Distribution of Quantum Coherence in Multipartite Systems

Abstract

The distribution of coherence in multipartite systems is examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence. The concept of wave particle duality introduced the importance of quantum coherence in physical phenomena such as low temperature thermodynamics [1], quantum thermodynamics [2-4], nanoscale physics [5], biological systems [6,7], and is one of the most basic aspects of quantum information science [8]. For this reason, understanding quantum coherence has a long history and is of fundamental importance to many fields. In quantum optics [9,10], the approach has been typically to examine quantities such as phase space distributions and higher order correlation functions [11]. While this method distinguishes between quantum and classical coherence, it does not quantify coherence in a rigorous sense. More recently, a procedure to quantify coherence using methods of quantum information science was developed [12][13][14][15]. In the seminal work of Ref. [12], basic quantities such as incoherent states, incoherent operations, maximally coherent states were defined and the set of properties a functional should satisfy to be considered as a coherence measure were listed.One fundamental task that is desirable is to pinpoint what part of a quantum system is responsible for any coherence that is present. To understand the possibilities, let us consider a two qubit system as an example. Coherence is a basis-dependent quantity [15,16], and the reference incoherent states are chosen as |0 , |1 . We can consider then two types of states which possess coher- S is the set of separable states in a fixed basis b. ρ d is the solution of (2) and σ min S is the solution of (4).ence, (|0 − |1 )(|0 − |1 ) and |0 |0 − |1 |1 . In the former, the coherence lies on each qubit, while the latter has a kind of collective coherence, i.e. entanglement. An interesting aspect of this is that the types of coherence are complementary to each other -an increase in one type leads to a corresponding decrease in the other. In order to have maximum coherence on a particular qubit, it is optimal to create a superposition on each one, which excludes entanglement. On the other hand, for the Bell state, tracing out one o...

Intrinsic coherence in assisted sub-state discrimination

“…To analytically express our results, we adopt tangle (squared concurrence) [19] as the measure of intrinsic coherence rather than the one based on the Jensen-Shannon divergence proposed in [11]. An evident advantage of our choice is that the symbols of approximately equal in (1) and (2) can be replaced by equal signs, since the three qubits in the procedure are in a pure state [20].…”

“…According to the results in [11], its total intrinsic coherence can be decomposed into bipartite coherences as…”

“…The intrinsic coherence in a multipartite system can be further decomposed into several bipartite coherences. These coherence contributions and their trade-off relations as quantum properties in a multipartite system have been illustrated by using some special states and many-body models in [11]. Here a natural question is left: What roles do they play in specific quantum information tasks?…”

“…On the other hand, the development of quantum information science provides a perspective to reassess these correlations in the formulation of resource theory [1,5]. Recently, this perspective has been used to quantify coherence [6], which gained widely attention and raised a subsequent stream of works relevant to quantum coherence [7][8][9][10][11].…”

Remote creation of quantum coherence

“…Unlike quantum entanglement and other quantum correlations, coherence, regarded as a physical resource [4,11,14], has been just investigated very recently in establishing the framework of quantifying coherence in the language of quantum information theory [13,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Due to its fundamental role in quantum physics and quantum information theory, it is still necessary to understand how coherence works in information processing and investigate the relations between coherence and quantum correlations.…”