quantum correlations requires mixtures of classical resources --- be it the ability to change the groupings or the time orderings of measurements. Thus, when seen from the perspective of biseparable one-way classical signaling resources, certain tripartite quantum correlations do not admit a definite causal order. In the four- partite scenario, we obtain a superset description of the set of biseparable correlations which can be produced by allowing two groups of bipartite non-signaling resources. Quantum violation of the resulting Bell-like inequalities are investigated. As a byproduct, we obtain some new examples of device-independent witnesses for genuine four-partite entanglement, and also device-independent witnesses that allows one to infer the structure of the underlying multipartite entanglement.
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